有向图强连通分量

给你一个有向图，然后问你，加入多少条边，能使这个图构成成一个强连通分量

首先，把强连通分量缩成一个点，然后现在就成了一个dag，这个dag中 看只有入度 和只有出度的点 取max就好了

#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <cstring>
#include <stack>
#include <vector>
#include <map>
#include <algorithm>
using namespace std;

const int MaxN = 50000, MaxM = 200000;

int T, n, m, all, Timetot, Scctot; 
int pre[MaxM + 5], last[MaxN + 5], other[MaxM + 5];
int pr[MaxM + 5], las[MaxN + 5], oth[MaxM + 5];
int dfn[MaxN + 5], low[MaxN + 5], col[MaxN + 5];
int ind[MaxN + 5], oud[MaxN + 5];
bool usedind[MaxN + 5], usedoud[MaxN + 5], usedused[MaxN + 5];
stack <int> sta;
vector <int> Scc[MaxN + 5];
map <pair<int, int>, bool> used;

void Build(int x, int y)
{
    pre[++all] = last[x];
    last[x] = all;
    other[all] = y;
}

void Init()
{
    all = -1; memset(last, -1, sizeof(last));
    scanf("%d%d", &n, &m);
    for (int i = 1; i <= m; i++) {
        int u, v;
        scanf("%d%d", &u, &v);
        Build(u, v); 
    }
}

void Dfs_Scc(int x, int fa)
{
    dfn[x] = low[x] = ++Timetot;
    sta.push(x);    //强连通分量 存点不存边
    int ed = last[x], dr;
    while (ed != -1) {
        dr = other[ed];
        if (!dfn[dr]) {
            Dfs_Scc(dr, x);
            low[x] = min(low[x], low[dr]);
        }
        else if (!col[dr] && dfn[dr] < dfn[x]) {
            low[x] = min(low[x], dfn[dr]);
        }
        ed = pre[ed];
    }
    if (low[x] >= dfn[x]) { //强连通分量注意是while出来以后判
        Scc[++Scctot].clear();
        while (true) {
            int u = sta.top(); sta.pop();
            col[u] = Scctot;
            Scc[Scctot].push_back(u);
            if (u == x) break;
        }
    }
}

void rBuild(int x, int y)
{
    pr[++all] = las[x];
    las[x] = all;
    oth[all] = y;
    ind[x]++;
    oud[y]++;
}

void ReBuildGraph()
{
    used.clear();
    all = -1; memset(las, -1, sizeof(las)); //all用原来的，las也记得清成-1
    for (int i = 1; i <= n; i++) {
        int ed = last[i], dr;
        while (ed != -1) {
            dr = other[ed];
            if (col[i] != col[dr] && !used[make_pair(col[i], col[dr])]) {
                used[make_pair(col[i], col[dr])] = true;
                rBuild(col[i], col[dr]);
            }
            ed = pre[ed];
        }
    }
}

void Solve()
{
    Timetot = Scctot = 0;
    memset(dfn, 0, sizeof(dfn));    //dfn, low每次必须清空
    memset(low, 0, sizeof(low));
    memset(col, 0, sizeof(col));
    memset(ind, 0, sizeof(ind));
    memset(oud, 0, sizeof(oud));
    for (int i = 1; i <= n; i++) 
        if (!dfn[i]) Dfs_Scc(i, -1);
    ReBuildGraph();
    memset(usedused, 0, sizeof(usedused));
    int num = 0;
    for (int i = 1; i <= n; i++) {
        if (!usedused[col[i]]) {
            usedused[col[i]] = true;
            num++;
        }
    }
    memset(usedind, 0, sizeof(usedind));
    memset(usedoud, 0, sizeof(usedoud));
    int sum_ind = 0, sum_oud = 0;
    for (int i = 1; i <= n; i++) {
        if (ind[col[i]] == 0 && !usedind[col[i]]) {
            usedind[col[i]] = true;
            sum_ind++;
        }
        if (oud[col[i]] == 0 && !usedoud[col[i]]) {
            usedoud[col[i]] = true;
            sum_oud++;
        }
    }
    if (num == 1) printf("0
");
    else printf("%d
", max(sum_ind, sum_oud));
}

int main()
{
    scanf("%d", &T);
    for (int cas = 1; cas <= T; cas++) {
        Init();
        Solve();
    }
    return 0;
}

