triangle.js

/**
 * Triangle
 *
 * Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers
 * on the row below.
 *
 * For example, given the following triangle
 *
 * [
 *      [2],
 *     [3,4],
 *    [6,5,7],
 *   [4,1,8,3]
 * ]
 * The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).
 *
 * Note:
 *
 * Bonus point if you are able to do this using only O(n) extra space, where n is the total number of
 * rows in the triangle.
 */

/**
 * @param {number[][]} triangle
 * @return {number}
 */
const minimumTotal = triangle => {
  const m = triangle.length;
  const dp = Array(m).fill(0);

  for (let i = 0; i < m; i++) {
    dp[i] = triangle[m - 1][i];
  }

  for (let i = m - 2; i >= 0; i--) {
    for (let j = 0; j <= i; j++) {
      dp[j] = Math.min(dp[j], dp[j + 1]) + triangle[i][j];
    }
  }

  return dp[0];
};

export { minimumTotal };