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Number of Valid Move Combinations On Chessboard

HardArrayStringBacktracking
Solve on LeetCode

Hard · dynamic programming solution for Number of Valid Move Combinations On Chessboard. Python, Go, and a step-by-step animation.

01

Problem

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

LeetCode 2056. Number of Valid Move Combinations On Chessboard. 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

Number of Valid Move Combinations On Chessboard — dynamic programming

Each answer is a combination of smaller answers already in the table. Built for LeetCode 2056. Number of Valid Move Combinations On Chessboard.

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 numberOfValidMoveCombinationsOnChessboard(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 “Number of Valid Move Combinations On Chessboard — dynamic programming”. Edit the input, hit Run, then scrub.

Approach: Number of Valid Move Combinations On Chessboard — dynamic programming

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