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question:In a distant world, there exist mystical trees known as Leafaltrons. Each Leafaltron has a certain number of leaves, and their health is determined by the energy level of these leaves, which is some positive integer. When a Leafaltron loses a leaf, its overall health decreases proportionally to the energy of that leaf. During the annual celebration, Leafaltrons from different regions gather to exchange leaves. The exchange of leaves between two Leafaltrons of the same region follows certain rules: - A Leafaltron with more leaf energy will lose a leaf to a Leafaltron with less or equal leaf energy from the same region. - The process continues until no more leaves can be exchanged between two Leafaltrons from the same region. Each Leafaltron can be represented by a tuple (R, E), where R signifies the region and E represents the total energy of its leaves. For example, a Leafaltron with 50 units of energy in region 1 can be represented as (1, 50). The celebration aims for a perfect exchange cycle, meaning after the exchanges, every Leafaltron within a region should ideally acquire leaves such that their energy levels are as equal as possible. Your task is to determine the final health status of each Leafaltron after the exchanges. ----Input---- The first line of the input contains an integer T, the number of test cases. T test cases follow. Each test case starts with an integer N, the number of Leafaltrons participating in the celebration. Each of the next N lines contains two space-separated integers Ri and Ei, denoting the region and the initial leaf energy of the ith Leafaltron. ----Output---- For each test case, output the final energy levels of Leafaltrons after the leaf exchanges in each region, sorted by the initial order of input. ----Constraints---- - Each integer in the input file is positive and does not exceed 100. - 1 ≤ T ≤ 100 - 1 ≤ N ≤ 100 - 1 ≤ Ri, Ei ≤ 100 ----Example---- Input: 2 3 1 30 1 50 1 10 4 2 25 2 75 3 20 3 30 Output: 30 30 30 25 75 25 25 Explanation: Case 1: - Initial Leafaltrons: (1, 30), (1, 50), (1, 10) - After exchanges within region 1: - (30, 50) exchange leaves once since 50 > 30, resulting in (40, 40) - (10, 40) exchange leaves once since 40 > 10, resulting in (20, 30) - Continue the process to achieve as equal energy levels as possible, resulting in (30, 30, 30) Case 2: - Initial Leafaltrons: (2, 25), (2, 75) - After exchanges within region 2: - Since 75 > 25, exchange results in (50, 50) - Initial Leafaltrons: (3, 20), (3, 30) - After exchanges within region 3: - Since 30 > 20, exchange results in (25, 25) Thus the final energies are outputted in the initial input sequence order.
answer:def leafaltron_exchanges(T, test_cases): This function takes in the number of test cases T and the test cases as input, and returns the final energy levels of Leafaltrons after the leaf exchanges in each region. result = [] for i in range(T): N = test_cases[i][0] leafaltrons = test_cases[i][1] regions = {} for region, energy in leafaltrons: if region not in regions: regions[region] = [] regions[region].append(energy) final_energies = [] for region, energies in regions.items(): total_energy = sum(energies) num_leafaltrons = len(energies) average_energy = total_energy // num_leafaltrons remainder = total_energy % num_leafaltrons balanced_energies = [average_energy] * num_leafaltrons for j in range(remainder): balanced_energies[j] += 1 regions[region] = sorted(balanced_energies) for region, energy in leafaltrons: final_energies.append(regions[region].pop(0)) result.append(final_energies) return result
question:Two friends, Alice and Bob, like to play a game involving sequences of numbers. They take turns in picking a number from the sequence such that Alice always picks the largest remaining even number, and Bob always picks the largest remaining odd number. If the required type of number is not available (i.e., Alice needs to pick an even number but none are left, or Bob needs to pick an odd number but none are left), then the game stops. The player who cannot make a move loses the game. Given a sequence of integers, determine the winner assuming Alice always goes first. -----Input----- The first line contains an integer N, the length of the sequence (1 ≤ N ≤ 500). The second line contains N integers separated by space - the elements of the sequence. Each integer in the sequence is in the range -10^7 to 10^7. -----Output----- Output "ALICE" if Alice wins the game, "BOB" if Bob wins the game, and "TIE" if neither can make a move from the start. -----Example----- Input: 6 1 2 3 5 7 8 Output: BOB Explanation: Initially, the sequence is [1, 2, 3, 5, 7, 8]. Alice starts and picks the largest even number: 8. Sequence now: [1, 2, 3, 5, 7]. Bob picks the largest odd number: 7. Sequence now: [1, 2, 3, 5]. Alice picks the largest even number: 2. Sequence now: [1, 3, 5]. Bob picks the largest odd number: 5. Sequence now: [1, 3]. Alice can no longer pick an even number since none are left. Bob wins. Note that if no even numbers were in the sequence from the beginning, Alice could never make a move and "BOB" would be the output since Alice would lose immediately. Similarly, if no odd numbers were present, "ALICE" would be the output since Bob could not move. If the sequence started as empty (N = 0), output "TIE".
