LeetCode【410】 Split Array Largest Sum

最新推荐文章于 2020-10-16 12:34:20 发布

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#leetcode #算法

本文介绍了一种使用二分查找算法解决将数组分成m个连续子数组并使这些子数组的最大和最小化的问题的方法。该算法首先确定了可能的解的空间范围，并通过迭代缩小这个范围来寻找最终解。

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

下面是用二分查找的方法。

class Solution {
public:

    bool canSplit(vector<int>& nums, int m, long long sum) {
        int c = 1;
        long long s = 0;
        for (auto& num : nums) {
            s += num;
            if (s > sum) {
                s = num;
                ++c;
            }
        }
        return c <= m;
    }

    int splitArray(vector<int>& nums, int m) {
        long long left = 0, right = 0;
        for (auto& num : nums) {
            left = max(left, (long long)num);
            right += num;
        }
        while (left <= right) {
            long long mid = left + (right-left)/2;
            if (canSplit(nums, m, mid))
                right = mid-1;
            else
                left = mid+1;
        }
        return left;
    }
};