vgel/INTELLECT-2-RL-Dataset-Code-Only huggingface dataset:
Title: Letter A

Time Limit: 1 seconds

Memory Limit: 64 megabytes

Problem Description:
Little Petya learns how to write. The teacher gave pupils the task to write the letter *A* on the sheet of paper. It is required to check whether Petya really had written the letter *A*.

You are given three segments on the plane. They form the letter *A* if the following conditions hold:
 -  Two segments have common endpoint (lets call these segments first and second), while the third segment connects two points on the different segments. -  The angle between the first and the second segments is greater than 0 and do not exceed 90 degrees. -  The third segment divides each of the first two segments in proportion not less than 1<=/<=4 (i.e. the ratio of the length of the shortest part to the length of the longest part is not less than 1<=/<=4).

Input Specification:
The first line contains one integer *t* (1<=≤<=*t*<=≤<=10000) — the number of test cases to solve. Each case consists of three lines. Each of these three lines contains four space-separated integers — coordinates of the endpoints of one of the segments. All coordinates do not exceed 108 by absolute value. All segments have positive length.

Output Specification:
Output one line for each test case. Print «YES» (without quotes), if the segments form the letter *A* and «NO» otherwise.

Demo Input:
['3\n4 4 6 0\n4 1 5 2\n4 0 4 4\n0 0 0 6\n0 6 2 -4\n1 1 0 1\n0 0 0 5\n0 5 2 -1\n1 2 0 1\n']

Demo Output:
['YES\nNO\nYES\n']

Note:
none

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given a positive integer N denoting the length of a stick, return the number of ways to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.
Example 1:
Input: N = 10
Output: 2
Explanation: The 2 ways to split 
the stick are {1,1,4,4} , {2,2,3,3} 
Ã¢â¬â¹Example 2:
Input: n = 20
Output: 4
Explanation: The 4 ways to split 
the stick are {1,1,9,9} , {2,2,8,8}, 
{3,3,7,7} and {4,4,6,6}. Note that 
{5,5,5,5} forms square so it is not 
considered.
Your Task:  
You don't need to read input or print anything. Your task is to complete the function count() which takes N as input and returns the answer.
Expected Time Complexity: O(1)
Expected Auxiliary Space: O(1)
Constraints:
1 ≤ N ≤ 10^{9}

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
The only difference between easy and hard versions is constraints.

You are given a sequence $a$ consisting of $n$ positive integers.

Let's define a three blocks palindrome as the sequence, consisting of at most two distinct elements (let these elements are $a$ and $b$, $a$ can be equal $b$) and is as follows: $[\underbrace{a, a, \dots, a}_{x}, \underbrace{b, b, \dots, b}_{y}, \underbrace{a, a, \dots, a}_{x}]$. There $x, y$ are integers greater than or equal to $0$. For example, sequences $[]$, $[2]$, $[1, 1]$, $[1, 2, 1]$, $[1, 2, 2, 1]$ and $[1, 1, 2, 1, 1]$ are three block palindromes but $[1, 2, 3, 2, 1]$, $[1, 2, 1, 2, 1]$ and $[1, 2]$ are not.

Your task is to choose the maximum by length subsequence of $a$ that is a three blocks palindrome.

You have to answer $t$ independent test cases.

Recall that the sequence $t$ is a a subsequence of the sequence $s$ if $t$ can be derived from $s$ by removing zero or more elements without changing the order of the remaining elements. For example, if $s=[1, 2, 1, 3, 1, 2, 1]$, then possible subsequences are: $[1, 1, 1, 1]$, $[3]$ and $[1, 2, 1, 3, 1, 2, 1]$, but not $[3, 2, 3]$ and $[1, 1, 1, 1, 2]$.


-----Input-----

The first line of the input contains one integer $t$ ($1 \le t \le 2000$) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains one integer $n$ ($1 \le n \le 2000$) — the length of $a$. The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 26$), where $a_i$ is the $i$-th element of $a$. Note that the maximum value of $a_i$ can be up to $26$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2000$ ($\sum n \le 2000$).


-----Output-----

For each test case, print the answer — the maximum possible length of some subsequence of $a$ that is a three blocks palindrome.