answer:def determine_winner(sequence): Determines the winner of the game where Alice picks the largest remaining even number and Bob picks the largest remaining odd number. Parameters: sequence (list): List of integers representing the sequence. Returns: str: "ALICE" if Alice wins, "BOB" if Bob wins, "TIE" if neither can make a move from the start. evens = sorted([num for num in sequence if num % 2 == 0], reverse=True) odds = sorted([num for num in sequence if num % 2 != 0], reverse=True) turn = 'ALICE' while True: if turn == 'ALICE': if evens: evens.pop(0) else: return 'BOB' turn = 'BOB' else: if odds: odds.pop(0) else: return 'ALICE' turn = 'ALICE' # Examples for verification print(determine_winner([1, 2, 3, 5, 7, 8])) # Output: "BOB" print(determine_winner([2, 4, 6])) # Output: "ALICE" print(determine_winner([1, 3, 5])) # Output: "BOB" print(determine_winner([1, 2, 3, 4, 5, 6])) # Output: "BOB" print(determine_winner([1])) # Output: "BOB"
question:In this task, you need to write a function that takes a list of integers and returns the maximum sum of any non-empty contiguous subarray within the list. This is a common problem in computer science, known as the Maximum Subarray Problem or Kandane’s Algorithm. You are given an integer array `nums`. Find the contiguous subarray (containing at least one number) which has the largest sum and return its sum. # Example ```python # Example 1: # Input: nums = [-2,1,-3,4,-1,2,1,-5,4] # Output: 6 # Explanation: [4,-1,2,1] has the largest sum = 6. # Example 2: # Input: nums = [1] # Output: 1 # Explanation: [1] has the largest sum = 1. # Example 3: # Input: nums = [5,4,-1,7,8] # Output: 23 # Explanation: [5,4,-1,7,8] has the largest sum = 23. ``` # Constraints - 1 <= nums.length <= 10^4 - -10^5 <= nums[i] <= 10^5 # Instructions 1. Define a function `max_subarray_sum(nums: List[int]) -> int`. 2. The function should take a list of integers as input. 3. It should return an integer, which is the maximum sum of any contiguous subarray within the input list. 4. Ensure that your solution is optimized to handle the upper limit of the input constraints efficiently.
answer:from typing import List def max_subarray_sum(nums: List[int]) -> int: Returns the maximum sum of any non-empty contiguous subarray within the list nums. This is solved using Kadane's Algorithm. max_current = max_global = nums[0] for num in nums[1:]: max_current = max(num, max_current + num) if max_current > max_global: max_global = max_current return max_global
question:Chef has been working hard calculating various operations manually. To take a break, he decided to create a simpler, yet interesting task for fellow coders. Chef wants to find out the sum of all even digits present in a given natural number. -----Input:----- - The first line will contain T, the number of test cases. Then the test cases follow. - Each test case contains a single line of input, a natural number N. -----Output:----- For each test case, output a single line with the sum of all even digits in N. If there are no even digits, output 0. -----Constraints----- - 1 leq T leq 10^6 - 1 leq N leq 10^{18} -----Sample Input:----- 3 123456 24680 13579 -----Sample Output:----- 12 20 0 -----EXPLANATION:----- For 1) The even digits in 123456 are 2, 4, and 6, and their sum is 12. For 2) All digits in 24680 are even, and their sum is 2 + 4 + 6 + 8 + 0 = 20. For 3) There are no even digits in 13579, so the output is 0.
answer:def sum_of_even_digits(N): Returns the sum of all even digits in the given natural number N. even_digits_sum = 0 for digit in str(N): if int(digit) % 2 == 0: even_digits_sum += int(digit) return even_digits_sum def process_test_cases(T, test_cases): For each test case, return the sum of all even digits of the given natural number. results = [] for i in range(T): N = test_cases[i] results.append(sum_of_even_digits(N)) return results