1031. Maximum Sum of Two Non-Overlapping Subarrays

Posted 2021-03-05 北叶青藤

Given an array A of non-negative integers, return the maximum sum of elements in two non-overlapping (contiguous) subarrays, which have lengths L and M.  (For clarification, the L-length subarray could occur before or after the M-length subarray.)

Formally, return the largest V for which V = (A[i] + A[i+1] + ... + A[i+L-1]) + (A[j] + A[j+1] + ... + A[j+M-1]) and either:

• 0 <= i < i + L - 1 < j < j + M - 1 < A.length, or
• 0 <= j < j + M - 1 < i < i + L - 1 < A.length.

Example 1:

Input: A = [0,6,5,2,2,5,1,9,4], L = 1, M = 2
Output: 20
Explanation: One choice of subarrays is [9] with length 1, and [6,5] with length 2.

Example 2:

Input: A = [3,8,1,3,2,1,8,9,0], L = 3, M = 2
Output: 29
Explanation: One choice of subarrays is [3,8,1] with length 3, and [8,9] with length 2.

Example 3:

Input: A = [2,1,5,6,0,9,5,0,3,8], L = 4, M = 3
Output: 31
Explanation: One choice of subarrays is [5,6,0,9] with length 4, and [3,8] with length 3.

分析：
https://xingxingpark.com/Leetcode-1031-Maximum-Sum-of-Two-Non-Overlapping-Subarrays/

动态规划

凡是要求数组某一段的和，要想到用pre_sum，pre_sum[i]表示指数i之前左右数的和。 这样我们要求A[i]到A[j]之间所有数的和，
就可以用pre_sum[j] - pre_sum[i - 1] 回到这道题，我们第一遍遍历数组A求pre_sum。 第二遍遍历，指数为i，
用max_L记录指数i - M之前的最大连续L个数之和， 每次更新
max_L为max(max_L, pre_sum[i - M] - pre_sum[i - L - M]) max_L + pre_sum[i] - pre_sum[i - M]
表示以i结尾最后连续M个数，与之前最大的连续L个数的和。 同理max_M + pre_sum[i] - pre_sum[i - L]
就表示以i结尾最后连续L个数，与之前最大的连续M个数的和。 取其中较大的与最终要返回的值res比较，并更新即可。

 1 class Solution {
 2     public int maxSumTwoNoOverlap(int[] A, int L, int M) {
 3         for (int i = 1; i < A.length; ++i) {
 4             A[i] += A[i - 1];
 5         }
 6         int res = A[L + M - 1], max_L = A[L - 1], max_M = A[M - 1];
 7         for (int i = L + M; i < A.length; ++i) {
 8             max_L = Math.max(max_L, A[i - M] - A[i - L - M]);
 9             max_M = Math.max(max_M, A[i - L] - A[i - L - M]);
10             res = Math.max(res, Math.max(max_L + A[i] - A[i - M], max_M + A[i] - A[i - L]));
11         }
12         return res;
13     }
14 }