1289. Minimum Falling Path Sum II

 Given an n x n integer matrix grid, return the minimum sum of a falling path with non-zero shifts.

A falling path with non-zero shifts is a choice of exactly one element from each row of grid such that no two elements chosen in adjacent rows are in the same column.

 

Example 1:

Input: grid = [[1,2,3],[4,5,6],[7,8,9]]
Output: 13
Explanation: 
The possible falling paths are:
[1,5,9], [1,5,7], [1,6,7], [1,6,8],
[2,4,8], [2,4,9], [2,6,7], [2,6,8],
[3,4,8], [3,4,9], [3,5,7], [3,5,9]
The falling path with the smallest sum is [1,5,7], so the answer is 13.

Example 2:

Input: grid = [[7]]
Output: 7

 

Constraints:

• n == grid.length == grid[i].length
• 1 <= n <= 200
• -99 <= grid[i][j] <= 99

ANSWER:

class Solution {

    public int minFallingPathSum(int[][] grid) {

        int firstMin = 0;

        int secondMin = 0;

        int firstMinPos = -1;

        final int INF = Integer.MAX_VALUE;

        for (int[] row : grid) {

            int curFirstMin = INF;

            int curSecondMin = INF;

            int curFirstMinPos = -1;

            for (int j = 0; j < row.length; ++j) {

                int sum = (j != firstMinPos ? firstMin : secondMin) + row[j];

                if (sum < curFirstMin) {

                    curSecondMin = curFirstMin;

                    curFirstMin = sum;        

                    curFirstMinPos = j;        

                } else if (sum < curSecondMin) {

                    curSecondMin = sum;

                }

            }

            firstMin = curFirstMin;

            secondMin = curSecondMin;

            firstMinPos = curFirstMinPos;

        }

        return firstMin;

    }

}