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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.
1public class Solution {
2 public long MaxRunTime(int n, int[] batteries) {
3 long totalSum = 0;
4 foreach (var battery in batteries) {
5 totalSum += battery;
6 }
7 long left = 0, right = totalSum / n;
8 while (left < right) {
9 long mid = right - (right - left) / 2;
10 if (CanRunSimultaneously(mid, batteries, n)) {
11 left = mid;
12 } else {
13 right = mid - 1;
}
}
return left;
}
private bool CanRunSimultaneously(long t, int[] batteries, int n) {
long timeSum = 0;
foreach (var battery in batteries) {
timeSum += Math.Min(battery, t);
}
return timeSum >= t * n;
}
}The C# implementation of binary search operates similarly to its Java counterpart. It computes the total capacity of batteries and checks feasibility with CanRunSimultaneously() method using a straightforward array operation and mathematical functions.
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.
In this Python approach, the batteries are sorted in decreasing order. The objective is to evenly distribute the total sum of battery runtimes. The while loop readjusts totalSum and active n as necessary, observing whether the divided times exceed the runtime of sorted battery values at each iteration.