From 22edf84110d24bdb6478305a0c5906e1c7c8dec8 Mon Sep 17 00:00:00 2001
From: Bruno Freitas Tissei <bft15@inf.ufpr.br>
Date: Fri, 22 Feb 2019 20:32:41 -0300
Subject: [PATCH] Add ford-fulkerson
Signed-off-by: Bruno Freitas Tissei <bft15@inf.ufpr.br>
---
algorithms/graph/articulations_bridges.cpp | 4 +-
algorithms/graph/bfs.cpp | 4 +-
algorithms/graph/bipartite_match.cpp | 6 +--
algorithms/graph/dfs.cpp | 4 +-
algorithms/graph/dijkstra.cpp | 4 +-
algorithms/graph/floyd_warshall.cpp | 4 +-
algorithms/graph/ford_fulkerson.cpp | 59 ++++++++++++++++++++++
algorithms/graph/kosaraju.cpp | 4 +-
algorithms/graph/kruskal.cpp | 4 +-
algorithms/graph/lca.cpp | 6 +--
algorithms/graph/prim.cpp | 4 +-
algorithms/graph/tarjan.cpp | 4 +-
algorithms/graph/topological_sort.cpp | 4 +-
algorithms/structure/lazy_segment_tree.cpp | 2 +-
algorithms/structure/segment_tree.cpp | 38 +++++++++-----
notebook/gen_latex.py | 19 ++++---
testing.py | 53 +++++++++++++++++++
17 files changed, 172 insertions(+), 51 deletions(-)
create mode 100644 algorithms/graph/ford_fulkerson.cpp
create mode 100644 testing.py
diff --git a/algorithms/graph/articulations_bridges.cpp b/algorithms/graph/articulations_bridges.cpp
index 7ddb90e..73c9b6e 100644
--- a/algorithms/graph/articulations_bridges.cpp
+++ b/algorithms/graph/articulations_bridges.cpp
@@ -1,8 +1,8 @@
/**
* Tarjan - Articulations and Bridges
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
vector<int> graph[MAX];
diff --git a/algorithms/graph/bfs.cpp b/algorithms/graph/bfs.cpp
index 6431f2b..2317e9a 100644
--- a/algorithms/graph/bfs.cpp
+++ b/algorithms/graph/bfs.cpp
@@ -1,8 +1,8 @@
/**
* Breadth First Search (BFS)
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
bool cont[MAX];
diff --git a/algorithms/graph/bipartite_match.cpp b/algorithms/graph/bipartite_match.cpp
index dde0774..92215e4 100644
--- a/algorithms/graph/bipartite_match.cpp
+++ b/algorithms/graph/bipartite_match.cpp
@@ -1,8 +1,8 @@
/**
- * Bipartite Matching (simplified Ford-Fulkerson)
+ * Bipartite Matching
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
vector<int> graph[MAX];
diff --git a/algorithms/graph/dfs.cpp b/algorithms/graph/dfs.cpp
index 6408d40..1dd2da5 100644
--- a/algorithms/graph/dfs.cpp
+++ b/algorithms/graph/dfs.cpp
@@ -1,8 +1,8 @@
/**
* Depth First Search (DFS)
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
bool cont[MAX];
diff --git a/algorithms/graph/dijkstra.cpp b/algorithms/graph/dijkstra.cpp
index afb03e5..3328a27 100644
--- a/algorithms/graph/dijkstra.cpp
+++ b/algorithms/graph/dijkstra.cpp
@@ -1,8 +1,8 @@
/**
* Dijkstra
*
- * Complexity (Time): O(m + n log n)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(E + V log V)
+ * Complexity (Space): O(V + E)
*/
int dist[MAX];
diff --git a/algorithms/graph/floyd_warshall.cpp b/algorithms/graph/floyd_warshall.cpp
index f913d87..8774a58 100644
--- a/algorithms/graph/floyd_warshall.cpp
+++ b/algorithms/graph/floyd_warshall.cpp
@@ -1,8 +1,8 @@
/**
* Floyd Warshall Algorithm
*
- * Complexity (Time): O(n^3)
- * Complexity (Space): O(n^2)
+ * Complexity (Time): O(V^3)
+ * Complexity (Space): O(V^2)
*/
int dist[MAX][MAX];
diff --git a/algorithms/graph/ford_fulkerson.cpp b/algorithms/graph/ford_fulkerson.cpp
new file mode 100644
index 0000000..87da194
--- /dev/null
+++ b/algorithms/graph/ford_fulkerson.cpp
@@ -0,0 +1,59 @@
+/**
+ * Ford-Fulkerson
+ *
+ * Complexity (time): O(Ef)
+ * Complexity (space): O(V + E)
+ */
+
