• Question
• Solution

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: $O(1)$