119. Pascal’s Triangle II

Problem:

Given a non-negative index k where k ≤ 33, return the kth index row of the Pascal’s triangle.

Note that the row index starts from 0.

In Pascal’s triangle, each number is the sum of the two numbers directly above it.

Example:

Input: 3
Output: [1,3,3,1]

Follow up:

Could you optimize your algorithm to use only O(k) extra space?

Solution:

Dynamic Programming 101 with dynamic array.

State (i, j) depends on (i-1, j) and (i-1, j-1). So to access (i-1, j-1) iteration must be from right to left.

/**
 * @param {number} rowIndex
 * @return {number[]}
 */
var getRow = function(rowIndex) {
  if (rowIndex < 0) { return [] }

  const row = [1]
  for (let i = 1; i <= rowIndex; i++) {
    for (let j = i - 1; j > 0; j--) {
      row[j] += row[j-1]
    }
    row.push(1)
  }

  return row
};

Template generated via Leetmark.