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Max Dot Product of Two Subsequences

HardArrayDP
Solve on LeetCode

Hard · dynamic programming solution for Max Dot Product of Two Subsequences. Python, Go, and a step-by-step animation.

01

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 1458. Max Dot Product of Two Subsequences. The copyrighted prompt is on LeetCode. This page is a working dynamic programming solution for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

  • —Player inputs are capped so the animation stays readable.
  • —Match LeetCode's own constraints when you submit there.

Examples

Input

n =
5

Output

8

Ways to climb 5 stairs with 1- or 2-steps: Fibonacci, 8.

02

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Max Dot Product of Two Subsequences — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 1458. Max Dot Product of Two Subsequences.

The classic recurrence dp[i] = dp[i−1] + dp[i−2] (ways to climb i stairs) is the shape of a huge family of 1-D DP problems. Fill left to right; two rolling variables are enough.

Algorithm

  1. Base: a, b = 1, 1 (ways to reach step 0 and 1).
  2. For i from 2 to n, a, b = b, a+b.
  3. Return b.
Time
O(n)
Space
O(1)
Solution.py
class Solution:    def maxDotProductOfTwoSubsequences(self, n: int) -> int:        a, b = 1, 1        for _ in range(2, n + 1):            a, b = b, a + b        return b
Watch this run

03

Interactive walkthrough

Playing “Max Dot Product of Two Subsequences — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Max Dot Product of Two Subsequences — dynamic programming

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