0019_P931_Minimum_Falling_Path_Sum.cpp

/* 
Day: 19
Problem Number: 931 (https://leetcode.com/problems/minimum-falling-path-sum)
Date: 19-01-2024 
Description:
Given an n x n array of integers matrix, return the minimum sum of any falling path through matrix.
A falling path starts at any element in the first row and chooses the element in the next row that is either directly below or diagonally left/right. Specifically, the next element from position (row, col) will be (row + 1, col - 1), (row + 1, col), or (row + 1, col + 1).

Example 1:
Input: matrix = [[2,1,3],[6,5,4],[7,8,9]]
Output: 13
Explanation: There are two falling paths with a minimum sum as shown.

Example 2:
Input: matrix = [[-19,57],[-40,-5]]
Output: -59
Explanation: The falling path with a minimum sum is shown.

Constraints:
* n == matrix.length == matrix[i].length
* 1 <= n <= 100
* -100 <= matrix[i][j] <= 100
 
Code:  */
class Solution {
public:
    int minFallingPathSum(vector<vector<int>>& matrix) {
        int n = matrix.size();
        vector<int> f(n);
        for (auto& row : matrix) {
            auto g = f;
            for (int j = 0; j < n; ++j) {
                if (j) {
                    g[j] = min(g[j], f[j - 1]);
                }
                if (j + 1 < n) {
                    g[j] = min(g[j], f[j + 1]);
                }
                g[j] += row[j];
            }
            f = move(g);
        }
        return *min_element(f.begin(), f.end());
    }
};