Homework Assignment 3
Write code that finds a maximum flow in a directed graph, using the Ford-Fulkerson
algorithm. The graph is given as adjacency matrix with cap[i][j] being the capacity
of the directed edge from i to j. The function received another argument, the matrix
flow[][], which is used to return the flow values in the maximum flow from s to t
void maximum flow(int n, int s, int t, int *cap, int *flow)
Your function has the following arguments:
- n: the number of vertices of the graph,
- s: the start vertex,
- t: the target vertex
- cap: 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 nonnegative integers; in standard
C the size of a matrix cannot be a variable, so we use pointer arithmetic, and treat
the matrix as a one-dimensional matrix. The array element cap[i][j] can be accessed
as *(cap + 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 at least 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.
