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Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.The Chef likes to stay in touch with his staff. So, the Chef, the head server, and the sous-chef all carry two-way transceivers so they can ... | Okay, let's see. I need to solve this problem where three people (Chef, head server, sous-chef) have transceivers that can communicate directly if within R meters. If not, but there's a third person acting as a bridge, then they can still communicate. The goal is to check if all three can communicate with each other, p... | [
"**Approach:** Connected Graph Analysis\n\n**Problem:** Given R and three points (Chef, head server, sous-chef), determine if all three can communicate with each other. Communication is direct if the distance between them is <= R. Communication is indirect if there's a third person within R of both.\n\n**Step 1 — C... | [
"**Problem:** Determine if three points in a plane can communicate with each other, given a communication radius R and pairwise distances. Communication can be direct (distance <= R) or indirect (through a single intermediary).\n\n**Problem Type & Trap Profile:** Graph Theory (Connectivity) — Failure to correctly h... | [
"**Problem:** Given three points representing the locations of three communicators, and a communication radius $R$, determine if all three can communicate with each other, either directly or indirectly via a third party.\n\n**Pass 1 — Full Solution Outline:**\nFor each test case, the solution proceeds as follows. F... |
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Frank explained its friend Felman the algorithm of Euclides to calculate the GCD
of two numbers. Then Felman implements it algorithm
int... | Okay, let's tackle this problem. So the task is to compute the GCD of two numbers, A and B. But here's the catch: A is a regular integer (up to 40000), but B can be a very large number with up to 250 digits. The standard Euclidean algorithm uses modulo operations, but when B is that big, we can't compute B mod A direct... | [
"**Approach:** Digit-by-Digit Modulo and Euclidean Algorithm\n\n**Problem:** Given pairs of integers (A, B) where 0 ≤ A ≤ 40000 and A ≤ B < 10^250, compute the greatest common divisor (GCD) of A and B. B is given as a string.\n\n**Step 1 — Read Input and Handle A = 0 Case:** Read the number of test cases and for ea... | [
"**Problem:** Calculate the greatest common divisor (GCD) of two integers, A and B, where A is a standard integer, and B is a very large integer represented as a string.\n\n**Problem Type & Trap Profile:** Number Theory - Integer Overflow / Efficient Modulo Calculation\n\n**Common Mistakes in This Problem Type:**\n... | [
"**Problem:** Given two integers, *A* (up to 40000) and *B* (up to 10<sup>250</sup>), compute their greatest common divisor (GCD). *B* is given as a string.\n\n**Pass 1 — Full Solution Outline:**\nThe solution involves calculating GCD(*A*, *B*) where *B* is represented as a string. First, handle the edge case where... |
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.A Little Elephant from the Zoo of Lviv likes lucky strings, i.e., the strings that consist only of the lucky digits 4 and 7.
The Little Elep... | Okay, I need to solve this problem where I have to find the number of balanced substrings in a given string of 4s and 7s. Let's see what the problem says.
A balanced substring T of length M is one where there's at least one X between 1 and M such that the number of 4s in T[1..X-1] equals the number of 7s in T[X..M]. H... | [
"**Approach:** Prefix Sums and Binary Indexed Tree (Fenwick Tree)\n\n**Problem:** Given a string *S* of length *N* consisting of only the characters '4' and '7', find the number of balanced substrings. A substring *T* is balanced if there exists an index *X* such that the number of '4's in *T*[1..*X*-1] equals the ... | [
"**Problem:** Determine the number of balanced substrings within a given string composed of the characters '4' and '7', where a substring is balanced if there exists a point within the substring such that the number of '4's to the left of that point equals the number of '7's to the right of that point.\n\n**Problem... | [
"**Problem:** Given a string *S* of 4s and 7s, find the number of balanced substrings. A substring is balanced if it can be split into two parts such that the number of 4s in the left part equals the number of 7s in the right part.\n\n**Pass 1 — Full Solution Outline:**\nFor a substring *S*\\[L..R], let *M* = *R* -... |
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Given a string s. Can you make it a palindrome by deleting exactly one character? Note that size of the string after deletion would be one l... | Okay, I need to solve this problem where for each given string, I have to determine if deleting exactly one character can make it a palindrome. The output should be YES or NO for each test case.
Let me think about the approach. So, a palindrome reads the same forwards and backwards. The problem allows deleting exactly... | [
"**Approach:** Two-Pointer with Palindrome Check\n\n**Problem:** Determine if a given string can be made a palindrome by deleting exactly one character. Input is a string `s`. Output is \"YES\" or \"NO\".\n\n**Step 1 — Define Helper Function is_palindrome(s, left, right):**\nCreate a function to check if the substr... | [
"**Problem:** Determine, for each input string, if it can be transformed into a palindrome by deleting exactly one character. Output \"YES\" or \"NO\" for each string.\n\n**Problem Type & Trap Profile:** String manipulation — confusing conditions for palindrome recognition when deleting a character.\n\n**Common Mis... | [
"**Problem:** Determine if a given string can be transformed into a palindrome by deleting exactly one character. The output for each string is YES or NO.\n\n**Pass 1 — Full Solution Outline:**\nFor a given string *s* of length *n*, define a function *is_palindrome(s, left, right)* that checks if the substring from... |
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.An established group of scientists are working on finding solution to NP hard problems. They claim Subset Sum as an NP-hard problem. The pr... | Okay, I need to solve this subset sum problem. Let's think about how to approach it. The problem states that given a set of non-negative integers, determine if there's a subset that sums up to exactly K. Hmm. Since all numbers are non-negative, that might help in optimizing the solution.
