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question:In a faraway land, there is a kingdom ruled by an eccentric king who loves puzzles. One day, he challenges his courtiers with the following problem: There are n magic jars aligned in a row, numbered from 1 to n. Each jar i initially contains a_i units of a special elixir. The special property of these jars is that if you perform a spell on them, any two adjacent jars will swap their contents. Each time a spell is cast, you have to choose a pair of adjacent jars and swap their contents. The king will be happy if, after some number of spells, the amount of elixir in every jar becomes a perfect square. He commands you to determine the minimum number of spells required to achieve this. If it is impossible to make all the elixirs in the jars perfect squares, return -1. A number x is a perfect square if there exists an integer y such that x = y^2. Input The first line contains a single integer n (1 ≤ n ≤ 100,000) — the number of magic jars. The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 10^9) — the amount of elixir in the i-th jar. Output If there is no way to make every jar contain a perfect square amount of elixir, print -1. Otherwise, print a single integer x — the minimum number of spells needed to make all the amounts of elixir perfect squares. Examples Input 5 1 4 9 16 25 Output 0 Input 3 2 3 5 Output -1
answer:import math def min_spells_to_perfect_squares(n, elixir_amounts): Returns the minimum number of spells required to make all elixirs in the jars perfect squares. If it's impossible, returns -1. # Helper function to determine if a number is a perfect square def is_perfect_square(x): root = int(math.isqrt(x)) return root * root == x # First, check how many perfect squares are already present perfect_squares = [is_perfect_square(x) for x in elixir_amounts] num_perfect_squares = sum(perfect_squares) # If all jars already contain perfect squares, return 0 if num_perfect_squares == n: return 0 # Otherwise, let's try to find out if we can make all jars perfect squares return -1 # For now, return -1, indicating it's impossible # Example Usage print(min_spells_to_perfect_squares(5, [1, 4, 9, 16, 25])) # Output: 0 print(min_spells_to_perfect_squares(3, [2, 3, 5])) # Output: -1
question:Celia is organizing a company's annual team-building exercise and has a list of n employees, each represented by a unique integer ID ranging from 1 to n. She wants to form pairs of employees such that each pair consists of employees with IDs that sum up to exactly x, a target sum. Write a program that identifies and prints all unique pairs of employee IDs that meet this criterion. A pair (a, b) and (b, a) should be treated as the same and should only be counted once. If no such pairs exist, print "No pairs found". Input The first line contains two integers n (1 ≤ n ≤ 100000) and x (2 ≤ x ≤ 200000) — the number of employees and the target sum, respectively. Output Print all unique pairs of employee IDs that sum up to x. Each pair should be printed on a new line. If no pairs exist, print "No pairs found". Examples Input 6 10 Output 4 6 Example Explanation In this example, IDs range from 1 to 6. The pairs of IDs that sum up to 10 are (4, 6) and (6, 4). We only print (4, 6) as the pair (6, 4) is considered the same. Input 5 7 Output 2 5 3 4 Example Explanation In this example, IDs range from 1 to 5. The pairs of IDs that sum up to 7 are (2, 5) and (3, 4). Input 3 5 Output 2 3 Input 4 9 Output No pairs found Example Explanation In this example, IDs range from 1 to 4. There are no pairs of IDs that sum up to 9.
answer:def find_pairs(n, x): Finds and prints all unique pairs of employee IDs that sum up to x. found_pairs = False for i in range(1, n + 1): j = x - i if i < j <= n: print(i, j) found_pairs = True if not found_pairs: print("No pairs found")
question:You have landed a job as a software engineer at a freight shipping company. Your first task is to write a program that will help load containers onto ships in the most efficient manner. There are multiple containers, each with a certain weight, and a single ship that has a maximum weight capacity. Your goal is to determine the maximum number of containers that can be loaded onto the ship without exceeding its weight capacity. Write a program that takes the number of containers, their respective weights, and the ship's weight capacity as inputs, and outputs the maximum number of containers that can be loaded onto the ship without exceeding the capacity. Input The input is given in the following format: N W w_1 w_2 ... w_N The first line provides the number of containers N (1 leq N leq 100) and the weight capacity of the ship W (1 leq W leq 1000). The second line provides an array of integers w_i (1 leq w_i leq 100), each of which shows the weight of the i-th container. Output Output the maximum number of containers that can be loaded onto the ship without exceeding the maximum weight capacity. Examples Input 5 50 10 20 30 40 50 Output 2 Input 6 75 10 20 30 40 50 60 Output 3 Input 4 100 25 25 25 25 Output 4
answer:def max_containers_loaded(N, W, weights): Determines the maximum number of containers that can be loaded onto a ship without exceeding its weight capacity. Parameters: N (int): The number of containers. W (int): The weight capacity of the ship. weights (list of int): The weights of the containers. Returns: int: The maximum number of containers that can be loaded onto the ship. weights.sort() current_weight = 0 count = 0 for weight in weights: if current_weight + weight <= W: current_weight += weight count += 1 else: break return count
question:You are given an array of integers of length n. Your task is to partition the array into the smallest possible number of contiguous subarrays such that each subarray is sorted in non-decreasing order. Input The first input line contains a single integer n (1 ≤ n ≤ 105) — the length of the array. The second input line contains n space-separated integers ai (1 ≤ ai ≤ 109) — the elements of the array. Output Print a single integer k — the minimum number of contiguous subarrays the array should be partitioned into. Examples Input 5 2 1 3 4 5 Output 2 Input 4 1 3 2 4 Output 2 Note In the first test sample, the array can be partitioned into two subarrays [2, 1] and [3, 4, 5], each of which is sorted in non-decreasing order. In the second test sample, the array can be partitioned into two subarrays [1, 3] and [2, 4], each of which is sorted in non-decreasing order.
answer:def min_sorted_subarrays(arr): Returns the minimum number of contiguous subarrays that the input array can be partitioned into such that each subarray is sorted in non-decreasing order. if not arr: return 0 subarrays_count = 1 for i in range(1, len(arr)): if arr[i] < arr[i - 1]: subarrays_count += 1 return subarrays_count