vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Title: Trip For Meal

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Winnie-the-Pooh likes honey very much! That is why he decided to visit his friends. Winnie has got three best friends: Rabbit, Owl and Eeyore, each of them lives in his own house. There are winding paths between each pair of houses. The length of a path between Rabbit's and Owl's houses is *a* meters, between Rabbit's and Eeyore's house is *b* meters, between Owl's and Eeyore's house is *c* meters.

For enjoying his life and singing merry songs Winnie-the-Pooh should have a meal *n* times a day. Now he is in the Rabbit's house and has a meal for the first time. Each time when in the friend's house where Winnie is now the supply of honey is about to end, Winnie leaves that house. If Winnie has not had a meal the required amount of times, he comes out from the house and goes to someone else of his two friends. For this he chooses one of two adjacent paths, arrives to the house on the other end and visits his friend. You may assume that when Winnie is eating in one of his friend's house, the supply of honey in other friend's houses recover (most probably, they go to the supply store).

Winnie-the-Pooh does not like physical activity. He wants to have a meal *n* times, traveling minimum possible distance. Help him to find this distance.

Input Specification:
First line contains an integer *n* (1<=≤<=*n*<=≤<=100) — number of visits.

Second line contains an integer *a* (1<=≤<=*a*<=≤<=100) — distance between Rabbit's and Owl's houses.

Third line contains an integer *b* (1<=≤<=*b*<=≤<=100) — distance between Rabbit's and Eeyore's houses.

Fourth line contains an integer *c* (1<=≤<=*c*<=≤<=100) — distance between Owl's and Eeyore's houses.

Output Specification:
Output one number — minimum distance in meters Winnie must go through to have a meal *n* times.

Demo Input:
['3\n2\n3\n1\n', '1\n2\n3\n5\n']

Demo Output:
['3\n', '0\n']

Note:
In the first test case the optimal path for Winnie is the following: first have a meal in Rabbit's house, then in Owl's house, then in Eeyore's house. Thus he will pass the distance 2 + 1 = 3.

In the second test case Winnie has a meal in Rabbit's house and that is for him. So he doesn't have to walk anywhere at all.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Title: Message

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
Dr. Moriarty is about to send a message to Sherlock Holmes. He has a string *s*. 

String *p* is called a substring of string *s* if you can read it starting from some position in the string *s*. For example, string "aba" has six substrings: "a", "b", "a", "ab", "ba", "aba".

Dr. Moriarty plans to take string *s* and cut out some substring from it, let's call it *t*. Then he needs to change the substring *t* zero or more times. As a result, he should obtain a fixed string *u* (which is the string that should be sent to Sherlock Holmes). One change is defined as making one of the following actions: 
 -  Insert one letter to any end of the string. -  Delete one letter from any end of the string. -  Change one letter into any other one. 
Moriarty is very smart and after he chooses some substring *t*, he always makes the minimal number of changes to obtain *u*. 

Help Moriarty choose the best substring *t* from all substrings of the string *s*. The substring *t* should minimize the number of changes Moriarty should make to obtain the string *u* from it.

Input Specification:
The first line contains a non-empty string *s*, consisting of lowercase Latin letters. The second line contains a non-empty string *u*, consisting of lowercase Latin letters. The lengths of both strings are in the range from 1 to 2000, inclusive.

Output Specification:
Print the only integer — the minimum number of changes that Dr. Moriarty has to make with the string that you choose.

Demo Input:
['aaaaa\naaa\n', 'abcabc\nbcd\n', 'abcdef\nklmnopq\n']

Demo Output:
['0\n', '1\n', '7\n']

Note:
In the first sample Moriarty can take any substring of length 3, and it will be equal to the required message *u*, so Moriarty won't have to make any changes.

In the second sample you should take a substring consisting of characters from second to fourth ("bca") or from fifth to sixth ("bc"). Then you will only have to make one change: to change or to add the last character.

In the third sample the initial string *s* doesn't contain any character that the message should contain, so, whatever string you choose, you will have to make at least 7 changes to obtain the required message.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Treeland is a country in which there are n towns connected by n - 1 two-way road such that it's possible to get from any town to any other town. 

In Treeland there are 2k universities which are located in different towns. 

Recently, the president signed the decree to connect universities by high-speed network.The Ministry of Education understood the decree in its own way and decided that it was enough to connect each university with another one by using a cable. Formally, the decree will be done! 

To have the maximum sum in the budget, the Ministry decided to divide universities into pairs so that the total length of the required cable will be maximum. In other words, the total distance between universities in k pairs should be as large as possible. 

