【BZOJ1093】[ZJOI2007]最大半连通子图【SCC】【DAG】【DP】

【题目链接】

先SCC缩点，在DAG上跑最长路，顺便统计出到达每个点的最长路的路径个数。

/* Pigonometry */
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <map>

using namespace std;

typedef pair<int, int> pii;

const int maxn = 100005, maxm = 1000005, maxs = 100005, maxq = maxs;

int n, m, p, head[maxn], cnt, dfn[maxn], low[maxn], clo, belong[maxn], tot, size[maxn], du[maxn], dp[maxn], num[maxn];
int sta[maxs], top, q[maxq];
int ans1, ans2;
bool ins[maxn];

struct _edge {
int v, next;
} g[maxm << 1];

vector<int> e[maxn];
map<pii, bool> vis;

inline int iread() {
int f = 1, x = 0; char ch = getchar();
for(; ch < '0' || ch > '9'; ch = getchar()) f = ch == '-' ? -1 : 1;
for(; ch >= '0' && ch <= '9'; ch = getchar()) x = x * 10 + ch - '0';
return f * x;
}

inline void add(int u, int v) {
g[cnt] = (_edge){v, head[u]};
head[u] = cnt++;
}

inline void tarjan(int x) {
dfn[x] = low[x] = ++clo;
ins[sta[++top] = x] = 1;
for(int i = head[x]; ~i; i = g[i].next)
if(!dfn[g[i].v]) tarjan(g[i].v), low[x] = min(low[x], low[g[i].v]);
else if(ins[g[i].v]) low[x] = min(low[x], dfn[g[i].v]);
if(dfn[x] == low[x]) {
tot++;
while(1) {
int u = sta[top--];
ins[u] = 0;
belong[u] = tot;
size[tot]++;
if(u == x) break;
}
}
}

inline void topo() {
int h = 0, t = 0;
for(int i = 1; i <= tot; i++) if(!du[i]) dp[q[t++] = i] = size[i], num[i] = 1;
while(h != t) {
int u = q[h++];
for(int i = 0; i < e[u].size(); i++) {
int v = e[u][i];
if(dp[v] < dp[u] + size[v]) {
dp[v] = dp[u] + size[v];
num[v] = num[u];
}
else if(dp[v] == dp[u] + size[v])
(num[v] += num[u]) %= p;
du[v]--;
if(!du[v]) q[t++] = v;
}
}
}

int main() {
n = iread(); m = iread(); p = iread();
for(int i = 1; i <= n; i++) head[i] = -1; cnt = 0;

for(int i = 1; i <= m; i++) {
int u = iread(), v = iread();
add(u, v);
}

for(int i = 1; i <= n; i++) if(!dfn[i]) tarjan(i);

for(int u = 1; u <= n; u++) for(int i = head[u]; ~i; i = g[i].next) if(belong[u] != belong[g[i].v] && !vis[pii(belong[u], belong[g[i].v])])
e[belong[u]].push_back(belong[g[i].v]), du[belong[g[i].v]]++, vis[pii(belong[u], belong[g[i].v])] = 1;

topo();

for(int i = 1; i <= tot; i++)
if(dp[i] > ans1) ans1 = dp[i], ans2 = num[i];
else if(dp[i] == ans1) (ans2 += num[i]) %= p;

printf("%d\n%d\n", ans1, ans2);
return 0;
}