## Triangle

07/11/2016 Array Dynamic Programming

## Question

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.

## Solution

Result: Accepted Time: 8 ms

Here should be some explanations.

int tmin(int** tri,int r,int c,int csz)
{
if(c+1 >= csz) return tri[r][c];
if(tri[r][c] > tri[r][c+1])
return tri[r][c+1];
return tri[r][c];
}
int minimumTotal(int** tri, int row, int *cols) {
for(int i = row -2 ; i >= 0 ; i--)
for(int c = 0; c < cols[i]; c++)
tri[i][c] += tri[i+1][c] < tri[i+1][c+1]?tri[i+1][c] : tri[i+1][c+1];
return tri[0][0];
}


Complexity Analytics

• Time Complexity: $O(n)$
• Space Complexity: $O(1)$