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question:You are given an array of N integers. Your goal is to minimize the sum of the absolute differences of each pair of adjacent elements in the array by performing a certain type of operation. The allowed operation is to increment or decrement any element of the array by 1 at a cost of 1 coin per operation. You need to calculate the minimal cost required to reach this objective. -----Input----- The first line of the input contains an integer N denoting the number of elements in the given array. The second line contains N space-separated integers A1, A2, ..., AN denoting the given array. -----Output----- For each test case, output a single line containing the minimal cost required to minimize the sum of the absolute differences of each pair of adjacent elements in the array. -----Constraints----- - 2 ≤ N ≤ 105 - -109 ≤ Ai ≤ 109 -----Example----- Input: 4 1 3 2 -2 Output: 2 -----Explanation----- Example case 1: - Increment the second element from 3 to 2, so the array becomes [1, 2, 2, -2] with a cost of 1. - Increment the fourth element from -2 to -1, so the array becomes [1, 2, 2, -1] with another cost of 1. Now, the sum of absolute differences is minimized with a total cost of 2 coins.
answer:def minimal_cost_to_minimize_abs_diff(N, A): Calculates the minimal cost required to minimize the sum of the absolute differences of each pair of adjacent elements in the array. median_A = sorted(A)[N // 2] cost = sum(abs(x - median_A) for x in A) return cost
question:Riya loves reading books and she has N books in her library. Each book has a specific height. She wants to arrange them in a vertical stack such that the heights of the books in the stack do not form an increasing sequence when viewed from the bottom to the top. She can pick any book from the library and place it on top of the stack. Find the maximum height of the stack she can achieve. -------Input:------- - First line will contain T, number of test cases. Then the test cases follow. - Each test case contains two lines of input. - The first line has one integer N, the number of books. - The second line contains N space-separated integers denoting the heights of the books. -------Output:------- For each test case, output the maximum height of the stack in a single line. -------Constraints------- - 1 leq T leq 10 - 1 leq N leq 10^5 - 1 leq height leq 10^9 -------Sample Input:------- 2 5 3 1 4 1 5 4 5 4 3 2 -------Sample Output:------- 6 14
answer:def max_stack_height(T, test_cases): results = [] for i in range(T): N = test_cases[i][0] heights = test_cases[i][1] # Sort the books in descending order heights.sort(reverse=True) # Calculate the sum of heights max_height = sum(heights) results.append(max_height) return results # Example usage: # T = 2 # test_cases = [ # (5, [3, 1, 4, 1, 5]), # (4, [5, 4, 3, 2]) # ] # print(max_stack_height(T, test_cases)) # Output should be: [14, 14]
question:It is high summer, and you have a series of reservoirs connected in a network. Each reservoir has a certain amount of water in it. Your task is to help the municipality manage the water distribution in a way that maximizes the minimum amount of water across all reservoirs. Each reservoir can either give water to its connected reservoirs or receive water from them, and it can be connected to more than one reservoir. The water transfer between connected reservoirs is done one unit at a time. Create an algorithm to determine the maximum possible amount of water that the reservoir with the least water can hold by the end of the redistribution process. Input Format: - The first line contains an integer T, the number of test cases. - The first line of each test case contains an integer N, the number of reservoirs. - The second line contains N integers denoting the amount of water in each reservoir. - The third line contains an integer M, the number of direct connections between the reservoirs. - The next M lines each contain two integers u and v, that indicate a bidirectional connection between reservoir u and reservoir v (1-based index). Output Format: For each test case, print the maximum possible amount of water in the reservoir with the least water by the end of the redistribution process. Constraints: - 1 ≤ T ≤ 5 - 1 ≤ N ≤ 1000 - 0 ≤ M ≤ 5000 - 0 ≤ Amount of water in each reservoir ≤ 1000 Example Input: 2 3 3 6 9 2 1 2 2 3 4 5 5 5 5 3 1 2 2 3 3 4 Example Output: 6 5 Explanation: In the first test case, the reservoirs and their connections can be visualized as a graph. The trick is to balance the water among connected nodes until no more water can be transferred or all are equalized. In the second test case, since all reservoirs have the same amount of water initially and are connected equally, the output remains the same.
answer:def maximize_min_water(T, test_cases): def dfs(node, graph, visited): connected_component = [] stack = [node] while stack: current = stack.pop() if not visited[current]: visited[current] = True connected_component.append(current) for neighbor in graph[current]: if not visited[neighbor]: stack.append(neighbor) return connected_component results = [] for i in range(T): N = test_cases[i]['N'] waters = test_cases[i]['waters'] M = test_cases[i]['M'] connections = test_cases[i]['connections'] graph = {x: [] for x in range(N)} for u, v in connections: graph[u-1].append(v-1) graph[v-1].append(u-1) visited = [False] * N max_min_water = 0 for reservoir in range(N): if not visited[reservoir]: connected_component = dfs(reservoir, graph, visited) total_water = sum(waters[j] for j in connected_component) max_min_water = max(max_min_water, total_water // len(connected_component)) results.append(max_min_water) return results def parse_input(input_str): input_list = input_str.strip().split("n") T = int(input_list[0]) index = 1 test_cases = [] for _ in range(T): N = int(input_list[index]) waters = list(map(int, input_list[index + 1].split())) M = int(input_list[index + 2]) connections = [] for j in range(M): u, v = map(int, input_list[index + 3 + j].split()) connections.append((u, v)) test_cases.append({ "N": N, "waters": waters, "M": M, "connections": connections }) index += 3 + M return T, test_cases def format_output(output): return "n".join(map(str, output))
question:A student is trying to identify the longest palindromic subsequence within a given string. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. A palindrome is a sequence that reads the same backward and forward. Help the student by writing a function that takes a string s as input and returns the length of the longest palindromic subsequence in s. Input The input consists of a single line containing a string s (1 ≤ |s| ≤ 100), which contains only lowercase English letters. Output Output the length of the longest palindromic subsequence of the given string. Examples Input bbbab Output 4 Input cbbd Output 2 Input abcdef Output 1
answer:def longest_palindromic_subsequence(s): n = len(s) # Create a 2D array to store lengths of longest palindromic subsequence dp = [[0] * n for _ in range(n)] # Every single character is a palindrome of length 1 for i in range(n): dp[i][i] = 1 # Build the table for length in range(2, n + 1): # length of the substring for i in range(n - length + 1): j = i + length - 1 if s[i] == s[j] and length == 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 + 1][j], dp[i][j - 1]) # dp[0][n-1] contains the length of the longest palindromic subsequence return dp[0][n-1]