-----Example-----
Input
6
8
1 1 2 2 3 2 1 1
3
1 3 3
4
1 10 10 1
1
26
2
2 1
3
1 1 1

Output
7
2
4
1
1
3

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A Word Ladder is a puzzle in which you transform one word into another, by changing one letter at a time. But, there’s a catch: every word that you form in each step must be in the dictionary! Here’s an example of how to transform CAT into GAS:CAT $\rightarrow $ CAR $\rightarrow $ WAR $\rightarrow $ WAS $\rightarrow $ GAS

Of course, you want to use the fewest number of transitions possible. These puzzles can be tough, and often you’ll think to yourself: “Darn it! If only [some word] was in the dictionary!”

Well, now is your chance! Given a dictionary, and a starting and ending word, what ONE single word could you add to the dictionary to minimize the number of steps to get from the starting word to the ending word, changing only one letter at a time, and making sure that every word at every step is in the dictionary?

-----Input-----
Each input will consist of a single test case. Note that your program may be run multiple times on different inputs. Each test case will start with a line with a single integer $n$ ($2 \le n \le 1000$) which indicates the number of words in the dictionary. The dictionary will follow on the next $n$ lines, with one word per line. All words will consist of between $1$ and $8$ capital letters only, and all of the words in a test case will be of the same length. The first word in the list will be the starting word of the word ladder, and the second will be the ending word of the word ladder.

-----Output-----
Output exactly two lines. The first line holds the one single word that you would add to the dictionary, and the second holds an integer indicating the minimum number of steps to get from the starting word to the ending word, adding your word.

It is possible that there’s more than one word you can add that will make your path as short as possible. In this case, output the solution word that comes first alphabetically.

It is possible that there’s no word you can add that will that will make your path any shorter. In this case, output 0 (zero) as the word.

It is possible that there’s no word you can add that makes the solution possible. In this case, output 0 (zero) as the word, and -1 as the number of steps.

-----Examples-----
Sample Input 1:
3
CAT
DOG
COT
Sample Output 1:
COG
3

Sample Input 2:
2
CAT
DOG
Sample Output 2:
0
-1

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Little Jhool is just not a smart algorithmic coder, he regularly contributes to open source, too. This year, he's managed to be selected for a project in the prestigious Google Summer of Code, too. More than the project, he's happy about the money he's going to receive. He's already started day dreaming about what he will do with the money, - he's settled on for going to a tour of couple of countries. Now, he's a bit confused about which countries he wants to consider, so he buys a globe, and starts rotating it like some boss.

The globe has n different countries on it, and let's say they are labeled as 0, 1, 2, 3, 4... n-1, but since it is a globe, after n-1, country order follows again. That is to say, if there are n countries - 0, 1, 2, 3, 4, . . . , n-1, then, their arrangement would be: first 0, then 1, then 2, ..., then n-1, and then again 0... 

Let us take m = 6, then {4, 5, 0} can be a valid range of countries, {2} can be a valid range, too, {3, 4, 5, 0, 1, 2} is a valid range, too. Since it is a globe, the range can  wrap around itself. 

Now, his girlfriend decides a range of countries. Since, his girlfriend is confusing him a lot, he just wants to pick up ONLY ONE country from a range. He does NOT want to any country to be chosen more than once for different ranges.

Given number of countries, and number of ranges (And their range!) - help Little Jhool figure out if he'll be able to do this.

Input format:
The first line contains test cases, tc, followed by two integers N,M- the first one depicting the number of countries on the globe, the second one depicting the number of ranges his girlfriend has given him. After which, the next M lines will have two integers describing the range, X and Y. If (X ≤ Y), then range covers countries [X,X+1... Y] else range covers [X,X+1,.... N-1,0,1..., Y].

Output format:
Print "YES" if it is possible for Little Jhool to do so, print "NO", if it is not.

