Max Dot Product of Two Subsequences

Similar Problems:

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

Github: code.dennyzhang.com

Credits To: leetcode.com

Leave me comments, if you have better ways to solve.

- Solution:

## https://code.dennyzhang.com/max-dot-product-of-two-subsequences ## Basic Ideas: dynamic programming ## ## dp(i, j) ## ## dp(i-1, j), dp(i, j-1) ## ## Complexity: Time ?, Space ? class Solution: def maxDotProduct(self, nums1: List[int], nums2: List[int]) -> int: m, n = len(nums1), len(nums2) dp = [[-sys.maxsize for _ in range(n+1)] for _ in range(m+1)] for i in range(1, m+1): for j in range(1, n+1): # don't take nums1[i-1], nums2[j-1] dp[i][j] = max(dp[i-1][j], dp[i][j-1]) v = dp[i-1][j-1] if v<0: v = 0 dp[i][j] = max(dp[i][j], nums1[i-1]*nums2[j-1]+v) return dp[-1][-1]