MapCoder: Multi-Agent Code Generation for Competitive Problem Solving (2024)

Abstract: Code synthesis, which requires a deep understanding of complex natural language (NL) problem descriptions, generation of code instructions for complex algorithms and data structures, and the successful execution of comprehensive unit tests, presents a significant challenge. Thus, while large language models (LLMs) demonstrate impressive proficiency in natural language processing (NLP), their performance in code generation tasks remains limited. In this paper, we introduce a new approach to code generation tasks leveraging the multi-agent prompting that uniquely replicates the full cycle of program synthesis as observed in human developers. Our framework, MapCoder, consists of four LLM agents specifically designed to emulate the stages of this cycle: recalling relevant examples, planning, code generation, and debugging. After conducting thorough experiments, with multiple LLMs ablations and analyses across eight challenging competitive problem-solving and program synthesis benchmarks—MapCoder showcases remarkable code generation capabilities, achieving their new state-of-the-art (pass@1) results—(HumanEval 93.9%, MBPP 83.1%, APPS 22.0%, CodeContests 28.5%, and xCodeEval 45.3%). Moreover, our method consistently delivers superior performance across various programming languages and varying problem difficulties. We open-source our framework at https://github.com/ Md-Ashraful-Pramanik/MapCoder.

heading: 1 Introduction
text: Computer Programming has emerged as an ubiquitous problem-solving tool that brings tremendous benefits to every aspects of our life (Li et al., 2022a; Parvez et al., 2018; Knuth, 1992). To maximize programmers’ productivity, and enhance accessibility, automation in program synthesis is paramount. With the growth of LLMs, significant
advancements have been made in program synthesis—driving us in an era where we can generate fully executable code, requiring no human intervention (Chowdhery et al., 2022; Nijkamp et al., 2022).
Despite LLMs’ initial success and the scaling up of model size and data, many of these models still struggle to perform well on complex problemsolving tasks, especially in competitive programming problems (Austin et al., 2021). To mitigate this gap, in this paper, we introduce MapCoder: a Multi-Agent Prompting Based Code Generation approach that can seamlessly synthesize solutions for competition-level programming problems.
Competitive programming or competition-level code generation, often regarded as the pinnacle of problem-solving, is an challenging task. It requires a deep comprehension of NL problem descriptions, multi-step complex reasoning beyond mere memorization, excellence in algorithms and data structures, and the capability to generate substantial code that produces desired outputs aligned with comprehensive test cases (Khan et al., 2023).
Early approaches utilizing LLMs for code generation employ a direct prompting approach, where LLMs generate code directly from problem descriptions and sample I/O (Chen et al., 2021a). Recent methods like chain-of-thought (Wei et al., 2022a) advocates modular or pseudo code-based generation to enhance planning and reduce errors, while retrieval-based approaches such as Parvez et al. (2021) leverage relevant problems and solutions to guide LLMs’ code generations. However, gains in such approaches remains limited in such a complex task like code generation where LLMs’ generated code often fails to pass the test cases and they do not feature bug-fixing schema (Ridnik et al., 2024).
A promising solution to the above challenge is self-reflection (Shinn et al., 2023; Chen et al., 2022), which iteratively evaluates the generated code against test cases, reflects on mistakes and
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modifies accordingly. However, such approaches have limitations too. Firstly, while previous studies indicate that superior problem-solving capabilities are attained when using in-context exemplars (Shum et al., 2023; Zhang et al., 2022; Wei et al., 2022a) or plans (Jiang et al., 2023b), these approaches, during both code generation and debugging, only leverage the problem description itself in a zero-shot manner. Consequently, their gains can be limited.
To confront the above challenge, we develop MapCoder augmenting the generation procedure with possible auxiliary supervision. We draw inspiration from human programmers, and how they use various signals/feedback while programming. The human problem-solving cycle involves recalling past solutions, planning, code writing, and debugging. MapCoder imitates these steps using LLM agents - retrieval, planning, coding, and debugging. In contrast to relying on human annotated examples, or external code retrieval models, we empower our retrieval agent to autonomously retrieve relevant problems itself (Yasunaga et al., 2023). Moreover, we design a novel structured pipeline schema that intelligently cascades the LLM agents and incorporates a dynamic iteration protocol to enhance the generation procedure at every step. Figure 1 shows an overview of our approach, MapCoder.
Additionally, existing iterative self-reflection methods rely on extra test cases generated by LLM agents (e.g., AgentCoder (Huang et al., 2023), LATS (Zhou et al., 2023), self-reflection (Shinn
et al., 2023)) or external tools, compounding the challenges. Test case generation is equally challenging as code generation (Pacheco et al., 2007), and incorrect test cases can lead to erroneous code. Blindly editing code based on these test cases can undermine problem-solving capabilities. For instance, while self-reflection boosts GPT-4’s performance on the HumanEval dataset, it drops by 3% on the MBPP dataset (Shinn et al., 2023). Upon identification, to validate this, on the HumanEval dataset itself, we replace their GPT-4 with ChatGPT, and see that model performance drops by 26.3%. Therefore, our debugging agent performs unit tests and bug fixing using only the sample I/O, without any artifact-more plausible for real-world widespread adoption.
We evaluate MapCoder on seven popular programming synthesis benchmarks including both basic programming like HumanEval, MBPP and challenging competitive program-solving benchmarks like APPS, CodeContests and xCodeEval. With multiple different LLMs including ChatGPT, GPT-4, and Gemini Pro, our approach significantly enhances their problem-solving capabilities - consistently achieving new SOTA performances, outperforming strong baselines like Reflexion (Shinn et al., 2023), and AlphaCodium (Ridnik et al., 2024). Moreover, our method consistently delivers superior performance across various programming languages and varying problem difficulties. Furthermore, with detailed ablation studies, we analyze MapCoder to provide more insights.
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heading: 2 Related Work
text: Program Synthesis: Program synthesis has a long standing history in AI systems (Manna and Waldinger, 1971). A large number of prior research attempted to address it via search/data flow approaches (Li et al., 2022a; Parisotto and Salakhutdinov, 2017; Polozov and Gulwani, 2015; Gulwani, 2011). LMs, prior to LLMs, attempt to generate code by fine-tuning (i.e., training) neural language models (Wang et al., 2021; Ahmad et al., 2021; Feng et al., 2020; Parvez et al., 2018; Yin and Neubig, 2017; Hellendoorn and Devanbu, 2017; Rabinovich et al., 2017; Hindle et al., 2016), conversational intents or data flow features (Andreas et al., 2020; Yu et al., 2019).
Large Language Models: Various LLMs have been developed for Code synthesis (Li et al., 2022b; Fried et al., 2022; Chen et al., 2021b; Austin et al., 2021; Nijkamp et al., 2022; Allal et al., 2023). Recent open source LLMs include Llama-2 (Touvron et al., 2023), CodeLlama-2 (Roziere et al., 2023), Mistral (Jiang et al., 2023a) Deepseek Coder (Guo et al., 2024), MoTCoder (Li et al., 2023) that are capable of solving many basic programming tasks. Prompting LLMs: As indicated in Section 1, LLM prompting can be summarized into three categories: retrieval (Yasunaga et al., 2023; Parvez et al., 2023, 2021); planning (Wei et al., 2022b; Jiang et al., 2023b); debugging (Ridnik et al., 2024; Chen et al., 2023, 2022; Le et al., 2022) apart from the direct code generation approaches. In contrast, we combine all these paradigms and bridge their gaps (See Table 1). Among others, in different contexts of generic problem-solving, Tree-ofthoughts (Yao et al., 2023), and Cumulative reasoning (Zhang et al., 2023) approaches consider a tree traversal approach to explore different substeps towards a solution while our code generation approach mirrors the human programming cycle through various LLM agents. Notably, our traversal does not rely on sub-steps toward the solution but instead utilizes different forms of full solutions.

