Leetcode Problem 1269. Number of Ways to Stay in the Same Place After Some Steps

1269. Number of Ways to Stay in the Same Place After Some Steps

Leetcode Solutions

Approach: Space-Optimized Dynamic Programming

  1. Set arrLen to the minimum of arrLen and steps to avoid unnecessary computation.
  2. Initialize two arrays dp and prevDp of size arrLen.
  3. Set prevDp[0] to 1 as the base case, representing the number of ways to be at position 0 with 0 steps.
  4. Iterate from remain = 1 to steps: a. Reset dp to all zeros. b. Iterate curr from 0 to arrLen - 1: i. Calculate dp[curr] by adding the number of ways to stay in place (prevDp[curr]), move left (prevDp[curr - 1] if curr > 0), and move right (prevDp[curr + 1] if curr < arrLen - 1). c. Update prevDp to be the same as dp.
  5. Return dp[0], which represents the number of ways to be at position 0 after steps steps.
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Approach: Top-Down Dynamic Programming

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