From 17d387c87952c0796907253eef1c9f4a6079ea61 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Sat, 23 Feb 2019 19:32:56 -0300
Subject: [PATCH] Add Edmonds-Karp
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/edmonds_karp.cpp | 66 +++++++++++++++++++++++++++++
algorithms/graph/ford_fulkerson.cpp | 2 +-
testing.py | 1 +
3 files changed, 68 insertions(+), 1 deletion(-)
create mode 100644 algorithms/graph/edmonds_karp.cpp
diff --git a/algorithms/graph/edmonds_karp.cpp b/algorithms/graph/edmonds_karp.cpp
new file mode 100644
index 0000000..b5c55bb
--- /dev/null
+++ b/algorithms/graph/edmonds_karp.cpp
@@ -0,0 +1,66 @@
+/**
+ * Edmonds-Karp
+ *
+ * Complexity (time): O(V*E^2)
+ * Complexity (space): O(V^2)
+ */
+
+int N;
+int par[MAX];
+int graph[MAX][MAX], rg[MAX][MAX];
+
+bool cont[MAX];
+
+// Finds if there's a path between s and t using non-full
+// residual edges
+bool path(int s, int t) {
+ queue<int> Q;
+ Q.push(s);
+ cont[s] = true;
+
+ while (!Q.empty()) {
+ int u = Q.front(); Q.pop();
+
+ if (u == t)
+ return true;
+
+ for (int i = 0; i < N; ++i)
+ if (!cont[i] && rg[u][i]) {
+ cont[i] = true;
+ par[i] = u;
+ Q.push(i);
+ }
+ }
+
+ return false;
+}
+
+
+// Returns maximum flow between s (source) and t (sink)
+int edmonds_karp(int s, int t) {
+ int ans = 0;
+ par[s] = -1;
+
+ mset(cont, 0);
+ memcpy(rg, graph, sizeof(graph));
+
+ // Repeat while there's a valid path between s and t
+ while (path(s, t)) {
+ int flow = inf;
+
+ // Get the minimum capacity among all edges of the chosen path
+ for (int i = t; par[i] != -1; i = par[i])
+ flow = min(f, rg[par[i]][i]);
+
+ // Update residual graph
+ for (int i = t; par[i] != -1; i = par[i]) {
+ rg[par[i]][i] -= flow;
+ rg[i][par[i]] += flow;
+ }
+
+ ans += flow;
+ mset(cont, 0);
+ }
+
+ return ans;
+}
diff --git a/algorithms/graph/ford_fulkerson.cpp b/algorithms/graph/ford_fulkerson.cpp
index 0507b51..4e87378 100644
--- a/algorithms/graph/ford_fulkerson.cpp
+++ b/algorithms/graph/ford_fulkerson.cpp
@@ -2,7 +2,7 @@
* Ford-Fulkerson
*
* Complexity (time): O(Ef)
- * Complexity (space): O(V + E)
+ * Complexity (space): O(V^2)
*/
int N;
diff --git a/testing.py b/testing.py
index 74cd716..51b14e2 100644
--- a/testing.py
+++ b/testing.py
@@ -32,6 +32,7 @@ def gen_code_latex(arr, depth):
for i in arr:
print('\\' + depth + '{' + i + '}')
+
def gen_latex(tree):
stack = [ (tree, 0) ]
depth = ['chapter', 'section', 'subsection']
--
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