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question:There are n workers in a factory that produce widgets. Each worker i has a specific rate ri (widgets per hour). The factory operates for precisely T hours each day, and every worker is given exactly one machine to use. However, to maximize the efficiency of production, workers may swap machines with each other exactly once if they choose to do so. After one swap, their widget production rate will remain the same, as will the machines they were originally using. Determine the maximum number of widgets produced by the end of the day if workers can make at most one machine swap. Input The first line of input contains two integers n and T (1 ≤ n ≤ 105, 1 ≤ T ≤ 109). The second line contains n space-separated integers representing the widget production rate of each worker r1, r2, ..., rn (1 ≤ ri ≤ 109). Output Print a single integer — the maximum number of widgets that can be produced by all workers in one day after at most one swap. Examples Input 3 10 5 3 8 Output 160 Input 4 5 2 8 3 7 Output 100 Note In the first sample test: * Total widgets produced without swap: 5*10 + 3*10 + 8*10 = 160 * Maximum production as no beneficial swap is possible. In the second sample test: * Total widgets produced without swap: 2*5 + 8*5 + 3*5 + 7*5 = 100 * Swapping won't change the total as well, so maximum remains 100.
answer:def max_widgets_produced(n, T, rates): Calculate the maximum widgets produced by all workers in one day given at most one swap of machines. Parameters: n (int): Number of workers T (int): Number of hours the factory operates per day rates (list): List of widget production rate per hour for each worker Returns: int: Maximum number of widgets produced # Initial production without any swap total_production = sum(rates) * T return total_production
question:You are given two arrays of integers, `A` and `B`, both of length `n`. You want to merge them into a single sorted array `C` of length `2n`. The challenge is to perform this merge step with the least amount of memory usage and without using any built-in sort function. Input The first line contains an integer `n` (1 ≤ n ≤ 10^5) — the length of arrays `A` and `B`. The second line contains `n` integers — the elements of array `A` (0 ≤ A[i] ≤ 10^9). The third line contains `n` integers — the elements of array `B` (0 ≤ B[i] ≤ 10^9). Output Output a single line containing `2n` integers — the elements of the merged array `C` in non-decreasing order. Examples Input 5 1 3 5 7 9 2 4 6 8 10 Output 1 2 3 4 5 6 7 8 9 10 Input 3 10 20 30 15 25 35 Output 10 15 20 25 30 35 Note In the first example, the arrays can be merged directly into a sorted array by comparing and inserting elements in ascending order. In the second example, arrays `A` and `B` can also be merged step by step by comparing the next smallest elements of both arrays and keeping the order sorted.
answer:def merge_sorted_arrays(A, B): Merges two sorted arrays A and B into a single sorted array C. n = len(A) C = [] i, j = 0, 0 # Merge arrays A and B while i < n and j < n: if A[i] <= B[j]: C.append(A[i]) i += 1 else: C.append(B[j]) j += 1 # If there are remaining elements in A while i < n: C.append(A[i]) i += 1 # If there are remaining elements in B while j < n: C.append(B[j]) j += 1 return C
question:You are assisting a factory in managing their inventory of raw materials for manufacturing products. Each raw material is stored in a different shipment and has a unique quantity recorded. The factory aims to maximize the utilization of raw materials while minimizing the leftover waste. Due to warehouse constraints, the factory can only keep track of a limited number of shipments with the most substantial quantities at any given time. Hence, you must design a system that, given a list of shipments and a limit on the number of shipments they can store, maintains the top `K` largest quantities from the list. When a new shipment arrives, it should be added to the inventory while maintaining the total number of shipments tracked to `K`. If adding the new shipment exceeds `K`, the shipment with the smallest quantity among the current K shipments should be discarded to ensure the inventory size remains `K`. Input The first line contains integer T representing the number of test cases. Each test case consists of two parts: 1. The first line of each test case contains two space-separated integers `N` (the total number of shipments) and `K` (the number of largest shipments to keep track of). 2. The second line contains `N` space-separated integers representing the quantities of the shipments. Output For each test case, output a single line containing K space-separated integers in descending order representing the top K quantities maintained in the factory's inventory. Constraints 1 ≤ T ≤ 100 1 ≤ N ≤ 100000 1 ≤ K ≤ N 1 ≤ Quantity of each shipment ≤ 1000000 Example Input: 1 8 3 10 20 30 40 50 60 70 80 Output: 80 70 60
answer:import heapq def manage_shipments(T, cases): results = [] for case in cases: N, K, shipments = case if K >= N: results.append(sorted(shipments, reverse=True)[:K]) else: largest_shipments = [] for quantity in shipments: if len(largest_shipments) < K: heapq.heappush(largest_shipments, quantity) elif quantity > largest_shipments[0]: heapq.heappushpop(largest_shipments, quantity) results.append(sorted(largest_shipments, reverse=True)) return results def parse_input(input_str): lines = input_str.strip().split("n") T = int(lines[0]) cases = [] index = 1 for _ in range(T): N, K = map(int, lines[index].split()) shipments = list(map(int, lines[index + 1].split())) cases.append((N, K, shipments)) index += 2 return T, cases def format_output(results): output_lines = [] for result in results: output_lines.append(" ".join(map(str, result))) return "n".join(output_lines)
question:Problem Alice has a collection of marbles arranged in a row. Each marble has a color represented by a lowercase letter, so the sequence of marbles can be described by a string. The goal is to determine the largest number of marbles that can be consecutively removed from the collection if each move consists of removing a contiguous substring of the same colored marbles. You can perform as many moves as you want, but you must maximize the total number of marbles removed in a single move. Write a program to find the maximum number of consecutive marbles that can be removed in a single move and output this number. Constraints The input satisfies the following conditions. * The length of the string 1 leq len(S) leq 10^5 * The string S consists of lowercase English letters only. Input The input is given as a single string S, which represents the sequence of marbles' colors. Output The output should be a single integer, representing the maximum number of consecutive marbles that can be removed in a single move. Examples Input abccbaabccba Output 2 Input aabbbcccc Output 4 Input xyz Output 1 Input aaabbbaaa Output 3
answer:def max_consecutive_marbles(s): Returns the maximum number of consecutive marbles of the same color that can be removed in a single move. max_count = 1 current_count = 1 for i in range(1, len(s)): if s[i] == s[i - 1]: current_count += 1 max_count = max(max_count, current_count) else: current_count = 1 return max_count