Given an array which consists of non-negative integers and an integer m, you can split the array into m non-empty continuous subarrays. Write an algorithm to minimize the largest sum among these m subarrays.
**Note:**If n is the length of array, assume the following constraints are satisfied:
- 1 ≤ n ≤ 1000
- 1 ≤ m ≤ min(50, n)
Examples:
Input:
nums = [7,2,5,10,8]
m = 2
Output:
18
Explanation:
There are four ways to split nums into two subarrays.
The best way is to split it into [7,2,5] and [10,8],
where the largest sum among the two subarrays is only 18.
给定一个非负整数数组和一个整数 m，你需要将这个数组分成 m 个非空的连续子数组。设计一个算法使得这 m 个子数组各自和的最大值最小。
注意: 数组长度 n 满足以下条件:
- 1 ≤ n ≤ 1000
- 1 ≤ m ≤ min(50, n)
- 给出一个数组和分割的个数 M。要求把数组分成 M 个子数组，输出子数组和的最大值。
- 这一题可以用动态规划 DP 解答，也可以用二分搜索来解答。这一题是二分搜索里面的 max-min 最大最小值问题。题目可以转化为在
M次划分中，求一个x，使得x满足：对任意的S(i)，都满足S(i) ≤ x。这个条件保证了x是所有S(i)中的最大值。要求的是满足该条件的最小的x。x的搜索范围在[max, sum]中。逐步二分逼近 low 值，直到找到能满足条件的 low 的最小值，即为最终答案。