Help the Ministry to find the maximum total distance. Of course, each university should be present in only one pair. Consider that all roads have the same length which is equal to 1. 


-----Input-----

The first line of the input contains two integers n and k (2 ≤ n ≤ 200 000, 1 ≤ k ≤ n / 2) — the number of towns in Treeland and the number of university pairs. Consider that towns are numbered from 1 to n. 

The second line contains 2k distinct integers u_1, u_2, ..., u_2k (1 ≤ u_{i} ≤ n) — indices of towns in which universities are located. 

The next n - 1 line contains the description of roads. Each line contains the pair of integers x_{j} and y_{j} (1 ≤ x_{j}, y_{j} ≤ n), which means that the j-th road connects towns x_{j} and y_{j}. All of them are two-way roads. You can move from any town to any other using only these roads. 


-----Output-----

Print the maximum possible sum of distances in the division of universities into k pairs.


-----Examples-----
Input
7 2
1 5 6 2
1 3
3 2
4 5
3 7
4 3
4 6

Output
6

Input
9 3
3 2 1 6 5 9
8 9
3 2
2 7
3 4
7 6
4 5
2 1
2 8

Output
9



-----Note-----

The figure below shows one of possible division into pairs in the first test. If you connect universities number 1 and 6 (marked in red) and universities number 2 and 5 (marked in blue) by using the cable, the total distance will equal 6 which will be the maximum sum in this example. 

 [Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a string S on which you need to perform Q replace operations.
Each replacement operation has 3 parameters: a starting index i, a source word x and a target word y. The rule is that if x starts at position i in the original string S, then we will replace that occurrence of x with y. If not, we do nothing.
Note:  All these operations occur simultaneously. It's guaranteed that there won't be any overlap in replacement: for example, S = "abc", indexes = [0,1], sources = ["ab", "bc"] is not a valid test case. 
Example 1:
Input: 
S = "gforks"
Q = 2
index[] = {0, 4}
sources[] = {"g", "ks"}
targets[] = {"geeks", "geeks"}
Output: 
geeksforgeeks
Explanation:
"g" starts at index 0, so, it's replaced by
"geeks". Similarly, "ks" starts at index 4,
and is replaced by "geeks".
Example 2:
Input: 
S = "gforks"
Q = 2
index[] = {0, 3}
sources[] = {"g", "ss"}
targets[] = {"geeks", "geeks"}
Output: 
geeksforks
Explanation:
"g" starts at index 0, so, it's replaced by
"geeks". "ss" doesn't start at index 3 in
original S, so it's not replaced.
Your Task:
You don't need to read input or print anything. You only need to complete the function findAndReplace() that takes a string S, an integer Q, and 3 arrays index, sources, and targets of size Q, as input and returns the new string after all the operations. index[i], sources[i], and targets[i] denotes the index, sources, and targets for i_{th} query.
Expected Time Complexity:  O(|S| * Q)
Expected Auxilliary Space: O(Q)
 
Constraints:
1 ≤ |S| ≤ 10^{4}
1 ≤ Q ≤ 100
1 ≤ length of sources_{i}, targets_{i} ≤ 100

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
# Task
 Consider the following algorithm for constructing 26 strings S(1) .. S(26):
```
S(1) = "a";
For i in [2, 3, ..., 26]:
S(i) = S(i - 1) + character(i) + S(i - 1).```

 For example:
```
S(1) = "a"
S(2) = S(1) + "b" + S(1) = "a" + "b" + "a" = "aba"
S(3) = S(2) + "c" + S(2) = "aba" + "c" +"aba" = "abacaba"
...
S(26) = S(25) + "z" + S(25)```
Finally, we got a long string S(26). Your task is to find the `k`th symbol (indexing from 1) in the string S(26). All strings consist of lowercase letters only.

# Input / Output


 - `[input]` integer `k`

  1 ≤ k < 2^(26)


 - `[output]` a string(char in C#)

  the `k`th symbol of S(26)

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Gerald bought two very rare paintings at the Sotheby's auction and he now wants to hang them on the wall. For that he bought a special board to attach it to the wall and place the paintings on the board. The board has shape of an a_1 × b_1 rectangle, the paintings have shape of a a_2 × b_2 and a_3 × b_3 rectangles.

Since the paintings are painted in the style of abstract art, it does not matter exactly how they will be rotated, but still, one side of both the board, and each of the paintings must be parallel to the floor. The paintings can touch each other and the edges of the board, but can not overlap or go beyond the edge of the board. Gerald asks whether it is possible to place the paintings on the board, or is the board he bought not large enough?


