(b) Suppose we have an n x n grid. We start in the upper-left corner (position (1,1)), and we would like to reach the lower-right corner (position (n,n)) by taking single steps down and right. Define a function cli, j) to be the cost of touching position (i, j), and assume it takes constant time to compute. Note that cli, j) can be negative. Give an algorithm for computing the minimum cost in the most efficient way. What is the runtime just give the big-O)? Hint: Define vi, j) to be the minimum cost to reach (ij) from (1,1). Can you find a recurrence for vi, j)? The naive way of implementing the recurrence will take exponential time due to the repeated computation of the same subproblems. Can you make it more efficient? (with the help of additional memory space, probably)