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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.
1function maxRunTime(n, batteries) {
2 let totalSum = batteries.reduce((a, b) => a + b, 0);
3 let left
This JavaScript solution takes advantage of high-order functions like reduce() for computations on the battery array. It implements the binary search process inside the function maxRunTime with a nested feasibility function.
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.
This Java method sorts the array using Arrays.sort() and calculates the totalSum similarly to adjust which batteries contribute directly towards effective run time by trimming down the excess use of potential runtime that's inefficient. It finds the maximal and optimal running time spread across n computers.