<p>Given an <code>n x n</code> integer matrix <code>grid</code>, return <em>the minimum sum of a <strong>falling path with non-zero shifts</strong></em>.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/10/falling-grid.jpg" style="width: 244px; height: 245px;" />
<pre>
<strong>Input:</strong> grid = [[1,2,3],[4,5,6],[7,8,9]]
<strong>Output:</strong> 13
<strong>Explanation:</strong> 
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&nbsp;[1,5,7], so the answer is&nbsp;13.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> grid = [[7]]
<strong>Output:</strong> 7
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>n == grid.length == grid[i].length</code></li>
	<li><code>1 &lt;= n &lt;= 200</code></li>
	<li><code>-99 &lt;= grid[i][j] &lt;= 99</code></li>
</ul>

class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& grid) {
        int n = grid.size();
        if (n == 1) return grid[0][0];
        
        vector<int> prev(n, 0), curr(n, 0);
        
        for (int j = 0; j < n; ++j) {
            prev[j] = grid[0][j];
        }
        
        for (int i = 1; i < n; ++i) {
            int min1 = INT_MAX, min2 = INT_MAX;
            int min1Index = -1;
            
            for (int j = 0; j < n; ++j) {
                if (prev[j] < min1) {
                    min2 = min1;
                    min1 = prev[j];
                    min1Index = j;
                } else if (prev[j] < min2) {
                    min2 = prev[j];
                }
            }
            
            for (int j = 0; j < n; ++j) {
                if (j == min1Index) {
                    curr[j] = grid[i][j] + min2;
                } else {
                    curr[j] = grid[i][j] + min1;
                }
            }
            
            swap(prev, curr);
        }
      
        int result = INT_MAX;
        for (int j = 0; j < n; ++j) {
            result = min(result, prev[j]);
        }
        
        return result;
    }
};

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