heading: 3 MapCoder
text: Our goal is to develop a multi-agent code generation approach for competitive problem-solving. In order to do so, our framework, MapCoder, replicates the human programming cycle through four LLM agents - retrieval, plan, code, and debug. We devise a pipeline sequence for MapCoder, intelligently cascading the agents in a structured way and enhancing each agent’s capability by augmenting in-context learning signals from previous agents in the pipeline. However, not all the agent responses/outputs are equally useful. Therefore, additionally, MapCoder features an adaptive agent traversal schema to interact among corresponding agents dynamically, iteratively enhancing the generated code by, for example, fixing bugs, while maximizing the usage of the LLM agents. In this section, we first discuss the agents (as per the pipeline), their prompts, and interactions, followed by the dynamic agent traversal protocol in MapCoder towards code generation for competitive problem-solving.

heading: 3.1 Retrieval Agent
text: Our first agent, the Retrieval Agent, recalls past relevant problem-solving instances, akin to human memory. It finds k (user-defined) similar problems without manual crafting or external retrieval models. Instead, we leverage the LLM agent itself, instructing it to generate such problems. Our prompt extends the analogical prompting principles (Yasunaga et al., 2023), generating examples and their solutions simultaneously, along with additional metadata (e.g., problem description, code, and plan) to provide the following agents as auxiliary data. We adopt a specific sequence of instructions, which is crucial for the prompt’s effectiveness. To achieve this, we instruct the LLM to produce similar and distinct problems and their solutions, facilitating problem planning through reverse-engineering. In particular, we prompt the LLM to generate solution code step-by-step, allowing for post-processing of thoughts sequences to form the corresponding plan. Finally, we direct the LLM to generate relevant algorithms and provide instructional tutorials, enabling the agent to reflect on underlying algorithms and generate algorithmically similar examples.

heading: 3.2 Planning Agent
text: The second agent, the Planning Agent, aims to create a step-by-step plan for the original problem.
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Planning Generation Prompt: Given a competitive programming problem generate a concrete planning to solve the problem. # Problem: {Description of a self-retrieved example problem} # Planning: {Planning of that problem} ## Relevant Algorithm to solve the next problem: {Algorithm retrieved by the Retrieval Agent} ## Problem to be solved: {Original Problem} ## Sample Input/Outputs: {Sample I/Os}
Confidence Generation Prompt: Given a competitive programming problem and a plan to solve the problem in {language} tell whether the plan is correct to solve this problem. # Problem: {Original Problem} # Planning: {Planning of our problem from previous step}
Planning Agent

heading: 3.3 Coding Agent

heading: 3.4 Debugging Agent
text: their plan while fixing bugs, our pipeline supplements the Debugging Agent with plans from the Planning Agent. This plan-derived debugging significantly enhances bug fixing in MapCoder, underscoring the pivotal roles played by both the Debugging Agent and the Planning Agent in the generation process. We verify this in Section 6. For each plan, this process is repeated t times. The prompt for this step is illustrated in Figure 3. Note that, different from Reflexion (Shinn et al., 2023) and AlphaCodium (Ridnik et al., 2024), our Debugging Agent does not require any additional test case generation in the pipeline.

heading: 3.5 Dynamic Agent Traversal
text: The dynamic traversal in MapCoder begins with the Planning Agent, which outputs the plans for the original problem with confidence scores. These plans are sorted, and the highest-scoring one is sent to the Coding Agent. The Coding Agent translates the plan into code, tested with sample I/Os. If all pass, the code is returned; otherwise, it’s passed to Debugging Agent. They attempt to rectify the code iteratively up to t times. If successful, the code is returned; otherwise, responsibility shifts back to the Planning Agent for the next highest confidence plan. This iterative process continues for k iterations, reflecting a programmer’s approach. We summarize our agent traversal in Algorithm A in Appendix. Our algorithm’s complexity is O(kt). An example illustrating MapCoder’s problem-solving compared to Direct, Chain-of-thought, and Reflexion approaches is in Figure 4. All detailed prompts for each agent are in Appendix B.

heading: 4 Experimental Setup

heading: 4.1 Datasets
text: For extensive evaluation, we have used eight benchmark datasets: five from basic programming and three from complex competitive programming domains. Five basic programming datasets are:
HumanEval (Chen et al., 2021a), HumanEvalET (Dong et al., 2023a), EvalPlus (Liu et al., 2023), MBPP) (Austin et al., 2021), and MBPPET (Dong et al., 2023a). HumanEval-ET, EvalPlus extend HumanEval and MBPP-ET comprehends MBPP by incorporating more test cases. The problem set size of HumanEval and MBPP (and their extensions) are 164 and 397, respectively. Due to the absence of sample I/O in MBPP and MBPPET, our approach for code moderation involves randomly removing one test-case from MBPP-ET for each problem and provide this test-case as a sample I/O for the problem. Importantly, this removed test-case is carefully selected to ensure mutual exclusivity from the hidden test sets in MBPP and MBPP-ET. Three competitive programming datasets are: Automated Programming Progress Standard (APPS), xCodeEval (Khan et al., 2023), and CodeContest, where we have used 150 (randomly selected from test set), 106 (compact set), and 165 (test set) problems, respectively, in our experiments.

heading: 4.2 Baselines
text: We have compared MapCoder with several baselines and state-of-the-art approaches. Direct
Prompting instructs language models to generate code without explicit guidance, relying on their inherent capabilities of LLM. Chain of Thought Prompting (CoT) (Wei et al., 2022b) breaks down problems into step-by-step solutions, enabling effective tackling of complex tasks. Self-Planning Prompting (Jiang et al., 2023b) divides the code generation task into planning and implementation phases. Analogical Reasoning Prompting (Yasunaga et al., 2023) instructs models to recall relevant problems from training data. Reflexion (Shinn et al., 2023) provides verbal feedback to enhance solutions based on unit test results. Selfcollaboration (Dong et al., 2023b) proposes a framework where different LLMs act as analyst, coder, and tester to cooperatively generate code for complex tasks, achieving better performance than directly using a single LLM. AlphaCodium (Ridnik et al., 2024) iteratively refines code based on AI-generated input-output tests.

