unique-paths.js

/**
 * Unique Paths
 *
 * A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).
 *
 * The robot can only move either down or right at any point in time. The robot is trying to reach the
 * bottom-right corner of the grid (marked 'Finish' in the diagram below).
 *
 * How many possible unique paths are there?
 *
 * Note: m and n will be at most 100.
 *
 * Example 1:
 *
 * Input: m = 3, n = 2
 * Output: 3
 *
 * Explanation:
 *
 * From the top-left corner, there are a total of 3 ways to reach the bottom-right corner:
 * 1. Right -> Right -> Down
 * 2. Right -> Down -> Right
 * 3. Down -> Right -> Right
 *
 * Example 2:
 *
 * Input: m = 7, n = 3
 * Output: 28
 */

/**
 * @param {number} m
 * @param {number} n
 * @return {number}
 */
const uniquePaths = (m, n) => {
  const dp = Array(m);
  for (let i = 0; i < m; i++) {
    dp[i] = Array(n).fill(0);
  }

  // first row
  for (let j = 0; j < n; j++) {
    dp[0][j] = 1;
  }

  // first col
  for (let i = 0; i < m; i++) {
    dp[i][0] = 1;
  }

  // others
  for (let i = 1; i < m; i++) {
    for (let j = 1; j < n; j++) {
      dp[i][j] = dp[i - 1][j] + dp[i][j - 1];
    }
  }

  return dp[m - 1][n - 1];
};

export { uniquePaths };