+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) {
+ cont[s] = true;
+ if (s == t)
+ return true;
+
+ for (int i = 0; i < N; ++i)
+ if (!cont[i] and rg[s][i]) {
+ par[i] = s;
+ if (path(i, t))
+ return true;
+ }
+
+ return false;
+}
+
+
+// Returns maximum flow between s (source) and t (sink)
+int ford_fulkerson(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/kosaraju.cpp b/algorithms/graph/kosaraju.cpp
index b675ca5..486883b 100644
--- a/algorithms/graph/kosaraju.cpp
+++ b/algorithms/graph/kosaraju.cpp
@@ -1,8 +1,8 @@
/**
* Kosaraju
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
stack<int> S;
diff --git a/algorithms/graph/kruskal.cpp b/algorithms/graph/kruskal.cpp
index 7cc272a..383808e 100644
--- a/algorithms/graph/kruskal.cpp
+++ b/algorithms/graph/kruskal.cpp
@@ -1,8 +1,8 @@
/**
* Kruskal
*
- * Complexity (Time): O (m log n)
- * Complexity (Space): O(m)
+ * Complexity (Time): O (E log V)
+ * Complexity (Space): O(E)
*
* #include <structure/disjoint_set>
*
diff --git a/algorithms/graph/lca.cpp b/algorithms/graph/lca.cpp
index 8919ff7..32a2fce 100644
--- a/algorithms/graph/lca.cpp
+++ b/algorithms/graph/lca.cpp
@@ -2,9 +2,9 @@
* Lowest Common Ancestor - LCA
*
* Complexity (Time):
- * - preprocess: O(n log n)
- * - query: O(log n)
- * Complexity (Space): O(n + m + n log n)
+ * - preprocess: O(V log V)
+ * - query: O(log V)
+ * Complexity (Space): O(V + E + V log V)
*
* OBS: * = return sum path to LCA
* ** = return max value on path to LCA
diff --git a/algorithms/graph/prim.cpp b/algorithms/graph/prim.cpp
index 1229061..2270fa3 100644
--- a/algorithms/graph/prim.cpp
+++ b/algorithms/graph/prim.cpp
@@ -1,8 +1,8 @@
/**
* Prim
*
- * Complexity (Time): O(m log m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(E log E)
+ * Complexity (Space): O(V + E)
*/
bool cont[MAX];
diff --git a/algorithms/graph/tarjan.cpp b/algorithms/graph/tarjan.cpp
index bfcccdc..ede8a49 100644
--- a/algorithms/graph/tarjan.cpp
+++ b/algorithms/graph/tarjan.cpp
@@ -1,8 +1,8 @@
/**
* Tarjan - Strongly Connected Components
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
vector<int> graph[MAX];
diff --git a/algorithms/graph/topological_sort.cpp b/algorithms/graph/topological_sort.cpp
index b4a7169..024828d 100644
--- a/algorithms/graph/topological_sort.cpp
+++ b/algorithms/graph/topological_sort.cpp
@@ -1,8 +1,8 @@
/**
* Topological Sort
*
- * Complexity (Time): O(n + m)
- * Complexity (Space): O(n + m)
+ * Complexity (Time): O(V + E)
+ * Complexity (Space): O(V + E)
*/
stack<int> S;
diff --git a/algorithms/structure/lazy_segment_tree.cpp b/algorithms/structure/lazy_segment_tree.cpp
index e53f12e..ea5c8a7 100644
--- a/algorithms/structure/lazy_segment_tree.cpp
+++ b/algorithms/structure/lazy_segment_tree.cpp
@@ -12,7 +12,7 @@ int N;
int v[MAX];
int tree[4 * MAX], lazy[4 * MAX];
-#define left(x) ((x << 1))
+#define left(x) (x << 1)
#define right(x) ((x << 1) + 1)
// Builds tree with elements from v (0-indexed)
diff --git a/algorithms/structure/segment_tree.cpp b/algorithms/structure/segment_tree.cpp
index 05d22eb..a579079 100644
--- a/algorithms/structure/segment_tree.cpp
+++ b/algorithms/structure/segment_tree.cpp
@@ -8,44 +8,54 @@
* Complexity (Space): O(n)
*/
-int N, tree[4 * MAX], v[MAX];
+int N;
+int v[MAX];
+int tree[4 * MAX];
+
+#define left(x) (x << 1)
+#define right(x) ((x << 1) + 1)
// Build tree with elements from v
-void build_tree(int node = 1, int a = 0, int b = N) {
- if (a > b) return;
