Question

Create a bottom-up solution to the minimum falling path sum problem. By bottom-up, I mean you should not use recursion and should instead use a loop which begins by finding the minimum falling path assuming you started in the last row.

Please use Java

Answer 1

public class Chegg {
static int minFallingPathSum(int[][] arr) {

// Extracting dimensions of 2-D array
int N = arr.length;

// R for rows and C for Columns
for (int R = N-2; R >= 0; R--) {
for (int C = 0; C < N; C++) {
// best = min(arr[R+1][C-1], arr[R+1][C], arr[R+1][C+1])

// extracting the best value
int best = arr[R+1][C];
if (C > 0)
best = Math.min(best, arr[R+1][C-1]);
if (C+1 < N)
best = Math.min(best, arr[R+1][C+1]);
arr[R][C] += best;
}
}

int ans = Integer.MAX_VALUE;
for (int x: arr[0])
ans = Math.min(ans, x);
return ans;
}
   public static void main (String[] args) {
int A[][] = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
  
// function to print required answer
System.out.println( minFallingPathSum(A));
}
}