heading: 4.3 Foundation Models, Evaluation Metric, k, and t
text: With k = t = 5 in HumanEval, and k = t = 3 for others, we evaluate all the datasets using ChatGPT (gpt-3.5-turbo-1106), GPT-4 (gpt-4-1106-preview)
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from OpenAI and Gemini Pro from Google. We have also evaluated our method using an opensource LLM, Mistral-7B-instruct. We have used the Pass@k evaluation metric, where the model is considered successful if at least one of the k generated solutions is correct.

heading: 5 Results
text: In this section, we evaluate the code generation capabilities of our framework, MapCoder, for competitive problem solving. Our experimental results are reported in Table 2. Overall, MapCoder shows a tremendous excellence in code generation, significantly outperforms all baselines, and achieves new state-of-the-art results in all benchmarks. In general the scales with GPT-4 are higher than ChatGPT.

heading: 5.1 Performance on basic code generation
text: The highest scale of performance (Pass@1) scores are observed in simple program synthesis tasks like HumanEval, MBPP in Table 2. Though with the simpler problem (non-contests) datasets such as HumanEval, HumanEval-ET, the current state-ofthe-art method, Reflexion (Shinn et al., 2023) perform reasonably well, this approach does not generalize across varying datasets depicting a wide variety of problems. Self-reflection techniques enhance
GPT-4’s performance on HumanEval but result in a 3% decrease on the MBPP dataset. Similarly, with ChatGPT, there’s a notable 26.3% drop in performance where in several cases their AI generated test cases are incorrect. We observe that 8% of failures in HumanEval and 15% in MBPP is caused by their AI generates incorrect test cases while our approach is independent of AI test cases, and consistently improves code generations in general. Consequently, even in HumanEval, with GPT-4, our Pass@1 surpasses Reflexion by ∼3%. On top, in all four simple programming datasets, MapCoder enhances the Direct prompting significantly with a maximum of 88% on HumanEvalET by ChatGPT.

heading: 5.2 Performance on competitive problem solving
text: The significance of MapCoder shines through clearly when evaluated in competitive problemsolving contexts. Across datasets such as APPS, xCodeEval, and CodeContests, MapCoder demonstrates substantial enhancements over Direct prompting methods, with improvements of 41.3%, 52.6%, and 132.8% for ChatGPT, and 73.7%, 41.2%, and 135.1% for GPT4, respectively. Notably, the most challenging datasets are APPS and CodeContest, where MapCoder’s performance stands out prominently. We deliberately com-
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pare against strong baselines on these datasets, regardless of whether they are prompt-based or not. Importantly, on CodeContest our Pass@1 results match the Pass@5 scores of the concurrent state-ofthe-art model AlphaCodium (Ridnik et al., 2024): 28.5% vs. their 29% (see Table 3). Furthermore, our Pass@5 results demonstrate an additional improvement of 12.8%. On APPS, MapCoder consistently surpasses the Pass@1 scores of all baseline prompts for both ChatGPT and GPT-4.

heading: 5.3 Performance with Varying Difficulty Levels
text: The APPS dataset comprises problems categorized into three difficulty levels: (i) Introductory, (ii) Interview, and (iii) Competition. Figure 6 illustrates the performance of various competitive approaches for these three categories. The results reveal that our MapCoder excels across all problem categories, with highest gain in competitive problem-solving indicating its superior code generation capabilities in general, and on top, remarkable effectiveness in competitive problem-solving. In order to gather more understanding on what algorithm problems it’s capable of solving and in fact much difficulty level it can solve, we have also conducted a comparison between MapCoder and the Direct approach,
considering the difficulty levels1 and tags2 present in the xCodeEval dataset. The results of this comparison are depicted in Figure 5. This comparison showcases that MapCoder is effective across various algorithm types and exhibits superior performance even in higher difficulty levels, compared to the Direct approach. However, beyond (mid-level: difficulties>1000), its gains are still limited.

heading: 5.4 Performance Across Different LLMs
text: To show the robustness of MapCoder across various LLMs, we evaluate MapCoder using Gemini Pro, a different family of SoTA LLM in Table 4. We also evaluate MapCoder using an open-source LLM Mistral-7B instruct in Table 5. As expected, our method shows performance gains over other baseline approaches in equitable trends on both simple (HumanEval) and contest-level problems (CodeContest).
1Difficulty levels in xCodeEval dataset represents an integer number, a higher value means more difficult problem
2Tags in xCodeEval dataset represents algorithm type that can be used to solve the problem i.e., greedy, dp, brute-force, constructive, and so on.
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heading: 5.5 Performance Across Different Programming Languages
text: Furthermore, we evaluate model performances using MapCoder across different programming languages. We utilize the xCodeEval dataset, which features multiple languages. Figure 7 shows that consistent proficiency across different programming languages is achieved by MapCoder with respect to baselines.

heading: 6 Ablations Studies and Analyses
text: We present the ablation study of the MapCoder on HumanEval dataset as the problems are simpler and easy to diagnose by us humans.

heading: 6.1 Impact of Different Agents
text: We have also conducted a study by excluding certain agents from our MapCoder, which helps us investigate each agent’s impact in our whole pipeline.
As expected, the results (Table 6) show that every agent has its role in the pipeline as turning off any agent decreases the performance of MapCoder. Furthermore, we observe that the Debugging Agent has the most significant impact on the pipeline, as evidenced by a performance drop of 17.5% when excluding this agent exclusively, and an avg performance drop of 24.83% in all cases. The Planning agent has the second best important with avg drop of 16.7% in all cases. In Table 6), we perform an ablation study of our multi-agent framework investigate each agent’s impact in our whole pipeline.

heading: 6.2 Qualitative Example
text: To verify the above numerical significance, and to understand how our method enhance the code generation, we have performed a qualitative analysis to find the underlying reason for the superior performance of MapCoder over other competitive prompting approaches. An example problem and the output with the explanation of Direct, CoT, Reflexion, and MapCoder prompting is shown in Figure 4. This example demonstrates how the Debugging Agent fixes the bugs leveraging the plan as a guide from the Planning Agent. This verifies the impact of these two most significant agents. We present more detailed examples in Appendix.

