[Leetcode]-Minimum Path Sum

Given a m x n grid filled with non-negative numbers, find a path from top left to bottom right which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Hide Tags ：Array ，Dynamic Programming

Hide Similar Problems ：(M) Unique Paths (H) Dungeon Game

题目：m*n的表格中每个格子存放有一个随机数（非负数），求出从左上角到右下角的一条路径使之为最小元素和。方向只能向右或者下。

思路：动态规划,状态转移矩阵：

　　　　　r[j] = grid[i][j] + (r[j] < r[j-1] ? r[j] : r[j-1]) ;

　　　　　r[0] = grid[0][0];

　　　　　r[j] = r[j-1] + grid[0][j];

O（space） = n 解决方案

int minPathSum(int** grid, int gridRowSize, int gridColSize) {
    int *r = (int*)malloc(sizeof(int)*gridColSize);

    for(int i=0;i<gridRowSize;i++)
    {
        for(int j=0;j<gridColSize;j++)
        {
            if(0 == i && 0 == j)
                r[0] = grid[0][0];
            else if(0 == i && 0 != j)
                r[j] = r[j-1] + grid[0][j];
            else if(0 != i && 0 == j)
                r[0] = r[0] + grid[i][0];
            else
                r[j] = grid[i][j] + (r[j] < r[j-1] ? r[j] : r[j-1]) ;
        }
    }
    int r1 = r[gridColSize - 1];
    free(r);
    return r1;

}