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We can use binary search to determine the maximum possible time all computers can run simultaneously. The key observation is that if it's possible to run the computers for t minutes, it's also possible to run them for any time less than t. Similarly, if you cannot run them for t minutes, you cannot for any time greater than t. Here's how we can implement this:
Time Complexity: O(m log(max_time)), where m is the number of batteries.
Space Complexity: O(1), as no extra space proportional to input size is used.
1#include <stdio.h>
2#include <stdbool.h>
3
4bool canRunSimultaneously(long t, long long sum, int n, int* batteries, int
The function maxRunTime implements a binary search to find the maximal possible minutes for which all computers can run simultaneously. The helper function canRunSimultaneously checks if the computers can run for t minutes by distributing available battery time. The binary search tweaks the possible time around the midpoint to find the maximum possible time.
A straightforward approach is sorting the batteries by their available time and then using a greedy method to allocate the longest available running time to any computer that can accommodate it. The goal is to utilize batteries to maximize the running time in descending order until we've depleted either the batteries or optimized distributions.
Time Complexity: O(m log m), because of the sorting step.
Space Complexity: O(1), in-place operations on the battery array.
The solution sorts battery times in descending order using qsort() and then checks where the median division (totalSum divided by n) matches or is exceeded by the battery times. It deducts the unusable surplus battery times from totalSum and decrements n accordingly, distributing the highest possible running time.