图论模板小汇总

涉及二分图，强连通分量，割点（边），点（边）双连通分量。

//二分图
bool dfs(int x) {
	for(int i = hd[x]; i; i = nxt[i]) if(!v[to[i]]) {
		v[to[i]] = 1;
		if(!f[to[i]] || dfs(f[to[i]])) {f[to[i]] = x; return 1;}
	}
	return 0;
}
for(int i = 1; i <= n; i++) {
	memset(v, 0, sizeof v);
	if(dfs(i)) ans++;
}

//强连通分量
void tj(int x) {
	dfn[x] = low[x] = ++tm, v[x] = 1, st[++tp] = x;
	for(int i = hd[x]; i; i = nxt[i])
	if(!dfn[to[i]]) tj(to[i]), low[x] = min(low[x], low[to[i]]);
	else if(v[to[i]]) low[x] = min(low[x], dfn[to[i]]);
	if(dfn[x] == low[x]) {
		cnt++;
		do bl[tmp=st[tp--]] = cnt, v[tmp] = 0; while(tmp != x);
	}
}

//求割点，v[x] = 2表示x是割点 
void tj(int x) {
	dfn[x] = low[x] = ++tm, v[x] = 1;
	for(int i = hd[x]; i; i = nxt[i])
	if(!v[to[i]]) {
		tj(to[i]), low[x] = min(low[x], low[to[i]]);
		if(dfn[x] <= low[to[i]]) v[x]++;
	} else low[x] = min(low[x], dfn[to[i]]);
	if(v[x] > 2-(x!=1)) v[x] = 2; else v[x] = 1;
}

//求割边，v[p] = 1表示p是割边 
void tj(int x, int p) {
	dfn[x] = low[x] = ++tm;
	for(int i = hd[x]; i; i = nxt[i]) if(i != p) {
		if(!dfn[to[i]]) tj(to[i], i^1), low[x] = min(low[x], low[to[i]]);
		else low[x] = min(low[x], dfn[to[i]]);
	}
	if(dfn[x] == low[x]) v[p] = 1;
}

//点双连通分量
void tj(int x) {
	dfn[x] = low[x] = ++tm;
	for(int i = hd[x]; i; i = nxt[i])
	if(!dfn[to[i]]) {
		st[++tp] = i, tj(to[i]), low[x] = min(low[x], low[to[i]]);
		if(dfn[x] <= low[to[i]]) {
			cnt++, bl[cnt][++sz[cnt]] = x;
			do bl[cnt][++sz[cnt]] = to[tmp=st[tp--]]; while(tmp != i);
		}
	} else low[x] = min(low[x], dfn[to[i]]);
}

//边双连通分量
void tj(int x, int p) {
	dfn[x] = low[x] = ++tm, st[++tp] = x;
	for(int i = hd[x]; i; i = nxt[i]) if(i != p) {
		if(!dfn[to[i]]) tj(to[i], i^1), low[x] = min(low[x], low[to[i]]);
		else low[x] = min(low[x], dfn[to[i]]);
	}
	if(dfn[x] == low[x]) {
		cnt++;
		do bl[tmp=st[tp--]] = cnt; while(tmp != x);
	}
}