Leetcode 120. Triangle (Python)

Related Topic

Dynamic-Programming.

Description

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

Sample I/O

Example 1

[
     [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.

Methodology

This question solved by Dynamic Programming. It is similar with question 64 64. Minimum Path Sum.

Find the base case:

The base case can be original 2D list, we will replace the value of each cell with minimum sum.

Find the pattern:

However, to use dynamic programming, we need to sum up each cell with it’s previous adjancent cell.

Answer:

When reach to the bottom row, then minimum number in the bottom row will be the answer.

Code

def minimumTotal(self, triangle: List[List[int]]) -> int:
        m = len(triangle)
        for i in range(1,m):
            triangle[i][0]+=triangle[i-1][0]
            triangle[i][-1]+=triangle[i-1][-1]
        for i in range(2,m):
            for j in range(1,i):
                triangle[i][j]+=min(triangle[i-1][j-1], triangle[i-1][j])
        print(triangle)
        return min(triangle[-1])

BigO

Init the triangle will cost O(m-1). Then iterate all 2D dp array, it will cost O((m-2)*(m-4)). In total will cost (m-1+(m-2)*(m-4)) equal to (m^2-5m+7) so generally is O(n^2)