Constraints:
1 ≤ TC ≤ 30
1 ≤ N ≤ 10^9
1 ≤ M ≤ 10^5
0 ≤ Xi, Yi < N

SAMPLE INPUT
2
4 3
0 1
1 2
2 0
5 5
0 0
1 2
2 3
4 4
4 0

SAMPLE OUTPUT
YES
NO

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
IPL 2021 knockouts are over, teams MI, CSK, DC, and RCB are qualified for the semis. 
Today is matchday 6 and it is between Delhi Capitals and Royal Challengers Banglore. Glenn Maxwell of RCB playing flawlessly. Rishabh Pant, the new captain of the team who is also a wicket-keeper wants to send a message to the bowler. But, he can't shout message directly as a batsman can hear. So, he decided to encrypt the message by putting '*'s in the message. And this is how the bowler decrypts the message. Bowler iterates over the message string from left to right, if he finds a '*', he removes it and adds all the letters read so far to the message. He keeps on doing this till he gets rid of all the '*'. Given a decrypted message in the form of the string, the task is to find the encrypted message.
Note: If the string can be encrypted in multiple ways, find the encrypted string of smallest length.
Example 1:
Input: s = "ababcababcd"
Output: ab*c*d
Explanation: We can encrypt the string 
in following way : "ababcababcd" -> 
"ababc*d" -> "ab*c*d"
Example 2:
Input: s = "zzzzzzz"
Output: z*z*z
Explanation: The string can be encrypted 
in 2 ways: "z*z*z" and "z**zzz". Out of 
the two "z*z*z" is smaller in length.
Your Task: 
You don't need to read input or print anything. Complete the function compress() which takes the message string s as input parameter and returns the shortest possible encrypted string.
Constraints: 
1 ≤ |s| ≤ 10^{5}

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You will be given a string (x) featuring a cat 'C', a dog 'D' and a mouse 'm'. The rest of the string will be made up of '.'. 

You need to find out if the cat can catch the mouse from it's current position. The cat can jump (j) characters. 

Also, the cat cannot jump over the dog.

So:

if j = 5:

```..C.....m.``` returns 'Caught!'  <-- not more than j characters between

```.....C............m......``` returns 'Escaped!'  <-- as there are more than j characters between the two, the cat can't jump far enough

if j = 10:

```...m.........C...D``` returns 'Caught!' <--Cat can jump far enough and jump is not over dog

```...m....D....C.......``` returns 'Protected!' <-- Cat can jump far enough, but dog is in the way, protecting the mouse

Finally, if all three animals are not present, return 'boring without all three'

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
A coin system $S$ is a finite (nonempty) set of distinct positive integers corresponding to coin values, also called denominations, in a real or imagined monetary system. For example, the coin system in common use in Canada is $\{ 1,5,10,25,100,200\} $, where $1$ corresponds to a $1$-cent coin and $200$ corresponds to a $200$-cent ($2$-dollar) coin. For any coin system $S$, we assume that there is an unlimited supply of coins of each denomination, and we also assume that $S$ contains $1$, since this guarantees that any positive integer can be written as a sum of (possibly repeated) values in $S$.

Cashiers all over the world face (and solve) the following problem: For a given coin system and a positive integer amount owed to a customer, what is the smallest number of coins required to dispense exactly that amount? For example, suppose a cashier in Canada owes a customer $83$ cents. One possible solution is $25+25+10+10+10+1+1+1$, i.e., $8$ coins, but this is not optimal, since the cashier could instead dispense $25+25+25+5+1+1+1$, i.e., $7$ coins (which is optimal in this case). Fortunately, the Canadian coin system has the nice property that the greedy algorithm always yields an optimal solution, as do the coin systems used in most countries. The greedy algorithm involves repeatedly choosing a coin of the largest denomination that is less than or equal to the amount still owed, until the amount owed reaches zero. A coin system for which the greedy algorithm is always optimal is called canonical.

Your challenge is this: Given a coin system $S = \{ c_1, c_2, \ldots , c_ n\} $, determine whether $S$ is canonical or non-canonical. Note that if $S$ is non-canonical then there exists at least one counterexample, i.e., a positive integer $x$ such that the minimum number of coins required to dispense exactly $x$ is less than the number of coins used by the greedy algorithm. An example of a non-canonical coin system is $\{ 1,3,4\} $, for which $6$ is a counterexample, since the greedy algorithm yields $4+1+1$ ($3$ coins), but an optimal solution is $3+3$ ($2$ coins). A useful fact (due to Dexter Kozen and Shmuel Zaks) is that if $S$ is non-canonical, then the smallest counterexample is less than the sum of the two largest denominations.

