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Maximum_Flow_Problem_I_Edmond_Karp.cpp
69 lines (61 loc) · 1.81 KB
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Maximum_Flow_Problem_I_Edmond_Karp.cpp
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// Ford-Fulkerson + Edmond Karp algorithm
// single source - single sink maximum flow
#define MAX 1005
vector<pair<int, int>> adj[MAX]; // adj[u] = {{v1, capacity1}, {v2, capacity2}}
vector<int> residual[MAX]; // residual[u][v1] = capacity1
int parent[MAX];
bool visited[MAX];
int n;
/* Returns true if there is a path from 'src' to 'sink' in
residual graph. Also fills parent[] to store the path */
bool bfs(int src, int sink) {
memset(visited, false, sizeof visited);
queue <int> q;
q.push(src);
visited[src] = true;
parent[src] = -1;
while (!q.empty()) {
int u = q.front();
q.pop();
for(int i = 0; i < (int)adj[u].size(); i++) {
int v = adj[u][i].first;
if(!visited[v] and residual[u][v] > 0) {
q.push(v);
parent[v] = u;
visited[v] = true;
}
}
}
// If we reached sink in BFS starting from source, then return true, else false
return visited[sink];
}
int edmondKarp(int src, int sink) {
int maxFlow = 0;
for(int u = 0; u < n; u++) {
for(int i = 0; i < (int)adj[u].size(); i++) {
int v = adj[u][i].first;
int capacity = adj[u][i].second;
residual[u][v] = capacity;
}
}
while(bfs(src, sink)) {
int pathFlow = INT_MAX;
// trace augmenting path
int v = sink;
while(v != src) {
int u = parent[v];
pathFlow = min(pathFlow, residual[u][v]);
v = u;
}
// update residual graph
v = sink;
while(v != src) {
int u = parent[v];
residual[u][v] -= pathFlow;
residual[v][u] += pathFlow;
v = u;
}
maxFlow += pathFlow;
}
return maxFlow;
}