+void build(int node = 1, int a = 0, int b = N - 1) {
+ if (a > b)
+ return;
if (a == b) {
tree[node] = v[a];
return;
}
- build_tree(node * 2, a, (a + b) / 2);
- build_tree(node * 2 + 1, 1 + (a + b) / 2, b);
+ build_tree(left(node), a, (a + b) / 2);
+ build_tree(right(node), 1 + (a + b) / 2, b);
tree[node] = tree[node * 2] + tree[node * 2 + 1];
}
// Update position idx with value val
-void update_tree(int idx, int val, int node = 1, int a = 0, int b = N) {
- if (a > b || a > idx || b < idx) return;
+void update(int idx, int val, int node = 1, int a = 0, int b = N - 1) {
+ if (a > b or a > idx or b < idx)
+ return;
if (a == b) {
tree[node] = val;
return;
}
- update_tree(idx, val, node * 2, a, (a + b) / 2);
- update_tree(idx, val, node * 2 + 1, 1 + (a + b) / 2, b);
+ update_tree(idx, val, left(node), a, (a + b) / 2);
+ update_tree(idx, val, right(node), 1 + (a + b) / 2, b);
tree[node] = tree[node * 2] + tree[node * 2 + 1];
}
// Return sum of [i,j]
-int query_tree(int i, int j, int node = 1, int a = 0, int b = N) {
- if (a > b || a > j || b < i) return 0;
+int query(int i, int j, int node = 1, int a = 0, int b = N - 1) {
+ if (a > b or a > j or b < i)
+ return 0;
- if (a >= i && b <= j) return tree[node];
+ if (i <= a and b <= j)
+ return tree[node];
- return query_tree(i, j, node * 2, a, (a + b) / 2) + \
- query_tree(i, j, node * 2 + 1, 1 + (a + b) / 2, b);
+ int q1 = query_tree(i, j, left(node), a, (a + b) / 2);
+ int q2 = query_tree(i, j, right(node), 1 + (a + b) / 2, b);
+ return q1 + q2;
}
diff --git a/notebook/gen_latex.py b/notebook/gen_latex.py
index 03ffba5..ef9134f 100644
--- a/notebook/gen_latex.py
+++ b/notebook/gen_latex.py
@@ -8,8 +8,8 @@ from pathlib import Path
dirs = [
'algorithms',
'misc',
-# 'contests',
-# 'problems'
+ 'contests',
+ 'problems'
]
parser = argparse.ArgumentParser()
@@ -67,22 +67,21 @@ for di in dirs:
if '*/' in line:
in_comment = False
- in_ctime = False
+ if len(sections) > 2:
+ output.write('\\subsubsection{' + title + '}\n')
+
+ in_complexity = 0
ctime, cspace = [], []
for line in comment:
if 'Complexity (time)' in line:
- in_ctime = True
+ in_complexity = 1
if 'Complexity (space)' in line:
- in_ctime = False
+ in_complexity = 2
- if in_ctime:
+ if in_complexity:
ctime.append(line)
-
- if len(sections) > 2:
- output.write('\\subsubsection{' + title + '}\n')
-
# Remove first \n after header comment
code = code[1:]
diff --git a/testing.py b/testing.py
new file mode 100644
index 0000000..74cd716
--- /dev/null
+++ b/testing.py
@@ -0,0 +1,53 @@
+from pathlib import Path
+
+dirs = [
+ 'algorithms',
+ 'misc',
+ 'contests',
+ 'problems'
+]
+
+def get_file_tree():
+ tree = {}
+ for di in dirs:
+ path_list = Path(di).glob('**/*.cpp')
+
+ for path in path_list:
+ branch = str(path).split('/')
+
+ curr = tree
+ for i in branch[:-2]:
+ if not i in curr:
+ curr[i] = {}
+ curr = curr[i]
+
+ if not branch[-2] in curr:
+ curr[branch[-2]] = []
+ curr[branch[-2]].append(str(path))
+
+ return tree
+
+
+def gen_code_latex(arr, depth):
+ for i in arr:
+ print('\\' + depth + '{' + i + '}')
+
+def gen_latex(tree):
+ stack = [ (tree, 0) ]
+ depth = ['chapter', 'section', 'subsection']
+
+ while len(stack) != 0:
+ x, h = stack.pop()
+ if type(x) == list:
+ for i in x:
+ gen_code_latex(x, depth[h])
+
+ #print('\\' + depth[h] + '{' + i + '}')
+ for i in x:
+ stack.append((x[i], h + 1))
+
+
+
+tree = get_file_tree()
+#print(tree)
+gen_latex(tree)
--
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