#include <cstdio>#include <cstdlib>#include <cmath>#include <cstring>#include <stack>#include <vector>#include <map>#include <algorithm>usingnamespacestd; constint MaxN = 50000, MaxM = 200000; int T, n, m, all, Timetot, Scctot; int pre[MaxM + 5], last[MaxN + 5], other[MaxM + 5]; int pr[MaxM + 5], las[MaxN + 5], oth[MaxM + 5]; int dfn[MaxN + 5], low[MaxN + 5], col[MaxN + 5]; int ind[MaxN + 5], oud[MaxN + 5]; bool usedind[MaxN + 5], usedoud[MaxN + 5], usedused[MaxN + 5]; stack <int> sta; vector <int> Scc[MaxN + 5]; map <pair<int, int>, bool> used; void Build(int x, int y) { pre[++all] = last[x]; last[x] = all; other[all] = y; } void Init() { all = -1; memset(last, -1, sizeof(last)); scanf("%d%d", &n, &m); for (int i = 1; i <= m; i++) { int u, v; scanf("%d%d", &u, &v); Build(u, v); } } void Dfs_Scc(int x, int fa) { dfn[x] = low[x] = ++Timetot; sta.push(x); //强连通分量 存点不存边int ed = last[x], dr; while (ed != -1) { dr = other[ed]; if (!dfn[dr]) { Dfs_Scc(dr, x); low[x] = min(low[x], low[dr]); } elseif (!col[dr] && dfn[dr] < dfn[x]) { low[x] = min(low[x], dfn[dr]); } ed = pre[ed]; } if (low[x] >= dfn[x]) { //强连通分量注意是while出来以后判 Scc[++Scctot].clear(); while (true) { int u = sta.top(); sta.pop(); col[u] = Scctot; Scc[Scctot].push_back(u); if (u == x) break; } } } void rBuild(int x, int y) { pr[++all] = las[x]; las[x] = all; oth[all] = y; ind[x]++; oud[y]++; } void ReBuildGraph() { used.clear(); all = -1; memset(las, -1, sizeof(las)); //all用原来的，las也记得清成-1for (int i = 1; i <= n; i++) { int ed = last[i], dr; while (ed != -1) { dr = other[ed]; if (col[i] != col[dr] && !used[make_pair(col[i], col[dr])]) { used[make_pair(col[i], col[dr])] = true; rBuild(col[i], col[dr]); } ed = pre[ed]; } } } void Solve() { Timetot = Scctot = 0; memset(dfn, 0, sizeof(dfn)); //dfn, low每次必须清空memset(low, 0, sizeof(low)); memset(col, 0, sizeof(col)); memset(ind, 0, sizeof(ind)); memset(oud, 0, sizeof(oud)); for (int i = 1; i <= n; i++) if (!dfn[i]) Dfs_Scc(i, -1); ReBuildGraph(); memset(usedused, 0, sizeof(usedused)); int num = 0; for (int i = 1; i <= n; i++) { if (!usedused[col[i]]) { usedused[col[i]] = true; num++; } } memset(usedind, 0, sizeof(usedind)); memset(usedoud, 0, sizeof(usedoud)); int sum_ind = 0, sum_oud = 0; for (int i = 1; i <= n; i++) { if (ind[col[i]] == 0 && !usedind[col[i]]) { usedind[col[i]] = true; sum_ind++; } if (oud[col[i]] == 0 && !usedoud[col[i]]) { usedoud[col[i]] = true; sum_oud++; } } if (num == 1) printf("0 "); elseprintf("%d ", max(sum_ind, sum_oud)); } int main() { scanf("%d", &T); for (int cas = 1; cas <= T; cas++) { Init(); Solve(); } return0; }