1031. Maximum Sum of Two Non-Overlapping Subarrays

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.

 

Note:

  1. L >= 1
  2. M >= 1
  3. L + M <= A.length <= 1000
  4. 0 <= A[i] <= 1000

Rust Solution

struct Solution;

use std::i32;

impl Solution {
    fn max_sum_two_no_overlap(mut a: Vec<i32>, l: i32, m: i32) -> i32 {
        let n = a.len();
        let l = l as usize;
        let m = m as usize;
        for i in 1..n {
            a[i] += a[i - 1];
        }
        let mut res = a[l + m - 1];
        let mut max_l = a[l - 1];
        let mut max_m = a[m - 1];
        for i in l + m..n {
            max_l = i32::max(a[i - m] - a[i - m - l], max_l);
            max_m = i32::max(a[i - l] - a[i - l - m], max_m);
            let last_l = a[i] - a[i - l];
            let last_m = a[i] - a[i - m];
            res = i32::max(i32::max(max_m + last_l, max_l + last_m), res);
        }
        res
    }
}

#[test]
fn test() {
    let a = vec![0, 6, 5, 2, 2, 5, 1, 9, 4];
    let l = 1;
    let m = 2;
    let res = 20;
    assert_eq!(Solution::max_sum_two_no_overlap(a, l, m), res);
    let a = vec![3, 8, 1, 3, 2, 1, 8, 9, 0];
    let l = 3;
    let m = 2;
    let res = 29;
    assert_eq!(Solution::max_sum_two_no_overlap(a, l, m), res);
    let a = vec![2, 1, 5, 6, 0, 9, 5, 0, 3, 8];
    let l = 4;
    let m = 3;
    let res = 31;
    assert_eq!(Solution::max_sum_two_no_overlap(a, l, m), res);
}

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