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SCC Readme 修正 #3

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Merged
suisen-cp merged 2 commits into from
Sep 9, 2020
Merged

SCC Readme 修正 #3

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4affbac
SCC: SCC#id を追加. Readme に使用例を追加
suisen-cp Sep 9, 2020
fba3f50
SCC: Readme 修正
suisen-cp Sep 9, 2020
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23 changes: 23 additions & 0 deletions SCC/Readme.md
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Original file line number Diff line number Diff line change
Expand Up @@ -48,3 +48,26 @@ public int[][] build()
計算量

追加した辺の本数を `m` として $O(n + m)$

### id

```java
public int id(int i)
```

頂点 `i` が (トポロジカル順序において) 何番目の強連結成分に属しているかを返します。即ち，`build` で得られる「頂点の配列」の配列を `g` とすると、`g[id(i)][j] = i` なる `j` が存在します。

__ただし、`build` を呼ぶ前にこのメソッドが呼ばれた場合は、実行時例外 `UnsupportedOperationException` が発生します。__

制約

- __`build` メソッドを既に呼んでいる__
- `0 <= i < n`

計算量

$O(1)$

## 使用例

[AtCoder Library Practice Contest G - SCC](https://atcoder.jp/contests/practice2/submissions/16603978)
14 changes: 13 additions & 1 deletion SCC/SCC.java
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Original file line number Diff line number Diff line change
Expand Up @@ -11,18 +11,30 @@ public Edge(int from, int to) {
int m;
final java.util.ArrayList<Edge> unorderedEdges;
final int[] start;
final int[] ids;
boolean hasBuilt = false;

public SCC(int n) {
this.n = n;
this.unorderedEdges = new java.util.ArrayList<>();
this.start = new int[n + 1];
this.ids = new int[n];
}

public void addEdge(int from, int to) {
unorderedEdges.add(new Edge(from, to));
start[from + 1]++;
this.m++;
}

public int id(int i) {
if (!hasBuilt) {
throw new UnsupportedOperationException(
"Graph hasn't been built."
);
}
return ids[i];
}

public int[][] build() {
for (int i = 1; i <= n; i++) {
Expand All @@ -42,7 +54,6 @@ public int[][] build() {
int[] vis = new int[n];
int[] low = new int[n];
int[] ord = new int[n];
int[] ids = new int[n];
java.util.Arrays.fill(ord, -1);
// u = lower32(stack[i]) : visiting vertex
// j = upper32(stack[i]) : jth child
Expand Down Expand Up @@ -110,6 +121,7 @@ public int[][] build() {
int cmp = ids[i];
groups[cmp][--counts[cmp]] = i;
}
hasBuilt = true;
return groups;
}
}