heading: 6.3 Impact of k and t
text: MapCoder involves two hyper-parameters: the number of self-retrieved exemplars, k, and the number of debugging attempts, t. Our findings (Table 7) reveal that higher k, t is proportionate performance gain at the expense of time.
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heading: 6.4 Impact of Number of Sample I/Os
text: Given the limited number of sample I/Os in the HumanEval dataset (average of 2.82 per problem), we supplemented it with an additional 5 sample I/Os from the HumanEval-ET dataset. Experiments with this augmented set showed an 1.5% performance gain.

heading: 6.5 Error Analysis and Challenges
text: Although MapCoder demonstrates strong performance compared to other methods, it faces challenges in certain algorithmic domains. For example, Figure 5 illustrates MapCoder’s reduced performance on more difficult problems requiring precise problem understanding and concrete planning—capabilities still lacking in LLMs. In the xCodeEval dataset (see Figure 5), it solves a limited number of problems in categories like Combinatorics, Constructive, Number Theory, Divide and Conquer, and Dynamic Programming (DP). Manual inspection of five DP category problems reveals occasional misinterpretation of problems, attempts to solve using greedy or brute-force approaches, and struggles with accurate DP table construction when recognizing the need for a DP solution.

heading: 7 Conclusion and Future Work
text: In this paper, we introduce MapCoder, a novel framework for effective code generation in complex problem-solving tasks, leveraging the multi-agent prompting capabilities of LLMs. MapCoder captures the complete problem-solving cycle by employing four agents - retrieval, planning, coding, and debugging - which dynamically interact to produce high-quality outputs. Evaluation across major benchmarks, including basic and competitive programming datasets, demonstrates MapCoder’s
consistent outperformance of well-established baselines and SoTA approaches across various metrics. Future work aims to extend this approach to other domains like question answering and mathematical reasoning, expanding its scope and impact.

heading: 8 Limitations
text: Among the limitations of our work, firstly, MapCoder generates a large number of tokens, which may pose challenges in resource-constrained environments. Table 8 shows the number of average API calls and token consumption with the default k and t (i.e., with respect to the reported performance) while Table 7) shows how k, t can be adjusted to proportionate the performance gain at the expense of time/token. We have not addressed the problem of minimizing tokens/API-calls in this paper and leave it for future works. Secondly, our method currently relies on sample input-output (I/O) pairs for bug fixing. Although sample I/Os provide valuable insights for LLMs’ code generation, their limited number may not always capture the full spectrum of possible test cases. Consequently, enhancing the quality of additional test case generation could reduce our reliance on sample I/Os and further improve the robustness of our approach. Additionally, future exploration of opensource code generation models, such as CodeLLaMa, LLaMa3, Mixtral 8x7B could offer valuable insights and potential enhancements to our approach. Another important concern is that while running machine-generated code, it is advisable to run it inside a sandbox to avoid any potential risks.

heading: Acknowledgements
text: We thank Tanvir Parvez (Department of Statistics, Islamic University, Bangladesh) and QCRI for their efforts and resources in running our experiments.
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heading: Appendix
text: A Algorithm of MapCoder
Algorithm 1 shows the pseudo-code of our prompting technique.
Algorithm 1 MapCoder 1: k ← number of self-retrieved exemplars 2: t← number of debugging attempts 3: 4: exemplars← RetrivalAgent(k) 5: 6: plans← empty array of size k 7: for example in exemplars do 8: plans[i]← PlanningAgent(example) 9: end for 10: 11: plans← SortByConfidence(plans) 12: 13: for i← 1 to k do 14: code← CodingAgent(code, plan[i]) 15: passed, log ← test(code, sample_io) 16: if passed then 17: Return code 18: else 19: for j ← 1 to t do 20: code← DebuggingAgent(code, log) 21: passed, log ← test(code, sample_io) 22: if passed then 23: Return code 24: end if 25: end for 26: end if 27: end for 28: Return code
B Details Promptings of MapCoder
The detailed prompting of the Retrieval Agent, Planning Agent, Coding Agent, and Debugging Agent are shown in Figure 8, 9, and 10 respectively. Note that we adopt a specific sequence of instructions in the prompt for Retrieval Agent which is a crucial design choice.
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heading: Debugging Agent
text: 13
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heading: C Example Problem
text: Two complete examples of how MapCoder works by showing all the prompts and responses for all
four agents is given below:
C.1 An example containing problem from HumanEval Dataset (k=5, t=5)

heading: Prompt for Self-retrieval Agent:
text: Given a problem, provide relevant problems then identify the algorithm behind it and also explain the tutorial
of the algorithm.
# Problem: def sum_squares(lst):
"""You are given a list of numbers. You need to return the sum of squared numbers in the given list, round each element in the list to the upper int(Ceiling) first. Examples: For lst = [1,2,3] the output should be 14 For lst = [1,4,9] the output should be 98 For lst = [1,3,5,7] the output should be 84 For lst = [1.4,4.2,0] the output should be 29 For lst = [-2.4,1,1] the output should be 6 """
# Exemplars:
Recall five (05) relevant and distinct problems (different from problem mentioned above). For each problem,
1. describe it
2. generate Python3 code step by step to solve that problem
3. finally generate a planning to solve that problem
# Algorithm:
----------------

heading: Important:
text: Your response must follow the following xml format-
<root>
<problem>
# Recall five (05) relevant and distinct problems (different from problem mentioned above). Write each
problem in the following format.
<description> # Describe the problem. </description>
<code> # Let's think step by step to solve this problem in Python3 programming language. </code>
<planning> # Planning to solve this problem. </planning>
</problem>
# similarly add more problems here...
<algorithm>
# Identify the algorithm (Brute-force, Dynamic Programming, Divide-and-conquer, Greedy, Backtracking,
Recursive, Binary search, and so on) that needs to be used to solve the original problem.
# Write a useful tutorial about the above mentioned algorithms. Provide a high level generic tutorial for
solving this types of problem. Do not generate code.
</algorithm>
</root>
We will refer this as original problem
from the next time
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heading: Response from Self-retrieval Agent:
text: <root>
<problem>
<description> 1. Problem: Find the sum of all even numbers in a list. </description>
<code>
def sum_even(lst):
total = 0 for num in lst:
if num % 2 == 0:
total += num
return total
</code>
<planning>
To solve this problem, we can iterate through the list and check if each number is even. If it is, we add it
to a running total. Finally, we return the total sum of all even numbers in the list.
</planning>
</problem>
<problem>
<description> 2. Problem: Find the product of all numbers in a list. </description>
<code>
def product_of_numbers(lst):
product = 1 for num in lst:
product *= num
return product
</code>
<planning>
To solve this problem, we can iterate through the list and multiply each number with a running product.
Finally, we return the total product of all numbers in the list.
</planning>
</problem>
Three more plans are generated in similar way…
<algorithm>
The algorithm behind the original problem of summing squared numbers in a list is a simple iteration
through the list and performing a calculation on each element. This can be solved using a brute-force
algorithm.
Tutorial:
Brute-force algorithm involves iterating through the input and checking all possible solutions to find the
best one. In the case of summing squared numbers in a list, we iterate through the list, square each
number, round it to the upper integer, and then sum them up. This algorithm is straightforward and easy to
implement, but it may not be the most efficient for large inputs.
</ algorithm>
</root>
We will refer this as Retrieved algorithm
from the next time
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heading: Prompt for Planning Agent (Plan Generation):
text: Given a competitive programming problem generate a concrete planning to solve the problem.
# Problem: 1. Problem: Find the sum of all even numbers in a list.
# Planning: To solve this problem, we can iterate through the list and check if each number is even. If it is, we
add it to a running total. Finally, we return the total sum of all even numbers in the list.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Sample Test cases:
assert sum_squares([1,2,3])==14 assert sum_squares([1,4,9])==98 assert sum_squares([1,3,5,7])==84 assert sum_squares([1.4,4.2,0])==29 assert sum_squares([-2.4,1,1])==6
## Planning:
----------------
Important: You should give only the planning to solve the problem. Do not add extra explanation or words.

