"Leetcode" Minimum Path Sum

Title Link: https://leetcode.com/problems/minimum-path-sum/

Topic:

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.

Ideas:

C[I][J] represents the minimum path from top left to i,j and the state transition equation: c[i][j]=min{c[i-1][j],c[i][j-1]}

Algorithm:

public int minpathsum (int[][] grid) {      int c[][] = new Int[grid.length][grid[0].length];      C[0][0] = grid[0][0];      for (int i = 1; I <grid.length; i++) {          c[i][0] = c[i-1][0]+grid[i][0];      }      for (int j=1;j<grid[0].length;j++) {          c[0][j] = c[0][j-1]+grid[0][j];      }            for (int i = 1, i <grid.length; i++) {for          (int j = 1; J <grid[0].length; J + +) {              C[i][j] = math.min (c[i-1][ J], C[i][j-1]) +grid[i][j];          }      }      return c[grid.length-1][grid[0].length-1];  }  

"Leetcode" Minimum Path Sum