931. Minimum Falling Path Sum

Given a square array of integers A, we want the minimum sum of a falling path through A.

A falling path starts at any element in the first row, and chooses one element from each row. The next row's choice must be in a column that is different from the previous row's column by at most one.

Example 1:

Input: [[1,2,3],[4,5,6],[7,8,9]]
Output: 12
Explanation: 
The possible falling paths are:

• [1,4,7], [1,4,8], [1,5,7], [1,5,8], [1,5,9]

• [2,4,7], [2,4,8], [2,5,7], [2,5,8], [2,5,9], [2,6,8], [2,6,9]

• [3,5,7], [3,5,8], [3,5,9], [3,6,8], [3,6,9]

The falling path with the smallest sum is [1,4,7], so the answer is 12.

Note:

1. 1 <= A.length == A[0].length <= 100

2. -100 <= A[i][j] <= 100

class Solution {
    public int minFallingPathSum(int[][] A) {
       if(A == null || A.length == 0 || A[0].length == 0) return 0;
        int min = Integer.MAX_VALUE;
        
       for(int i = 1; i < A.length; i++){
           for(int j = 0; j < A[0].length;j++){
               int left = j-1, mid = j, right = j+1;
               //track i - 1;   
               if(inBound(left,A) && inBound(right,A)){
                   A[i][j] = A[i][j] + Math.min(A[i-1][left],Math.min(A[i-1][mid],A[i-1][right]));
               }
               
              else if(!inBound(left,A)){
                   A[i][j] = A[i][j] + Math.min(A[i-1][mid],A[i-1][right]);
              }else{
                  A[i][j] = A[i][j] + Math.min(A[i-1][mid],A[i-1][left]);
              }
               
           }
       }
        
        
        for(int i = 0; i < A[0].length;i++){
            if(A[A.length-1][i] < min){
                min = A[A.length-1][i];
            }
        }
        
        return min;
        
    }
    
    public boolean inBound(int x, int[][] A){
        if(x < 0 || x >= A[0].length) return false;
        
        else return true;
    }
}