heading: Response from Planning Agent (Plan Generation):
text: To solve this problem, we can iterate through the list, round each number to the upper integer, square it, and
then add it to a running total. Finally, we return the total sum of all squared numbers in the list.

heading: Prompt for Planning Agent (Confidence Generation):
text: Given a competitive programming problem and a plan to solve the problem in Python3, tell whether the plan is
correct to solve this problem.
# Problem: {Original problem}
# Planning:
To solve this problem, we can iterate through the list, round each number to the upper integer, square it, and
then add it to a running total. Finally, we return the total sum of all squared numbers in the list.
----------------
Important: Your response must follow the following xml format-
<root>
<explanation>
Discuss whether the given competitive programming problem is solvable by using the above mentioned
planning.
</explanation>
<confidence>
Confidence score regarding the solvability of the problem. Must be an integer between 0 and 100.
</confidence>
</root>
We will refer this as Sample IO
from the next time
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heading: Response from Planning Agent (Confidence Generation):
text: <root>
<explanation>
The given competitive programming problem is solvable by using the above mentioned planning. The
plan correctly outlines the steps to iterate through the list, round each number to the upper integer,
square it, and then add it to a running total. Finally, returning the total sum of all squared numbers in
the list.
</explanation>
<confidence> 100 </confidence>
</root>
Similarly generate planning and their confidence using other examples….
Decision: As First Planning gets 100 as confidence score Coding Agent will work with first
Planning.

heading: Prompt for Coding Agent:
text: Given a competitive programming problem generate Python3 code to solve the problem.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Planning:
To solve this problem, we can iterate through the list, round each number to the upper integer, square it, and
then add it to a running total. Finally, we return the total sum of all squared numbers in the list.
## Sample Test cases: {Sample I/O}
## Let's think step by step.
----------------

heading: Important:
text: ## Your response must contain only the Python3 code to solve this problem. Do not add extra explanation or
words.

heading: Response from Coding Agent:
text: def sum_squares(lst):
total = 0 for num in lst:
total += (int(num) ** 2)
return total
Decision: Testing using Sample I/O will fail because this is wrong implementation. So, our
approach will go to Debugging Agent.
18

heading: Prompt for Debugging Agent: (1st iteration)
text: Given a competitive programming problem you have generated Python3 code to solve the problem. But the
generated code can not pass sample test cases. Improve your code to solve the problem correctly.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Planning: {Current Planning}
## Code: {Current Implementation}
## Test Report:
passed in test case: assert sum_squares([1,2,3]) == 14
passed in test case: assert sum_squares([1,4,9]) == 98
passed in test case: assert sum_squares([1,3,5,7]) == 84
failed in test case: assert sum_squares([1.4,4.2,0]) == 29
passed in test case: assert sum_squares([-2.4,1,1]) == 6
## Modified Planning:
## Let's think step by step to modify Python3 Code for solving this problem.
----------------

heading: Important:
text: ## Your response must contain the modified planning and then the Python3 code inside ``` block to solve this
problem.

heading: Response from Debugging Agent: (1st iteration)
text: ## Modified Planning:
To modify the code, we need to round each number to the upper integer before squaring it. We can use the
math.ceil() function to achieve this. After rounding each number, we can then square it and add it to the total
sum.
## Code:
```Python3
import math
def sum_squares(lst):
total = 0
for num in lst:
total += (math.ceil(num) ** 2)
return total
```
Decision: This time all Sample I/O passed. We return this implementation as the Final Code for final
evaluation. Finally, we evaluated this code with private test case and our implementation passed the
evaluation.
19
C.2 An example containing problem from CodeContest Dataset (k=3, t=5)

heading: Prompt for Self-retrieval Agent:
text: Given a problem, provide relevant problems then identify the algorithm behind it and also explain the tutorial
of the algorithm.
# Problem: Luntik has decided to try singing. He has a one-minute songs, b two-minute songs and c three-minute songs. He wants to distribute all songs into two concerts such that every song should be included to exactly one concert. He wants to make the absolute difference of durations of the concerts as small as possible. The duration of the concert is the sum of durations of all songs in that concert. Please help Luntik and find the minimal possible difference in minutes between the concerts durations.
Input The first line contains a single integer t (1 ≤ t ≤ 1000) — the number of test cases. Each test case consists of one line containing three integers a, b, c (1 ≤ a, b, c ≤ 10^9) — the number of one-minute, two-minute and three-minute songs. Output For each test case print the minimal possible difference in minutes between the concerts durations.
Example Input 4 1 1 1 2 1 3 5 5 5 1 1 2 Output 0 1 0 1

heading: Note

heading: In the first test case, Luntik can include a one-minute song and a two-minute song into the first concert, and a three-minute song into the second concert. Then the difference will be equal to 0.