-----Input-----

The first line contains two space-separated numbers a_1 and b_1 — the sides of the board. Next two lines contain numbers a_2, b_2, a_3 and b_3 — the sides of the paintings. All numbers a_{i}, b_{i} in the input are integers and fit into the range from 1 to 1000.


-----Output-----

If the paintings can be placed on the wall, print "YES" (without the quotes), and if they cannot, print "NO" (without the quotes).


-----Examples-----
Input
3 2
1 3
2 1

Output
YES

Input
5 5
3 3
3 3

Output
NO

Input
4 2
2 3
1 2

Output
YES



-----Note-----

That's how we can place the pictures in the first test:

[Image]

And that's how we can do it in the third one.

[Image]

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Calvin has a math assignment at school where he has to evaluate a lot of expressions. Calvin decides to not to waste much of his time. There are ${M}$ expressions overall. By looking at Susie’s answers, Calvin has figured that the answers to all questions form a non decreasing sequence. 

He decides that all his answers are going to be between ${1}$ and $N$ (inclusive). He fills his answer sheet with a random non-decreasing sequence of length ${M}$ where each element is between ${1}$ and $N$. 

Here is the part where the real problem starts for Calvin. He does not want to choose a large value of $N$, because, he will have a lot of options to choose from. Also, if he chooses a very small value of $N$, a lot of answers would become equal and the teacher will become suspicious.  

If $x=\text{max}_{1\leq i\leq N}(f(i))$, f(i) being the frequency or number of times ${i}$ occurs in the sequence of ${M}$ values he picked. Calvin wants to find out expected value of $\boldsymbol{x}$. Help him solve the problem.  

For example, if $M=3$ & $N=3$, the possible sequences are:  

1 1 1 (x = 3)  
1 1 2 (x = 2)  
1 1 3 (x = 2)  
1 2 2 (x = 2)  
1 2 3 (x = 1)  
1 3 3 (x = 2)  
2 2 2 (x = 3)  
2 2 3 (x = 2)  
2 3 3 (x = 2)  
3 3 3 (x = 3)  

expected value of $x=2.2$

Input Format 

The first line contains an integer ${T}$ which refers to the number of test cases. ${T}$ lines follow, each containing $2$ numbers, ${M}$ and $N$ for the corresponding test cases.  

Constraints 

$1\leq T\leq15$ 

$1\leq M\leq250$ 

$1\leq N\leq10^9$  

Output Format 

Output ${T}$ lines, each containing answer to the corresponding test case. Error of upto $10^{-3}$ is allowed.  

Sample Input  

4
1 5
3 3
2 9
9 6

Sample Output  

1.0000000000
2.2000000000
1.2000000000
4.3146853147

Explanation 

For second testcase we have  

$\begin{aligned}
&\text{Seq}\quad\text{Freq} \\
& 111\quad 3  \\
&112\quad2 \\
&113\quad 2 \\
&122\quad 2 \\
&123\quad1\\
&133\quad 2 \\
&222\quad3 \\
&223\quad2 \\
&233\quad 2 \\
&333\quad 3
\end{aligned}$


$\begin{aligned}E(x)&=\sum P_x\times x\\ &=P_1+2P_2+3P_3\\ &=\frac{1}{10}+\frac{2\times6}{10}+\frac{3\times3}{10}\\ &=\frac{22}{10}\end{aligned}$

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Calculate the value of the sum: n mod 1 + n mod 2 + n mod 3 + ... + n mod m. As the result can be very large, you should print the value modulo 10^9 + 7 (the remainder when divided by 10^9 + 7).

The modulo operator a mod b stands for the remainder after dividing a by b. For example 10 mod 3 = 1.


-----Input-----

The only line contains two integers n, m (1 ≤ n, m ≤ 10^13) — the parameters of the sum.


-----Output-----

Print integer s — the value of the required sum modulo 10^9 + 7.


-----Examples-----
Input
3 4

Output
4

Input
4 4

Output
1

Input
1 1

Output
0

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array 'D' with n elements: d[0], d[1], ..., d[n-1], you can perform the following two steps on the array.  

Randomly choose two indexes (l, r) with l < r, swap (d[l], d[r])   
Randomly choose two indexes (l, r) with l < r, reverse (d[l...r]) (both inclusive)   

After you perform the first operation a times and the second operation b times, you randomly choose two indices l & r with l < r and calculate the S = sum(d[l...r]) (both inclusive).  

Now, you are to find the expected value of S.

Input Format 

The first line of the input contains 3 space separated integers - n, a and b. 

