[2141. Maximum Running Time of N Computers](https://leetcode.com/problems/maximum-running-time-of-n-computers/)

### 題目描述

You have `n` computers. You are given the integer `n` and a **0-indexed** integer array `batteries` where the i^th^ battery can **run** a computer for `batteries[i]` minutes. You are interested in running **all** `n` computers **simultaneously** using the given batteries.

Initially, you can insert **at most one battery** into each computer. After that and at any integer time moment, you can remove a battery from a computer and insert another battery **any number of times**. The inserted battery can be a totally new battery or a battery from another computer. You may assume that the removing and inserting processes take no time.

Note that the batteries cannot be recharged.

Return *the **maximum** number of minutes you can run all the n computers simultaneously.*

### 範例

**Example 1:**


Input: n = 2, batteries = [3,3,3]
Output: 4
Explanation: 
Initially, insert battery 0 into the first computer and battery 1 into the second computer.
After two minutes, remove battery 1 from the second computer and insert battery 2 instead. Note that battery 1 can still run for one minute.
At the end of the third minute, battery 0 is drained, and you need to remove it from the first computer and insert battery 1 instead.
By the end of the fourth minute, battery 1 is also drained, and the first computer is no longer running.
We can run the two computers simultaneously for at most 4 minutes, so we return 4.

**Example 2:**


Input: n = 2, batteries = [1,1,1,1]
Output: 2
Explanation: 
Initially, insert battery 0 into the first computer and battery 2 into the second computer. 
After one minute, battery 0 and battery 2 are drained so you need to remove them and insert battery 1 into the first computer and battery 3 into the second computer. 
After another minute, battery 1 and battery 3 are also drained so the first and second computers are no longer running.
We can run the two computers simultaneously for at most 2 minutes, so we return 2.

**Constraints**:

* 1 <= `n` <= `batteries.length` <= 10^5^
* 1 <= `batteries[i]` <= 10^9^

### 解答
#### C++

using LL = long long;

class Solution {
public:
    LL maxRunTime(int n, vector<int>& batteries) {
        LL powerSum = 0;
        for (int b : batteries) {
            powerSum += b;
        }

        LL left = 1, right = powerSum / n + 1;
        while (left < right) {
            LL mid = left + (right - left) / 2;
            if (canRunSimultaneously(n, batteries, mid)) {
                left = mid + 1;
            } else {
                right = mid;
            }
        }
        return left - 1;
    }

    bool canRunSimultaneously(int n, vector<int>& batteries, LL timeLimit) {
        LL remainingPowerSum = 0;
        for (int b : batteries) {
            remainingPowerSum += min((LL) b, timeLimit);
        }
        return remainingPowerSum >= timeLimit * n;
    }
};

> [name=Jerry Wu][time=27 July, 2023]

### Reference

[回到題目列表](https://hackmd.io/@Marsgoat/leetcode_every_day)