-----Input-----
Input consists of a single case. The first line contains an integer $n$ $(2 \leq n \leq 100)$, the number of denominations in the coin system. The next line contains the $n$ denominations as space-separated integers $c_1 \ c_2 \ \ldots \ c_ n$, where $c_1 = 1$ and $c_1 < c_2 < \ldots < c_ n \leq 10^6$.

-----Output-----
Output “canonical” if the coin system is canonical, or “non-canonical” if the coin system is non-canonical.

-----Examples-----
Sample Input 1:
4
1 2 4 8
Sample Output 1:
canonical

Sample Input 2:
3
1 5 8
Sample Output 2:
non-canonical

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
You are given a positive integer X.
Find the largest perfect power that is at most X.
Here, a perfect power is an integer that can be represented as b^p, where b is an integer not less than 1 and p is an integer not less than 2.

-----Constraints-----
 - 1 ≤ X ≤ 1000
 - X is an integer.

-----Input-----
Input is given from Standard Input in the following format:
X

-----Output-----
Print the largest perfect power that is at most X.

-----Sample Input-----
10

-----Sample Output-----
9

There are four perfect powers that are at most 10: 1, 4, 8 and 9.
We should print the largest among them, 9.

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Everybody knows that the capital of Bergeria is connected to banson by a direct road. To improve the road's traffic capacity, there was placed just one traffic sign, limiting the maximum speed. Traffic signs in Bergeria are a bit peculiar, because they limit the speed only at that point on the road where they are placed. Right after passing the sign it is allowed to drive at any speed.

It is known that the car of an average Bergeria citizen has the acceleration (deceleration) speed of a km/h2, and has maximum speed of v km/h. The road has the length of l km, and the speed sign, limiting the speed to w km/h, is placed d km (1 ≤ d < l) away from the capital of Bergeria. The car has a zero speed at the beginning of the journey. Find the minimum time that an average Bergeria citizen will need to get from the capital to banson, if he drives at the optimal speed.

The car can enter banson at any speed.

Input
The first line of the input file contains two integer numbers a and v (1 ≤ a, v ≤ 10000). The second line contains three integer numbers l, d and w (2 ≤ l ≤ 10000; 1 ≤ d < l; 1 ≤ w ≤ 10000).

Output
Print the answer with at least five digits after the decimal point.

SAMPLE INPUT
1 1
2 1 3

SAMPLE OUTPUT
2.500000000000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
For a given string of binary number bi. Find the two’s complement of it.
Example 1:
Input: bi = 00000101
Output: 11111011
Explaination: 2's complement is reversing all 
the bits of the given number and then adding 
1 to it.
Example 2:
Input: bi = 101
Output: 011
Explaination: Follow the process of figuring 
out 2's complement. This will be the answer.
Your Task:
You do not need to read input or print anything. Your task is to complete the function complement() which takes bi as input parameter and returns the 2's complement of the number.
Expected Time Complexity: O(|bi|)
Expected Auxiliary Space: O(|bi|)
Constraints:
1 ≤ |bi| ≤ 10

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

Time Limit: None seconds

Memory Limit: None megabytes

Problem Description:
DZY loves planting, and he enjoys solving tree problems.

DZY has a weighted tree (connected undirected graph without cycles) containing *n* nodes (they are numbered from 1 to *n*). He defines the function *g*(*x*,<=*y*) (1<=≤<=*x*,<=*y*<=≤<=*n*) as the longest edge in the shortest path between nodes *x* and *y*. Specially *g*(*z*,<=*z*)<==<=0 for every *z*.

For every integer sequence *p*1,<=*p*2,<=...,<=*p**n* (1<=≤<=*p**i*<=≤<=*n*), DZY defines *f*(*p*) as . 

DZY wants to find such a sequence *p* that *f*(*p*) has maximum possible value. But there is one more restriction: the element *j* can appear in *p* at most *x**j* times.

Please, find the maximum possible *f*(*p*) under the described restrictions.

Input Specification:
The first line contains an integer *n* (1<=≤<=*n*<=≤<=3000).

Each of the next *n*<=-<=1 lines contains three integers *a**i*,<=*b**i*,<=*c**i* (1<=≤<=*a**i*,<=*b**i*<=≤<=*n*; 1<=≤<=*c**i*<=≤<=10000), denoting an edge between *a**i* and *b**i* with length *c**i*. It is guaranteed that these edges form a tree.