The next line contains n space separated integers which are the elements of the array d.   

n a b
d[0] d[1] ... d[n-1]

Output Format 

Print the expected value of S.  

E(S)

Constraints  

2 <= n <= 1000 

1 <= a <= 10^{9} 

1 <= b <= 10  

The answer will be considered correct, if the absolute or relative error doesn't exceed 10^{-4}.  

Sample Input #00:

3 1 1 
1 2 3

Sample Output #00:

4.666667

Explanation #00:

At step 1): 

You have three choices: 

1. swap(0, 1), 2 1 3 

2. swap(0, 2), 3 2 1 

3. swap(1, 2), 1 3 2  

At step 2): 

For every result you have three choices for reversing: 

1. [2 1 3] -> [1 2 3] [3 1 2] [2 3 1] 

2. [3 2 1] -> [2 3 1] [1 2 3] [3 1 2] 

3. [1 3 2] -> [3 1 2] [2 3 1] [1 2 3]  

So you have 9 possible arrays with each having a 1/9 probability.

For the last step: 

Each of the 9 arrays will have 3 possible sums with equal probability. For [1 2 3], you can get 1+2, 2+3 and 1+2+3. 

Since there will be 27 outcome for this input, one can calculate the expected value by finding sum of all 27 S and dividing it by 27.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a string S that contains parentheses and letters. You have to remove the minimum number of invalid parentheses to make the input string valid.
Return all the possible results in the sorted order.
Example 1:
Input: S = "()())()"
Output: ["(())()","()()()"]
Example 2:
Input: S = "(a)())()"
Output: ["(a())()","(a)()()"]
Example 3:
Input: S = ")("
Output: [""]
Your Task:  
You don't need to read input or print anything. Your task is to complete the function removeInvalidParentheses() which takes the string S as an input parameter and returns an array of strings representing all the valid parentheses that we can form by removing the minimum number of characters from the string.
 
Expected Time Complexity: O(2^{|S|})
Expected Auxiliary Space: O(1)
Constraints:
1 <= |S| <= 20
S consists of lowercase English letters and parentheses '(' and ')'

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
"Everything in the universe is balanced. Every disappointment you face in life will be balanced by something good for you! Keep going, never give up."
Let's call a string balanced if all characters that occur in this string occur in it the same number of times.
You are given a string $S$; this string may only contain uppercase English letters. You may perform the following operation any number of times (including zero): choose one letter in $S$ and replace it by another uppercase English letter. Note that even if the replaced letter occurs in $S$ multiple times, only the chosen occurrence of this letter is replaced.
Find the minimum number of operations required to convert the given string to a balanced string.

-----Input-----
- The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
- The first and only line of each test case contains a single string $S$.

-----Output-----
For each test case, print a single line containing one integer ― the minimum number of operations.

-----Constraints-----
- $1 \le T \le 10,000$
- $1 \le |S| \le 1,000,000$
- the sum of $|S|$ over all test cases does not exceed $5,000,000$
- $S$ contains only uppercase English letters

-----Subtasks-----
Subtask #1 (20 points):
- $T \le 10$
- $|S| \le 18$
Subtask #2 (80 points): original constraints

-----Example Input-----
2
ABCB
BBC

-----Example Output-----
1
1

-----Explanation-----
Example case 1: We can change 'C' to 'A'. The resulting string is "ABAB", which is a balanced string, since the number of occurrences of 'A' is equal to the number of occurrences of 'B'.
Example case 2: We can change 'C' to 'B' to make the string "BBB", which is a balanced string.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Recently Akash got this equation. Now being curious he wanted to know that for a given N ,  is it possible to find P1, P2, P3 and P4 for below equation under following conditions.

( P1-P2 ) + ( P3 - P4 ) = N
P1, P2, P3, P4 are prime numbers
P1 and P2 are consecutive Primes and P1 > P2
P3 and P4 are consecutive Primes and P3 > P4
It is possible that P1=P3 and P2=P4 
3 ≤ P1,P2,P3,P4 ≤ 10^7

NOTE : Consecutive primes are the primes next to each other. i.e, 2 and 3 ,   7 and 11 , 17 and 19  are considered as consecutive prime numbers.

Input : 
First line contains T - No. of Test cases. 
For each test case there is only one line containing N.

output :
Output "YES" if such P1,P2,P3,P4 are possible else print "NO" in each line

Constraints : 
1≤ T ≤ 10^5 
1≤ N ≤ 10^7
P1 , P2 ,P3 , P4 ≤ 10^7

SAMPLE INPUT
5
4
15
30
100
1000

SAMPLE OUTPUT
YES
NO
YES
YES
NO

Explanation

Test Case #1 :  You can choose P1=5 P2=3 P3=13 P4=11

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given the list of numbers, you are to sort them in non decreasing order.

