LeetCode 120: Triangle

Difficulty: 3

Frequency: 1

Problem:

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:

1. Use O(n^2) extra space, where n is the total number of rows in the triangle.

class Solution {public:    int minimumTotal(vector<vector<int> > &triangle) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        if (triangle.size()==0)            return 0;        if (triangle.size()==1)            return triangle[0][0];                    vector<vector<int> > pathSumTriangle (triangle);        int i_minimum = 0;        for (int i = 1; i<triangle.size(); i++)        {            for (int j = 0; j<triangle[i].size(); j++)            {                int i_left = j==0?0x7FFFFFFF:pathSumTriangle[i-1][j-1];                int i_right = (j==pathSumTriangle[i].size()-1)?0x7FFFFFFF:pathSumTriangle[i-1][j];                pathSumTriangle[i][j] += i_left<i_right?i_left:i_right;                if (i==triangle.size()-1)                {                    if (j==0)                        i_minimum = pathSumTriangle[i][j];                    else                        i_minimum = i_minimum<pathSumTriangle[i][j]?i_minimum:pathSumTriangle[i][j];                }            }        }        return i_minimum;    }};

2. Use O(n) extra space.

class Solution {public:    int minimumTotal(vector<vector<int> > &triangle) {        // Start typing your C/C++ solution below        // DO NOT write int main() function        if (triangle.size()==0)            return 0;        if (triangle.size()==1)            return triangle[0][0];                    vector<int> pathSumTriangle (triangle.back());        int i_minimum = 0;        pathSumTriangle[0] = triangle[0][0];        for (int i = 1; i<triangle.size(); i++)        {            pathSumTriangle[i] = pathSumTriangle[i-1] + triangle[i][i];            i_minimum = pathSumTriangle[i];            for (int j = i - 1; j>0; --j)            {                pathSumTriangle[j] = (pathSumTriangle[j]<pathSumTriangle[j-1]?pathSumTriangle[j]:pathSumTriangle[j-1]) + triangle[i][j];                if (i==triangle.size()-1)                {                    i_minimum = i_minimum<pathSumTriangle[j]?i_minimum:pathSumTriangle[j];                }            }            pathSumTriangle[0] += triangle[i][0];            i_minimum = i_minimum<pathSumTriangle[0]?i_minimum:pathSumTriangle[0];        }        return i_minimum;    }

};

Notes: