Problem
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
Solution
/**
* @param {number[]} nums1
* @param {number[]} nums2
* @return {number}
*/
var maxDotProduct = function(nums1, nums2) {
var dp = Array(nums1.length).fill(0).map(() => Array(nums2.length));
return helper(nums1, nums2, 0, 0, dp);
};
var helper = function(nums1, nums2, i, j, dp) {
if (i === nums1.length || j === nums2.length) return Number.MIN_SAFE_INTEGER;
if (dp[i][j] !== undefined) return dp[i][j];
var max = Number.MIN_SAFE_INTEGER;
// use i,j
max = Math.max(max, nums1[i] * nums2[j] + Math.max(0, helper(nums1, nums2, i + 1, j + 1, dp)));
// not use i,j
// not use i, j both
max = Math.max(max, helper(nums1, nums2, i + 1, j + 1, dp));
// not use j
max = Math.max(max, helper(nums1, nums2, i, j + 1, dp));
// not use i
max = Math.max(max, helper(nums1, nums2, i + 1, j, dp));
dp[i][j] = max;
return max;
};
Explain:
nope.
Complexity:
- Time complexity : O(n * m).
- Space complexity : O(n * m).