64. Minimum Path Sum

class Solution {
    public int minPathSum(int[][] grid) {
        int[] memo = new int[grid[0].length];
        
        for(int i=0; i<grid.length;i++){
            for (int j=0; j<grid[0].length; j++){
                if(i == 0){
                    // important! initialize the first row
                    memo[j]=j==0? grid[0][0] : grid[i][j]+memo[j-1];
                }
                else if(j == 0){
                    memo[j]=memo[j]+grid[i][j];
                }else{
                    // if first row does not get initialized, memo[j] is always 0;
                    memo[j] = grid[i][j]+Math.min(memo[j], memo[j-1]);
                }
            }
        }
        
        return memo[memo.length-1];
    }
}