Write code that finds a maximum flow in a directed graph, using the Ford-Fulkerson algorithm on capacities given as matrix void maximum flow(int n, int s, int t, int *capacity, int *flow)
Your function has the following arguments:
- n: the number of vertices of the graph,
- s: the start vertex,
- t: the target vertex
- capacity: the matrix of edge capacities.
- flow: the matrix used to return the maximum flow.
The vertices are numbered from 0 to n-1, so s and t are numbers in that range. capacity, flow are a pointers to n × n matrices of nonnegtive integers; the array element capacity[i][j] is the capacity of the edge from i to j, and can be accessed as *(capacity + i*n + j). Your function should return in the matrix flow the flow values of the maximum flow from s to t. The flow variable of your function points to space allocated for the flow matrix.
Your function will need the following auxiliary arrays:
- an n × n matrix to hold the current flow,
- an n × n matrix to hold the current residual capacities,
- an array to maintain which vertices are already visited in the search of an augmenting path from s to t with positive residual capacity.
You have to allocate the auxiliary arrays. You can use either BFS or DFS for the search of the augmenting path.