heading: In the second test case, Luntik can include two one-minute songs and a two-minute song and a three-minute song into the first concert, and two three-minute songs into the second concert. The duration of the first concert will be 1 + 1 + 2 + 3 =

heading: 7, the duration of the second concert will be 6. The difference of them is |7-6| =
text: 1. """ ------- Important Note: You must follow the input output format. Input must be taken from standard input and output must be given to standard output. The code will be tested against multiple test cases and all the test cases must be passed.
We will refer this as original problem
from the next time
20
# Exemplars:
Recall three (03) relevant and distinct problems (different from problem mentioned above). For each problem,
1. describe it
2. generate Python3 code step by step to solve that problem
3. finally generate a planning to solve that problem
# Algorithm:
----------------

heading: Important:
text: Your response must follow the following xml format-
<root>
<problem>
# Recall three (03) relevant and distinct problems (different from problem mentioned above). Write
each problem in the following format.
<description> # Describe the problem. </description>
<code> # Let's think step by step to solve this problem in Python3 programming language. </code>
<planning> # Planning to solve this problem. </planning>
</problem>
# similarly add more problems here...
<algorithm>
# Identify the algorithm (Brute-force, Dynamic Programming, Divide-and-conquer, Greedy, Backtracking,
Recursive, Binary search, and so on) that needs to be used to solve the original problem.
# Write a useful tutorial about the above mentioned algorithms. Provide a high level generic tutorial for
solving this types of problem. Do not generate code.
</algorithm>
</root>

heading: Response from Self-retrieval Agent:
text: <root>
<problem>
<description>
Problem 1:
You are given an array of integers, find the maximum sum of a contiguous subarray within the array.
</description>
<code>
def maxSubArray(nums):
max_sum = nums[0] current_sum = nums[0]
for i in range(1, len(nums)):
current_sum = max(nums[i], current_sum + nums[i]) max_sum = max(max_sum, current_sum)
return max_sum
</code>
<planning>
- Initialize two variables max_sum and current_sum to the first element of the array.
21
- Iterate through the array and at each index, update the current_sum to be the maximum of the
current element and the sum of the current element and the previous current_sum.
- Update max_sum to be the maximum of max_sum and current_sum.
- Return max_sum at the end.
</planning>
</problem>
<problem>
<description>
Problem 2:
You are given a list of tasks with their start and end times. Find the minimum number of meeting rooms
required to schedule all the tasks.
</description>
<code>
import heapq
def minMeetingRooms(intervals):
if not intervals:
return 0
intervals.sort(key=lambda x: x[0])
rooms = [] heapq.heappush(rooms, intervals[0][1])
for i in intervals[1:]:
if rooms[0] <= i[0]:
heapq.heappop(rooms)
heapq.heappush(rooms, i[1])
return len(rooms)
</code>
<planning>
- Sort the intervals based on their start times.
- Create a min heap to store the end times of the meetings.
- Push the end time of the first meeting into the heap.
- Iterate through the intervals, if the start time of the current interval is greater than or equal to the end
time at the top of the heap, pop the end time from the heap. Push the end time of the current interval
into the heap.
- Return the length of the heap at the end.
</planning>
</problem>
<problem>
<description>
Problem 3:
You are given a list of intervals representing the start and end times of meetings. Find the maximum
number of overlapping intervals.
</description>
<code>
22
def maxOverlap(intervals):
if not intervals:
return 0
start_times = sorted([i[0] for i in intervals]) end_times = sorted([i[1] for i in intervals])
max_overlap = 0 current_overlap = 0 start_ptr = 0 end_ptr = 0
while start_ptr < len(intervals):
if start_times[start_ptr] < end_times[end_ptr]:
current_overlap += 1 max_overlap = max(max_overlap, current_overlap) start_ptr += 1
else:
current_overlap -= 1 end_ptr += 1
return max_overlap
</code>
<planning>
- Sort the start times and end times of the intervals separately.
- Initialize max_overlap and current_overlap to 0, and start and end pointers to 0.
- Iterate through the start times, if the current start time is less than the current end time, increment
current_overlap and update max_overlap. Increment the start pointer.
- If the current start time is greater than or equal to the current end time, decrement current_overlap
and increment the end pointer.
- Return max_overlap at the end.
</planning>
</problem>
<algorithm>
The algorithm that can be used to solve the original problem of distributing songs into two concerts with
minimal possible difference in durations is the Greedy algorithm. The Greedy algorithm makes the locally
optimal choice at each stage with the hope of finding a global optimum.
To solve the original problem, we can use the following steps:
1. Sort the songs by their durations in non-increasing order.
2. Start with two empty concerts.
3. Iterate through the sorted songs and at each stage, assign the current song to the concert with the
smaller total duration.
4. Calculate the absolute difference in durations between the two concerts at the end.
This approach ensures that we are making the locally optimal choice at each stage by assigning the current
song to the concert with the smaller total duration, and it leads to the minimal possible difference in
durations between the concerts.
</ algorithm>
</root>
We will refer this as Retrieved algorithm
from the next time
23

heading: Prompt for First Planning Agent (Plan Generation):
text: Given a competitive programming problem generate a concrete planning to solve the problem.
# Problem:
Problem 1:
You are given an array of integers, find the maximum sum of a contiguous subarray within the array.
# Planning:
- Initialize two variables max_sum and current_sum to the first element of the array.
- Iterate through the array and at each index, update the current_sum to be the maximum of the current
element and the sum of the current element and the previous current_sum.
- Update max_sum to be the maximum of max_sum and current_sum.
- Return max_sum at the end.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Sample Test cases:
Input: 4 1 1 1 2 1 3 5 5 5 1 1 2

heading: Expected output:
text: 0 1 0 1
## Planning:
----------------
Important: You should give only the planning to solve the problem. Do not add extra explanation or words.

heading: Response from First Planning Agent (Plan Generation):
text: - Sort the songs by their durations in non-increasing order.
- Start with two empty concerts.
- Iterate through the sorted songs and at each stage, assign the current song to the concert with the smaller
total duration.
- Calculate the absolute difference in durations between the two concerts at the end.

heading: Prompt for First Planning Agent (Confidence Generation):
text: Given a competitive programming problem and a plan to solve the problem in Python3, tell whether the plan is
correct to solve this problem.
# Problem: {Original problem}
# Planning:
- Sort the songs by their durations in non-increasing order.
- Start with two empty concerts.
- Iterate through the sorted songs and at each stage, assign the current song to the concert with the smaller
total duration.
We will refer this as Sample IO
from the next time
49 4
24
- Calculate the absolute difference in durations between the two concerts at the end.
----------------
Important: Your response must follow the following xml format-
<root>
<explanation>
Discuss whether the given competitive programming problem is solvable by using the above mentioned
planning.
</explanation>
<confidence>
Confidence score regarding the solvability of the problem. Must be an integer between 0 and 100.
</confidence>
</root>

heading: Response from First Planning Agent (Confidence Generation):
text: <root>
<explanation>
The given competitive programming problem is solvable by using the above mentioned planning. The
plan involves sorting the songs by duration and then assigning them to two concerts in a way that
minimizes the absolute difference in durations between the concerts.
</explanation>
<confidence> 100 </confidence>
</root>

heading: Prompt for Second Planning Agent (Plan Generation):
text: Given a competitive programming problem generate a concrete planning to solve the problem.
# Problem:
Problem 2:
You are given a list of tasks with their start and end times. Find the minimum number of meeting rooms
required to schedule all the tasks.
# Planning:
- Sort the intervals based on their start times.
- Create a min heap to store the end times of the meetings.
- Push the end time of the first meeting into the heap.
- Iterate through the intervals, if the start time of the current interval is greater than or equal to the end time at
the top of the heap, pop the end time from the heap. Push the end time of the current interval into the heap.
- Return the length of the heap at the end.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Sample Test cases: {Sample I/O}
## Planning:
----------------
Important: You should give only the planning to solve the problem. Do not add extra explanation or words.
25

heading: Response from Second Planning Agent (Plan Generation):
text: - Sort the songs by their durations in non-increasing order.
- Start with two empty concerts.
- Iterate through the sorted songs and at each stage, assign the current song to the concert with the smaller
total duration.
- Calculate the absolute difference in durations between the two concerts at the end.

