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