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
class Solution {
public int maxDotProduct(int[] nums1, int[] nums2) {
int[][] marks = new int[nums1.length][nums2.length];
for (int i = 0; i < nums1.length; i++) {
for (int j = 0; j < nums2.length; j++) {
int max = nums1[i] * nums2[j];
if (i > 0 && j > 0) {
max = Math.max(max, max + marks[i - 1][j - 1]);
}
if (i > 0) {
max = Math.max(max, marks[i - 1][j]);
}
if (j > 0) {
max = Math.max(max, marks[i][j - 1]);
}
marks[i][j] = max;
}
}
return marks[nums1.length - 1][nums2.length - 1];
}
}
Explain:
nope.
Complexity:
- Time complexity : O(n).
- Space complexity : O(n).