-----Input-----
t – the number of numbers in list, then t lines follow [t <= 10^6]. 

Each line contains one integer: N [0 <= N <= 10^6]

-----Output-----
Output given numbers in non decreasing order.

-----Example-----
Input:
5
5
3
6
7
1

Output:
1
3
5
6
7

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a string containing only 4 kinds of characters 'Q', 'W', 'E' and 'R'.
A string is said to be balanced if each of its characters appears n/4 times where n is the length of the string.
Return the minimum length of the substring that can be replaced with any other string of the same length to make the original string s balanced.
Return 0 if the string is already balanced.
 
Example 1:
Input: s = "QWER"
Output: 0
Explanation: s is already balanced.
Example 2:
Input: s = "QQWE"
Output: 1
Explanation: We need to replace a 'Q' to 'R', so that "RQWE" (or "QRWE") is balanced.

Example 3:
Input: s = "QQQW"
Output: 2
Explanation: We can replace the first "QQ" to "ER". 

Example 4:
Input: s = "QQQQ"
Output: 3
Explanation: We can replace the last 3 'Q' to make s = "QWER".

 
Constraints:

1 <= s.length <= 10^5
s.length is a multiple of 4
s contains only 'Q', 'W', 'E' and 'R'.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
There are some rabbits in Singapore Zoo. To feed them, Zookeeper bought $n$ carrots with lengths $a_1, a_2, a_3, \ldots, a_n$. However, rabbits are very fertile and multiply very quickly. Zookeeper now has $k$ rabbits and does not have enough carrots to feed all of them. To solve this problem, Zookeeper decided to cut the carrots into $k$ pieces. For some reason, all resulting carrot lengths must be positive integers.

Big carrots are very difficult for rabbits to handle and eat, so the time needed to eat a carrot of size $x$ is $x^2$.

Help Zookeeper split his carrots while minimizing the sum of time taken for rabbits to eat the carrots.


-----Input-----

The first line contains two integers $n$ and $k$ $(1 \leq n \leq k \leq 10^5)$: the initial number of carrots and the number of rabbits.

The next line contains $n$ integers $a_1, a_2, \ldots, a_n$ $(1 \leq a_i \leq 10^6)$: lengths of carrots.

It is guaranteed that the sum of $a_i$ is at least $k$.


-----Output-----

Output one integer: the minimum sum of time taken for rabbits to eat carrots.


-----Examples-----
Input
3 6
5 3 1

Output
15

Input
1 4
19

Output
91



-----Note-----

For the first test, the optimal sizes of carrots are $\{1,1,1,2,2,2\}$. The time taken is $1^2+1^2+1^2+2^2+2^2+2^2=15$

For the second test, the optimal sizes of carrots are $\{4,5,5,5\}$. The time taken is $4^2+5^2+5^2+5^2=91$.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Alice has recently learned in her economics class that the market is said to be in equilibrium when the supply is equal to the demand.

Alice has market data for N time points in the form of two integer arrays S and D. Here, S_{i} denotes the supply at the i^{th} point of time and D_{i} denotes the demand at the i^{th} point of time, for each 1 ≤ i ≤ N.

Help Alice in finding out the number of time points at which the market was in equilibrium. 

------ Input Format ------ 

- The first line of input will contain an integer T — the number of test cases. The description of T test cases follows.
- Each test case contains three lines of input.
- The first line of each test case contains an integer N, the length of the arrays S and D.
- The second line of each test case contains N space-separated integers S_{1}, S_{2}, \ldots , S_{N}.
- The third line of each test case contains N space-separated integers D_{1}, D_{2}, \ldots , D_{N}. 

------ Output Format ------ 

For each test case, output the number of time points at which the market was in equilibrium.

------ Constraints ------ 

$1 ≤ T ≤ 10$
$1 ≤ N ≤ 100$
$1 ≤ S_{i}, D_{i} ≤ 100$ for every $1 ≤ i ≤ N$

----- Sample Input 1 ------ 
2
4
1 2 3 4
2 1 3 4
4
1 1 2 2
1 2 1 1
----- Sample Output 1 ------ 
2
1
----- explanation 1 ------ 
Test case $1$: For $i = 3$ and $i = 4$, we have supply equal to demand, hence the market is in equilibrium.

Test case $2$: For $i = 1$, we have supply equal to demand, hence the market is in equilibrium.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.