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

Hard • View on LeetCode • View on GitHub

Problem Description

You have a pointer at index 0 in an array of size arrLen. At each step, you can move 1 position to the left, 1 position to the right in the array, or stay in the same place (The pointer should not be placed outside the array at any time).

Given two integers steps and arrLen, return the number of ways such that your pointer is still at index 0 after exactly steps steps. Since the answer may be too large, return it modulo 109 + 7.

Solution

/**
 * @param {number} steps
 * @param {number} arrLen
 * @return {number}
 */
var numWays = function(steps, arrLen) {
  const MOD = 1e9 + 7;
  const maxPos = Math.min(steps, arrLen - 1);
  let dp = new Array(maxPos + 1).fill(0);
  dp[0] = 1;

  for (let step = 1; step <= steps; step++) {
    const prev = dp;
    dp = new Array(maxPos + 1).fill(0);
    for (let pos = 0; pos <= maxPos; pos++) {
      dp[pos] = prev[pos];
      if (pos > 0) dp[pos] = (dp[pos] + prev[pos - 1]) % MOD;
      if (pos < maxPos) dp[pos] = (dp[pos] + prev[pos + 1]) % MOD;
    }
  }

  return dp[0];
};