chat

🔍

question:Skye is a landscape architect, and she loves using pebbles of various weights to create miniature landscapes. She has a collection of pebbles with different weights and wants to create a balanced landscape by dividing her pebbles into two groups such that the weight difference between the two groups is minimized. Skye needs your help to determine the minimum possible weight difference between the two groups. You are given an array of integers representing the weights of the pebbles. # Input The first line contains an integer `n` (1 ≤ n ≤ 100) — the number of pebbles. The second line contains `n` integers `w1, w2, ..., wn` (1 ≤ wi ≤ 1000) — the weights of the pebbles. # Output Print a single integer — the minimum possible weight difference between the two groups. # Example Input ``` 5 3 1 4 2 2 ``` Output ``` 0 ``` Explanation One possible way to split the pebbles is into two groups: {3, 4} and {1, 2, 2}. The sum of the first group is 7 and the sum of the second group is also 7. The weight difference is |7 - 7| = 0, which is the minimal possible difference. Note: - In the first example, one possible way to split the pebbles is into two groups: {1, 3} and {1, 2}. The sum for these groups is the same, thus the minimum difference is 0.

answer:def minimum_weight_difference(n, weights): total_weight = sum(weights) dp = [0] * (total_weight // 2 + 1) for weight in weights: for j in range(total_weight // 2, weight - 1, -1): dp[j] = max(dp[j], dp[j - weight] + weight) return total_weight - 2 * dp[total_weight // 2] def main(): import sys input = sys.stdin.read data = input().split() n = int(data[0]) weights = list(map(int, data[1:n + 1])) print(minimum_weight_difference(n, weights)) if __name__ == '__main__': main()

question:Alice and Bob are playing a game with two arrays. Alice is given an array of integers **A** and Bob is given an array of integers **B**. The goal of the game is to find an array **C**, consisting of the pairwise maximums of corresponding elements from **A** and **B**. The pairwise maximums of two arrays **A** and **B** is defined as: C_i = max(A_i, B_i) for every valid index i. Given the arrays **A** and **B**, your task is to help Alice and Bob find the resulting array **C**. # Input - The first line contains a single integer n (1 leq n leq 10^5) — the number of elements in the arrays. - The second line contains n integers A_1, A_2, ldots, A_n (1 leq A_i leq 10^9) — the elements of array **A**. - The third line contains n integers B_1, B_2, ldots, B_n (1 leq B_i leq 10^9) — the elements of array **B**. # Output - Output a single line containing n integers — the elements of resulting array **C**. # Example Input ``` 5 1 4 3 2 5 3 2 5 1 4 ``` Output ``` 3 4 5 2 5 ``` Explanation - For the 1st element: max(1, 3) = 3 - For the 2nd element: max(4, 2) = 4 - For the 3rd element: max(3, 5) = 5 - For the 4th element: max(2, 1) = 2 - For the 5th element: max(5, 4) = 5 In summary, the resulting array **C** will be: `[3, 4, 5, 2, 5]`.

answer:def find_pairwise_maximums(A, B): Given two arrays A and B of the same length, computes the array C where each element is the maximum of the corresponding elements in A and B. Parameters: A (list of int): First list of integers. B (list of int): Second list of integers. Returns: list of int: List containing the pairwise maxima of A and B. return [max(a, b) for a, b in zip(A, B)]

question:Maria enjoys working with numbers. Recently she came across an interesting problem involving consecutive sums. She wants to find a subarray with the highest possible sum in a given list of integers. However, instead of a regular subarray, she is interested in finding a subarray where the sum of the squares of the integers is minimized. The problem can be formulated as follows: Given an array of integers, find the subarray for which the sum of the squares of the integers in that subarray is the minimum while maintaining the highest possible sum of elements within that subarray. # Input - The first line contains a single integer `n` (1 leq n leq 10^5), the number of integers in the array. - The second line contains `n` space-separated integers, the elements of the array, where each integer is between `-10^4` and `10^4`. # Output - One integer which is the highest possible sum of the subarray meeting the minimum sum of squares condition. # Example Input 1: ``` 5 2 -1 3 -2 4 ``` Output 1: ``` 6 ``` Explanation: - The possible subarrays are: [2], [-1], [3], [-2], [4], [2, -1], [-1, 3], [3, -2], [-2, 4], [2, -1, 3], [-1, 3, -2], [3, -2, 4], [2, -1, 3, -2], [-1, 3, -2, 4], [2, -1, 3, -2, 4] - The subarray with the highest sum while maintaining the minimum sum of squares is [2, -1, 3, -2, 4], with a sum of 6 and sum of squares equal to 30. Input 2: ``` 4 -1 -2 -3 -4 ``` Output 2: ``` -1 ``` Explanation: - The possible subarrays are: [-1], [-2], [-3], [-4], [-1, -2], [-2, -3], [-3, -4], [-1, -2, -3], [-2, -3, -4], [-1, -2, -3, -4] - The subarray with the highest sum while maintaining the minimum sum of squares is [-1], with a sum of -1 and sum of squares equal to 1. Make sure to consider the edge cases and optimal solutions for large input sizes.

answer:def max_subarray_with_min_sum_squares(arr): n = len(arr) if n == 0: return 0 max_sum = float('-inf') current_sum = 0 for i in range(n): current_sum = 0 for j in range(i, n): current_sum += arr[j] if current_sum > max_sum: max_sum = current_sum return max_sum

question:Given a string s, you are tasked to find the longest subsequence which is also a palindrome. Recall that a subsequence is derived from another sequence by deleting some or no elements without changing the order of the remaining elements. You need to implement a function that takes a string as input and returns the length of the longest palindromic subsequence. # Input - The input consists of a single string s of length n (1 leq n leq 1000), containing only lowercase English letters. # Output - Output the length of the longest palindromic subsequence in the given string s. # Example - Input: "bbabcbcab" - Output: 7 # Explanation For the given example, the longest palindromic subsequence is "babcbab", which has a length of 7.

answer:def longest_palindromic_subsequence(s): n = len(s) # Create a DP table to store results of subproblems dp = [[0 for _ in range(n)] for _ in range(n)] # Strings of length 1 are palindromes of length 1 for i in range(n): dp[i][i] = 1 # Build the table. The outer loop is for substrings of length cl. for cl in range(2, n + 1): for i in range(n - cl + 1): j = i + cl - 1 if s[i] == s[j] and cl == 2: dp[i][j] = 2 elif s[i] == s[j]: dp[i][j] = dp[i + 1][j - 1] + 2 else: dp[i][j] = max(dp[i][j - 1], dp[i + 1][j]) # The length of the longest palindromic subseq will be in dp[0][n-1] return dp[0][n-1]