heading: Prompt for Second Planning Agent (Confidence Generation):
text: Given a competitive programming problem and a plan to solve the problem in Python3, tell whether the plan is
correct to solve this problem.
# Problem: {Original problem}
# Planning:
- Sort the songs by their durations in non-increasing order.
- Start with two empty concerts.
- Iterate through the sorted songs and at each stage, assign the current song to the concert with the smaller
total duration.
- Calculate the absolute difference in durations between the two concerts at the end.
----------------
Important: Your response must follow the following xml format-
<root>
<explanation>
Discuss whether the given competitive programming problem is solvable by using the above mentioned
planning.
</explanation>
<confidence>
Confidence score regarding the solvability of the problem. Must be an integer between 0 and 100.
</confidence>
</root>

heading: Response from Second Planning Agent (Confidence Generation):
text: <root>
<explanation>
The given competitive programming problem is solvable by using the above mentioned planning. The
plan involves sorting the songs by duration, then assigning the songs to two concerts in a way that
minimizes the absolute difference in durations between the concerts.
</explanation>
<confidence> 100 </confidence>
</root>
Similarly generate the planning and the confidence of last example….
Decision: As First Planning gets 100 as confidence score Coding Agent will work with first
Planning.
26

heading: Prompt for Coding Agent:
text: Given a competitive programming problem generate Python3 code to solve the problem.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Planning:
- Sort the songs by their durations in non-increasing order.
- Start with two empty concerts.
- Iterate through the sorted songs and at each stage, assign the current song to the concert with the smaller
total duration.
- Calculate the absolute difference in durations between the two concerts at the end.
## Sample Test cases: {Sample I/O}
## Let's think step by step.
----------------

heading: Important:
text: ## Note: Strictly follow the input and output format. The input should be taken from Standard input and
output should be given to standard output. If you are writing a function then after the function definition take
input using `input()` function then call the function with specified parameters and finally print the output of
the function. Do not add extra print statement otherwise it will failed the test cases.
## Your response must contain only the Python3 code to solve this problem. Do not add extra explanation or
words.

heading: Response from Coding Agent:
text: def min_difference_in_concerts(t, test_cases):
for case in test_cases:
a, b, c = case songs = [(1, a), (2, b), (3, c)] songs.sort(key=lambda x: x[0], reverse=True) concert1 = 0 concert2 = 0 for song in songs:
if concert1 <= concert2:
concert1 += song[0] * song[1]
else:
concert2 += song[0] * song[1]
print(abs(concert1 - concert2))
t = 4 test_cases = [(1, 1, 1), (2, 1, 3), (5, 5, 5), (1, 1, 2)] min_difference_in_concerts(t, test_cases)
Decision: Testing using Sample I/O will fail because of incorrect implementation. The main
problem with this code is that it does not take input from the console. It writes a function
and just calls it with fixed value. So, our approach will go to the Debugging Agent.
27

heading: Prompt for Debugging Agent: (1st iteration)
text: Given a competitive programming problem you have generated Python3 code to solve the problem. But the
generated code can not pass sample test cases. Improve your code to solve the problem correctly.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Planning:
- Sort the songs by their durations in non-increasing order.
- Start with two empty concerts.
- Iterate through the sorted songs and at each stage, assign the current song to the concert with the smaller
total duration.
- Calculate the absolute difference in durations between the two concerts at the end.
## Code: def min_difference_in_concerts(t, test_cases):
for case in test_cases:
a, b, c = case songs = [(1, a), (2, b), (3, c)] songs.sort(key=lambda x: x[0], reverse=True) concert1 = 0 concert2 = 0 for song in songs:
if concert1 <= concert2:
concert1 += song[0] * song[1]
else:
concert2 += song[0] * song[1]
print(abs(concert1 - concert2))
t = 4 test_cases = [(1, 1, 1), (2, 1, 3), (5, 5, 5), (1, 1, 2)] min_difference_in_concerts(t, test_cases)
## Test Report:
## Tested passed:
No test cases passed.
## Tests failed:
Input:
4
1 1 1
2 1 3
5 5 5
1 1 2
Expected Output:
0 1 0 1
Your Output:
0 5 0 3
## Modified Planning:
28
## Let's think step by step to modify Python3 Code for solving this problem.
----------------

heading: Important:
text: ## Note: Strictly follow the input and output format. The input should be taken from Standard input and
output should be given to standard output. If you are writing a function then after the function definition take
input using `input()` function then call the function with specified parameters and finally print the output of
the function. Do not add extra print statement otherwise it will failed the test cases.
## Your response must contain the modified planning and then the Python3 code inside ``` block to solve this
problem.

heading: Response from Debugging Agent: (1st iteration)
text: ## Modified Planning:
1. Read the integer t from input to determine the number of test cases.
2. Create a function min_difference_in_concerts(t, test_cases) that takes t and test_cases as input parameters.
3. For each test case in test_cases, do the following:
- Read the integers a, b, and c from input.
- Calculate the total duration of each type of song (1-minute, 2-minute, 3-minute).
- Calculate the total duration of all songs.
- Calculate the minimum possible difference in minutes between the concerts durations.
- Print the minimum possible difference in minutes between the concerts durations.
4. Call the function min_difference_in_concerts with t and test_cases as input parameters.
## Code:
```Python3
def min_difference_in_concerts(t, test_cases):
for case in test_cases:
a, b, c = case
total_duration = a + 2*b + 3*c
if total_duration % 2 == 0:
print(total_duration // 2)
else:
print((total_duration - 1) // 2)
t = int(input())
test_cases = []
for _ in range(t):
a, b, c = map(int, input().split())
test_cases.append((a, b, c))
min_difference_in_concerts(t, test_cases)
```
Decision: This time, it takes input from the console and gives output to the console. It correct
that part. But again, it failed because of incorrect implementation. So, the Debugging Agent
tries to improve the code again.
29