The constraints are: T up to 1... | [
"**Approach:** Dynamic Programming with Bitmask Optimization\n\n**Problem:** Given a set of non-negative integers *S* of size *N* and an integer *K* (0 < *K* < 1000), determine if there exists a subset of *S* whose elements sum to exactly *K*.\n\n**Step 1 — Read Input and Check for Direct Solution:**\nRead *N*, *K*... | [
"**Problem:** Given a set of non-negative integers and a target integer *K*, determine if there exists a subset of the given set whose elements sum up to *K*.\n\n**Problem Type & Trap Profile:** Dynamic Programming (Subset Sum) — Inefficient time complexity due to uncontrolled nested loops and/or excessive memory c... | [
"**Problem:** Given a set of non-negative integers, determine if a subset sums exactly to a target value *K*.\n\n**Pass 1 — Full Solution Outline:** For each test case, read *N*, *K*, and the set *S*. First, check if any element in *S* equals *K*; return 1 if true. Filter *S* to retain elements less than or equal t... |
Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.Let's call a string a phone number if it has length 11 and fits the pattern "8xxxxxxxxxx", where each "x" is replaced by a digit.
For examp... | Okay, let's see. The problem is about determining the maximum number of phone numbers we can create from a given set of digit cards. Each phone number has to be exactly 11 digits long, starting with an 8, followed by 10 digits. So the structure is 8 followed by 10 x's.
The input gives us a string of digits. Each digi... | [
"**Approach:** Direct Calculation with Constraints\n\n**Problem:** Given a string of digits, determine the maximum number of 11-digit phone numbers that can be formed, each starting with '8'. Each digit can be used at most once, and a phone number requires one '8' and 10 other digits. Output 0 if no phone numbers c... | [
"**Problem:** Determine the maximum number of 11-digit phone numbers starting with '8' that can be formed from a given set of digit cards, where each card can be used at most once.\n\n**Problem Type & Trap Profile:** Counting & Optimization — overlooking constraints on required '8's and available digit cards, leadi... | [
"**Problem:** Determine the maximum number of 11-digit phone numbers starting with '8' that can be formed from a given string of digits, where each digit is a card used at most once per phone number. Output 0 if no phone numbers can be formed.\n\n**Pass 1 — Full Solution Outline:**\nCount the occurrences of the dig... |
"Generate an executable Python function generated from the given prompt. The function should take st(...TRUNCATED) | "Okay, let's see. I need to solve this problem where for each query with l, r, d, I have to find the(...TRUNCATED) | ["**Approach:** Direct Calculation with Candidate Evaluation\n\n**Problem:** Given *q* queries. For (...TRUNCATED) | ["**Problem:** Given intervals and divisors, find the smallest positive integer that is divisible by(...TRUNCATED) | ["**Problem:** Given queries with integers $l, r, d$, find the smallest positive integer $x$ divisib(...TRUNCATED) |
"Generate an executable Python function generated from the given prompt. The function should take st(...TRUNCATED) | "Okay, I need to solve this problem where given the array s, I have to restore the original permutat(...TRUNCATED) | ["**Approach:** Fenwick Tree with Reverse Iteration\n\n**Problem:** Given an array `s` of length `n`(...TRUNCATED) | ["**Problem:** Given an array `s` where each element represents the sum of elements preceding a posi(...TRUNCATED) | ["**Problem:** Given an array `s`, reconstruct the original permutation `p` where each element `s_i`(...TRUNCATED) |
"Generate an executable Python function generated from the given prompt. The function should take st(...TRUNCATED) | "Okay, let's try to figure out how to solve this problem. So, the task is, given a sequence of integ(...TRUNCATED) | ["**Approach:** Greedy Algorithm with Dynamic Programming Precomputation\n\n**Problem:** Given a seq(...TRUNCATED) | ["**Problem:**\nGiven a sequence of integers and multiple queries, each asking for the element at a (...TRUNCATED) | ["**Problem:** Given a sequence of integers and multiple queries, each asking for the element at a s(...TRUNCATED) |
"Generate an executable Python function generated from the given prompt. The function should take st(...TRUNCATED) | "Okay, let's try to figure out how to solve this problem. The task is to compute the sum of the mini(...TRUNCATED) | ["**Approach:** Fenwick Tree with Coordinate Compression\n\n**Problem:** Given n points with initial(...TRUNCATED) | ["**Problem:** Calculate the sum of the minimum distances between all pairs of moving points, given (...TRUNCATED) | ["**Problem:** Given $n$ points with initial positions $x_i$ and velocities $v_i$, compute the sum o(...TRUNCATED) |
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