From b459a160dbf0c1d027fb80a0ecbc77d579e725d0 Mon Sep 17 00:00:00 2001
From: Naoto Mizuno <naotomizuno@preferred.jp>
Date: Sat, 19 Sep 2020 20:34:00 +0900
Subject: [PATCH] Port SCC

---
 README.md               |   2 +-
 README_ja.md            |   2 +-
 atcoder/_scc.py         | 101 ++++++++++++++++++++++++++++++++++++++++
 atcoder/scc.py          |  17 +++++++
 example/scc_practice.py |  27 +++++++++++
 5 files changed, 147 insertions(+), 2 deletions(-)
 create mode 100644 atcoder/_scc.py
 create mode 100644 atcoder/scc.py
 create mode 100644 example/scc_practice.py

diff --git a/README.md b/README.md
index 2abe4d9..b866021 100644
--- a/README.md
+++ b/README.md
@@ -23,6 +23,7 @@ ac-library-python is a Python port of [AtCoder Library (ACL)](https://atcoder.jp
 #### Graph
 
 + [Disjoint Set Union (DSU)](https://github.com/atcoder/ac-library/blob/master/document_en/dsu.md)
++ scc
 
 ### Work in progress
 
@@ -41,7 +42,6 @@ ac-library-python is a Python port of [AtCoder Library (ACL)](https://atcoder.jp
 
 + maxflow
 + mincostflow
-+ scc
 + twosat
 
 ## Install
diff --git a/README_ja.md b/README_ja.md
index 0c29fc1..811e765 100644
--- a/README_ja.md
+++ b/README_ja.md
@@ -21,6 +21,7 @@ ac-library-pythonは、[AtCoder Library (ACL)](https://atcoder.jp/posts/517)のP
 #### グラフ
 
 + [Disjoint Set Union (DSU)](https://github.com/atcoder/ac-library/blob/master/document_ja/dsu.md)
++ scc
 
 ### 準備中
 
@@ -39,7 +40,6 @@ ac-library-pythonは、[AtCoder Library (ACL)](https://atcoder.jp/posts/517)のP
 
 + maxflow
 + mincostflow
-+ scc
 + twosat
 
 ## インストール
diff --git a/atcoder/_scc.py b/atcoder/_scc.py
new file mode 100644
index 0000000..7a4c850
--- /dev/null
+++ b/atcoder/_scc.py
@@ -0,0 +1,101 @@
+import copy
+import sys
+import typing
+
+
+class CSR:
+    def __init__(
+            self, n: int, edges: typing.List[typing.Tuple[int, int]]) -> None:
+        self.start = [0] * (n + 1)
+        self.elist = [0] * len(edges)
+
+        for e in edges:
+            self.start[e[0] + 1] += 1
+
+        for i in range(1, n + 1):
+            self.start[i] += self.start[i - 1]
+
+        counter = copy.deepcopy(self.start)
+        for e in edges:
+            self.elist[counter[e[0]]] = e[1]
+            counter[e[0]] += 1
+
+
+class SCCGraph:
+    '''
+    Reference:
+    R. Tarjan,
+    Depth-First Search and Linear Graph Algorithms
+    '''
+
+    def __init__(self, n: int) -> None:
+        self._n = n
+        self._edges = []
+
+    def num_vertices(self) -> int:
+        return self._n
+
+    def add_edge(self, from_vertex: int, to_vertex: int) -> None:
+        self._edges.append((from_vertex, to_vertex))
+
+    def scc_ids(self) -> typing.Tuple[int, typing.List[int]]:
+        g = CSR(self._n, self._edges)
+        now_ord = 0
+        group_num = 0
+        visited = []
+        low = [0] * self._n
+        order = [-1] * self._n
+        ids = [0] * self._n
+
+        sys.setrecursionlimit(max(self._n + 1000, sys.getrecursionlimit()))
+
+        def dfs(v: int) -> None:
+            nonlocal now_ord
+            nonlocal group_num
+            nonlocal visited
+            nonlocal low
+            nonlocal order
+            nonlocal ids
+
+            low[v] = now_ord
+            order[v] = now_ord
+            now_ord += 1
+            visited.append(v)
+            for i in range(g.start[v], g.start[v + 1]):
+                to = g.elist[i]
+                if order[to] == -1:
+                    dfs(to)
+                    low[v] = min(low[v], low[to])
+                else:
+                    low[v] = min(low[v], order[to])
+
+            if low[v] == order[v]:
+                while True:
+                    u = visited[-1]
+                    visited.pop()
+                    order[u] = self._n
+                    ids[u] = group_num
+                    if u == v:
+                        break
+                group_num += 1
+
+        for i in range(self._n):
+            if order[i] == -1:
+                dfs(i)
+
+        for i in range(self._n):
+            ids[i] = group_num - 1 - ids[i]
+
+        return group_num, ids
+
+    def scc(self) -> typing.List[typing.List[int]]:
+        ids = self.scc_ids()
+        group_num = ids[0]
+        counts = [0] * group_num
+        for x in ids[1]:
+            counts[x] += 1
+        groups = [[] for _ in range(group_num)]
+        for i in range(self._n):
+            groups[ids[1][i]].append(i)
+
+        return groups
diff --git a/atcoder/scc.py b/atcoder/scc.py
new file mode 100644
index 0000000..15ba45c
--- /dev/null
+++ b/atcoder/scc.py
@@ -0,0 +1,17 @@
+import typing
+
+import atcoder._scc
+
+
+class SCCGraph:
+    def __init__(self, n: int = 0) -> None:
+        self._internal = atcoder._scc.SCCGraph(n)
+
+    def add_edge(self, from_vertex: int, to_vertex: int) -> None:
+        n = self._internal.num_vertices()
+        assert 0 <= from_vertex < n
+        assert 0 <= to_vertex < n
+        self._internal.add_edge(from_vertex, to_vertex)
+
+    def scc(self) -> typing.List[typing.List[int]]:
+        return self._internal.scc()
diff --git a/example/scc_practice.py b/example/scc_practice.py
new file mode 100644
index 0000000..f75e85a
--- /dev/null
+++ b/example/scc_practice.py
@@ -0,0 +1,27 @@
+# https://atcoder.jp/contests/practice2/tasks/practice2_b
+
+import sys
+
+from atcoder.scc import SCCGraph
+
+
+def main() -> None:
+    n, m = map(int, sys.stdin.readline().split())
+    g = SCCGraph(n)
+
+    for i in range(m):
+        u, v = map(int, sys.stdin.readline().split())
+        g.add_edge(u, v)
+
+    scc = g.scc()
+
+    print(len(scc))
+    for v in scc:
+        print(len(v), end='')
+        for x in v:
+            print(f' {x}', end='')
+        print('')
+
+
+if __name__ == '__main__':
+    main()