heading: Prompt for Debugging Agent: (2nd iteration)
text: Given a competitive programming problem you have generated Python3 code to solve the problem. But the
generated code can not pass sample test cases. Improve your code to solve the problem correctly.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Planning:
1. Read the integer t from input to determine the number of test cases.
2. Create a function min_difference_in_concerts(t, test_cases) that takes t and test_cases as input parameters.
3. For each test case in test_cases, do the following:
- Read the integers a, b, and c from input.
- Calculate the total duration of each type of song (1-minute, 2-minute, 3-minute).
- Calculate the total duration of all songs.
- Calculate the minimum possible difference in minutes between the concerts durations.
- Print the minimum possible difference in minutes between the concerts durations.
4. Call the function min_difference_in_concerts with t and test_cases as input parameters.
## Code:
def min_difference_in_concerts(t, test_cases):
for case in test_cases:
a, b, c = case
total_duration = a + 2*b + 3*c
if total_duration % 2 == 0:
print(total_duration // 2)
else:
print((total_duration - 1) // 2)
t = int(input())
test_cases = []
for _ in range(t):
a, b, c = map(int, input().split())
test_cases.append((a, b, c))
min_difference_in_concerts(t, test_cases)
## Test Report:
## Tested passed:
No test cases passed.
## Tests failed:
Input:
4
1 1 1
2 1 3
5 5 5
1 1 2
Expected Output:
0 1 0 1
Your Output:
3 6 15 4
30
## Modified Planning:
## Let's think step by step to modify Python3 Code for solving this problem.
----------------

heading: Important:
text: ## Note: Strictly follow the input and output format. The input should be taken from Standard input and
output should be given to standard output. If you are writing a function then after the function definition take
input using `input()` function then call the function with specified parameters and finally print the output of
the function. Do not add extra print statement otherwise it will failed the test cases.
## Your response must contain the modified planning and then the Python3 code inside ``` block to solve this
problem.

heading: Response from Debugging Agent: (2nd iteration)
text: ## Modified Planning:
1. Read the integer t from input to determine the number of test cases.
2. Create a function min_difference_in_concerts(t, test_cases) that takes t and test_cases as input parameters.
3. For each test case in test_cases, do the following:
- Read the integers a, b, and c from input.
- Calculate the total duration of each type of song (1-minute, 2-minute, 3-minute).
- Calculate the total duration of all songs.
- Calculate the minimum possible difference in minutes between the concerts durations.
- Append the minimum possible difference to a list.
4. Return the list of minimum possible differences.
## Code:
```Python3
def min_difference_in_concerts(t, test_cases):
result = []
for case in test_cases:
a, b, c = case
total_duration = a + 2*b + 3*c
if total_duration % 2 == 0:
result.append(total_duration // 2)
else:
result.append((total_duration + 1) // 2)
return result
t = int(input())
test_cases = []
for _ in range(t):
a, b, c = map(int, input().split())
test_cases.append((a, b, c))
output = min_difference_in_concerts(t, test_cases)
for res in output:
print(res)
```
31
Decision: Again failed because of incorrect implementation. So, the Debugging Agent tries to
improve the code again.

heading: Prompt for Debugging Agent: (3rd iteration)
text: Given a competitive programming problem you have generated Python3 code to solve the problem. But the
generated code can not pass sample test cases. Improve your code to solve the problem correctly.
## Relevant Algorithm to solve the next problem: {Retrieved algorithm}
## Problem to be solved: {Original problem}
## Planning:
1. Read the integer t from input to determine the number of test cases.
2. Create a function min_difference_in_concerts(t, test_cases) that takes t and test_cases as input parameters.
3. For each test case in test_cases, do the following:
- Read the integers a, b, and c from input.
- Calculate the total duration of each type of song (1-minute, 2-minute, 3-minute).
- Calculate the total duration of all songs.
- Calculate the minimum possible difference in minutes between the concerts durations.
- Append the minimum possible difference to a list.
4. Return the list of minimum possible differences.
## Code:
def min_difference_in_concerts(t, test_cases):
result = []
for case in test_cases:
a, b, c = case
total_duration = a + 2*b + 3*c
if total_duration % 2 == 0:
result.append(total_duration // 2)
else:
result.append((total_duration + 1) // 2)
return result
t = int(input())
test_cases = []
for _ in range(t):
a, b, c = map(int, input().split())
test_cases.append((a, b, c))
output = min_difference_in_concerts(t, test_cases)
for res in output:
print(res)
## Test Report:
## Tested passed:
No test cases passed.
## Tests failed:
Input:
4
32
1 1 1
2 1 3
5 5 5
1 1 2
Expected Output:
0 1 0 1
Your Output:
3 7 15 5
## Modified Planning:
## Let's think step by step to modify Python3 Code for solving this problem.
----------------

heading: Important:
text: ## Note: Strictly follow the input and output format. The input should be taken from Standard input and
output should be given to standard output. If you are writing a function then after the function definition take
input using `input()` function then call the function with specified parameters and finally print the output of
the function. Do not add extra print statement otherwise it will failed the test cases.
## Your response must contain the modified planning and then the Python3 code inside ``` block to solve this
problem.

heading: Response from Debugging Agent: (3rd iteration)
text: ## Modified Planning:
1. Read the integer t from input to determine the number of test cases.
2. Create a function min_difference_in_concerts(t, test_cases) that takes t and test_cases as input parameters.
3. For each test case in test_cases, do the following:
- Read the integers a, b, and c from input.
- Calculate the total duration of each type of song (1-minute, 2-minute, 3-minute).
- Calculate the total duration of all songs.
- Calculate the minimum possible difference in minutes between the concerts durations.
- Append the minimum possible difference to a list.
4. Return the list of minimum possible differences.
## Code:
```Python3
def min_difference_in_concerts(t, test_cases):
result = []
for case in test_cases:
a, b, c = case
total_duration = a + 2*b + 3*c
if total_duration % 2 == 0:
result.append(0)
else:
result.append(1)
return result
t = int(input())
33
test_cases = []
for _ in range(t):
a, b, c = map(int, input().split())
test_cases.append((a, b, c))
output = min_difference_in_concerts(t, test_cases)
for res in output:
print(res)
```
Decision: This time all Sample I/O passed. We return this implementation as the Final Code for final
evaluation. Finally, we evaluated this code with a private test case, and our implementation passed
the evaluation. This way Debugging Agents debug the code like a human.

heading: Future Work
text: We have not addressed the problem of minimizing tokens/API-calls in this paper and leave it for future works. Secondly, our method currently relies on sample input-output (I/O) pairs for bug fixing. Although sample I/Os provide valuable insights for LLMs’ code generation, their limited number may not always capture the full spectrum of possible test cases. Consequently, enhancing the quality of additional test case generation could reduce our reliance on sample I/Os and further improve the robustness of our approach. Additionally, future exploration of opensource code generation models, such as CodeLLaMa, LLaMa3, Mixtral 8x7B could offer valuable insights and potential enhancements to our approach. Another important concern is that while running machine-generated code, it is advisable to run it inside a sandbox to avoid any potential risks