1458. Max Dot Product of Two Subsequences

Given two arrays nums1 and nums2.

Return the maximum dot product between non-empty subsequences of nums1 and nums2 with the same length.

A subsequence of a array is a new array which is formed from the original array by deleting some (can be none) of the characters without disturbing the relative positions of the remaining characters. (ie, [2,3,5] is a subsequence of [1,2,3,4,5] while [1,5,3] is not).

 

Example 1:

Input: nums1 = [2,1,-2,5], nums2 = [3,0,-6]
Output: 18
Explanation: Take subsequence [2,-2] from nums1 and subsequence [3,-6] from nums2.
Their dot product is (2*3 + (-2)*(-6)) = 18.

Example 2:

Input: nums1 = [3,-2], nums2 = [2,-6,7]
Output: 21
Explanation: Take subsequence [3] from nums1 and subsequence [7] from nums2.
Their dot product is (3*7) = 21.

Example 3:

Input: nums1 = [-1,-1], nums2 = [1,1]
Output: -1
Explanation: Take subsequence [-1] from nums1 and subsequence [1] from nums2.
Their dot product is -1.

 

Constraints:

  • 1 <= nums1.length, nums2.length <= 500
  • -1000 <= nums1[i], nums2[i] <= 1000

Rust Solution

struct Solution;

impl Solution {
    fn max_dot_product(nums1: Vec<i32>, nums2: Vec<i32>) -> i32 {
        let n = nums1.len();
        let m = nums2.len();
        let mut memo = vec![vec![std::i32::MIN; m + 1]; n + 1];
        Self::dp(n, m, &mut memo, &nums1, &nums2)
    }
    fn dp(n: usize, m: usize, memo: &mut Vec<Vec<i32>>, nums1: &[i32], nums2: &[i32]) -> i32 {
        if memo[n][m] > std::i32::MIN {
            memo[n][m]
        } else {
            let mut res = nums1[n - 1] * nums2[m - 1];
            if n > 1 && m > 1 {
                res = res.max(Self::dp(n - 1, m - 1, memo, nums1, nums2).max(0) + res);
            }
            if n > 1 {
                res = res.max(Self::dp(n - 1, m, memo, nums1, nums2));
            }
            if m > 1 {
                res = res.max(Self::dp(n, m - 1, memo, nums1, nums2));
            }
            memo[n][m] = res;
            res
        }
    }
}

#[test]
fn test() {
    let nums1 = vec![2, 1, -2, 5];
    let nums2 = vec![3, 0, -6];
    let res = 18;
    assert_eq!(Solution::max_dot_product(nums1, nums2), res);
    let nums1 = vec![3, -2];
    let nums2 = vec![2, -6, 7];
    let res = 21;
    assert_eq!(Solution::max_dot_product(nums1, nums2), res);
    let nums1 = vec![-1, -1];
    let nums2 = vec![1, 1];
    let res = -1;
    assert_eq!(Solution::max_dot_product(nums1, nums2), res);
}

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