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] <= 1000struct 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);
}