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Maximize the Number of Partitions After Operations

HardStringDPBitmask
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Hard · dynamic programming solution for Maximize the Number of Partitions After Operations. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 3003. Maximize the Number of Partitions After Operations. 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

Maximize the Number of Partitions After Operations — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 3003. Maximize the Number of Partitions After Operations.

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 maximizeTheNumberOfPartitionsAfterOperations(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 “Maximize the Number of Partitions After Operations — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Maximize the Number of Partitions After Operations — dynamic programming

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