120. Triangle

Description

Given a triangle array, return the minimum path sum from top to bottom.

For each step, you may move to an adjacent number of the row below. More formally, if you are on index i on the current row, you may move to either index i or index i + 1 on the next row.

 

Example 1:

Input: triangle = [[2],[3,4],[6,5,7],[4,1,8,3]]
Output: 11
Explanation: The triangle looks like:
   2
  3 4
 6 5 7
4 1 8 3
The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above).

Example 2:

Input: triangle = [[-10]]
Output: -10

 

Constraints:

• 1 <= triangle.length <= 200
• triangle[0].length == 1
• triangle[i].length == triangle[i - 1].length + 1
• -104 <= triangle[i][j] <= 104

 

Follow up: Could you do this using only O(n) extra space, where n is the total number of rows in the triangle?

 

Solutions

Solution: Dynamic Programming

• Time complexity: O(n²)
• Space complexity: O(n²)

 

JavaScript

/**
 * @param {number[][]} triangle
 * @return {number}
 */
const minimumTotal = function (triangle) {
  const n = triangle.length;
  const dp = Array.from({ length: n }, () => {
    return new Array(n).fill(Number.MAX_SAFE_INTEGER);
  });

  const getMinimumScore = (row, col) => {
    if (row === n - 1) return triangle[row][col];
    if (dp[row][col] !== Number.MAX_SAFE_INTEGER) return dp[row][col];

    const score = triangle[row][col];
    const nextRow = getMinimumScore(row + 1, col);
    const nextRowCol = getMinimumScore(row + 1, col + 1);
    const total = score + Math.min(nextRow, nextRowCol);

    dp[row][col] = total;

    return total;
  };

  return getMinimumScore(0, 0);
};