# Minimum sum falling path in a NxN grid in C++

## Problem statement

• Given a matrix A of integers of size NxN. The task is to find the minimum sum of a falling path through A.
• A falling path will start at any element in the first row and ends in last row.
• It chooses one element from each next row. The next row’s choice must be in a column that is different from the previous row’s column by at most ones

## Example

If N = 2 and matrix is:
{
{5, 10},
{25, 15}
} then output will be 20 as element 5 and 15 are selected

## Example

Live Demo

#include <bits/stdc++.h>
#define MAX 2
using namespace std;
int getMinSumPath(int matrix[MAX][MAX]) {
for (int row = MAX - 2; row >= 0; --row) {
for (int col = 0; col < MAX; ++col) {
int val = matrix[row + 1][col];
if (col > 0) {
val = min(val, matrix[row +1][col - 1]);
}
if (col + 1 < MAX) {
val = min(val, matrix[row +1][col + 1]);
}
matrix[row][col] = matrix[row][col] +val;
}
}
int result = INT_MAX;
for (int i = 0; i < MAX; ++i)
result = min(result, matrix[0][i]);
return result;
}
int main() {
int matrix[MAX][MAX] = {
{5, 10},
{25, 15},
};
cout << "Minimum sum path = " << getMinSumPath(matrix)
<< endl;
return 0;
}

When you compile and execute above program. It generates following output

## Output

Minimum sum path = 20