Question

a grid of NxN is given. each point is assigned a value say num

starting from 1,1 we have to traverse to N,N.

if i,j is current position we can go right or down.
How to find the min sum of digits by traversing from 1,1 to n,n along any path
any two points can have same number
ex

1 2 3

4 5 6

7 8 9

1+2+3+6+9 = 21
n <=10000000000

Output 21
Can someone explain how to approach the problem?

Answer 1

This is a dynamic programming problem. The subproblem here is the minimum cost/path to get to any given square. Because you can only move down and to the right, there are only two squares that can let you enter a given square, the one above and the one to the left. Therefore the cost of getting to a square (i,i) is min(cost[i-1][i], cost[i][i-1]) + num. If this would put you out of bounds, only consider the option that is inside the grid. Calculate each row from left to right, doing the top row first and working your way down. The cost you get at (N,N) will be the minimal cost.