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Maximum Number of Subsequences After One Inserting

MediumStringDPGreedyPrefix sum
Solve on LeetCode

Medium · dynamic programming solution for Maximum Number of Subsequences After One Inserting. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 3628. Maximum Number of Subsequences After One Inserting. 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

Maximum Number of Subsequences After One Inserting — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 3628. Maximum Number of Subsequences After One Inserting.

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 maximumNumberOfSubsequencesAfterOneInserting(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 “Maximum Number of Subsequences After One Inserting — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Maximum Number of Subsequences After One Inserting — dynamic programming

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