Each of the next *n* lines describes an element of sequence *x*. The *j*-th line contains an integer *x**j* (1<=≤<=*x**j*<=≤<=*n*).

Output Specification:
Print a single integer representing the answer.

Demo Input:
['4\n1 2 1\n2 3 2\n3 4 3\n1\n1\n1\n1\n', '4\n1 2 1\n2 3 2\n3 4 3\n4\n4\n4\n4\n']

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

Note:
In the first sample, one of the optimal *p* is [4, 3, 2, 1].

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Eugene loves sequences, especially arithmetic progressions. One day he was asked to solve a difficult problem.

If a sequence of numbers A1, A2, ... , AN form an arithmetic progression A, he was asked to calculate sum of F(Ai), for L ≤ i ≤ R.
F(X) is defined as:

If X < 10 then F(X) = X.

Else F(X) = F(sum_of_digits(X)).

Example:
F(1378) = 
F(1+3+7+8) = 
F(19) = 
F(1 + 9) = 
F(10) = 
F(1+0) = 
F(1) = 1

-----Input-----
- The first line of the input contains an integer T denoting the number of test cases.
- Each test case is described in one line containing four integers: A1 denoting the first element of the arithmetic progression A, D denoting the common difference between successive members of A, and L and R as described in the problem statement.

-----Output-----
- For each test case, output a single line containing one integer denoting sum of F(Ai).

-----Constraints-----
- 1 ≤ T ≤ 105
- 1 ≤ A1 ≤ 109
- 0 ≤ D ≤ 109
- 1 ≤ R ≤ 1018
- 1 ≤ L ≤ R

-----Subtasks-----
- Subtask 1:  0 ≤ D ≤ 100, 1 ≤ A1 ≤ 109, 1 ≤ R ≤ 100  - 15 points
- Subtask 2:  0 ≤ D ≤ 109, 1 ≤ A1 ≤ 109, 1 ≤ R ≤ 106  - 25 points
- Subtask 3: Original constraints - 60 points

-----Example-----
Input:
2
1 1 1 3
14 7 2 4

Output:
6
12

-----Explanation-----
Example case 1.
A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...}
A1 = 1
A2 = 2
A3 = 3
F(A1) = 1
F(A2) = 2
F(A3) = 3
1+2+3=6
Example case 2.
A = {14, 21, 28, 35, 42, 49, 56, 63, 70, 77,  ...}
A2 = 21
A3 = 28
A4 = 35
F(A2) = 3
F(A3) = 1
F(A4) = 8
3+1+8=12

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Convert a given string to its cross string (i.e Diagonal from left-right and from right-left).  
See examples for better understanding.
 
Example 1:
Input:
abc
Output:
a c  b  a c
Explanation:
The above is the proper 
cross manner for the 
test case.
a c
 b 
a c
Example 2:
Input:
geeks
Output:
g   s e k   e   e k g   s
Explanation:
For the 1st test case where 
the string is geeks
G   S
 E K
  E
 E K
G   S
The above is the proper cross 
the manner for the test case, but 
when printed in a single line 
it becomes as shown in the output.
 
Your Task:
You don't need to read input or print anything. Your task is to complete the function crossPattern() which takes the string S and returns a single string in the following way first-line output of the string concatenated with 2nd line and so on till the Nth line.
 
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)
 
Constraints:
1 ≤ length of string ≤ 1000

Write Python code to solve the problem. Present the code in 
```python
Your code
```
at the end.
Given an array s containing n strings, find the length of the string obtained by combining the strings. Two strings can be only combined if the last character of the first string and the first character of the second string are the same.
Example 1:
Input:
n = 3
s[] = {"RBR", "BBR", "RRR"}
Output: 9
Explanation: Combined string can 
             be: BRR + RBR + RRR
Example 2:
Input:
n = 2
s[] = {"RRR", "BBB"}
Output: 0
Explanation: Since combining condition
             isn't fulfilled answer is 0.
Your Task:
Your task is to complete the function combine() which takes 2 arguments(integer n and array of n strings) and returns the maximum length of combined strings possible. If no 2 strings can be combined return 0. 
Expected Time Complexity: O(n).
Expected Auxiliary Space: O(1).
Constraints:
2<=n<=1000
1<=|s_{i}|<=1000, where 0<=i<n
s will only contain {R,B}

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