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| #include <iostream> #include <cstdio> #include <cstring> #include <cmath> #include <algorithm> #include <vector> #include <map> #include <utility> #ifdef XLor #define dbg(args...) do { cout << #args << " -> "; err(args); } while (0) void err() { std::cout << std::endl; } template<typename T, typename...Args> void err(T a, Args...args) { std::cout << a << ' '; err(args...); } #else #define dbg(...) #endif #define ms(a,b) memset(a,b,sizeof(a)) using namespace std; typedef long long ll; typedef pair<int,int> PII; const int mod = 998244353; const int inf = 1 << 30; const int maxn = 100000 + 5; inline int add(int x, int y) { x += y; return x >= mod ? x -= mod : x; } inline int sub(int x, int y) { x -= y; return x < 0 ? x += mod : x; } inline int mul(int x, int y) { return 1ll * x * y % mod; } inline int qpow(int x, ll n) { int r = 1; while (n > 0) { if (n & 1) r = 1ll * r * x % mod; n >>= 1; x = 1ll * x * x % mod; } return r; } inline int inv(int x) { return qpow(x, mod - 2); } int n, m, ans[maxn]; vector<int> edge[maxn * 2], bcc[maxn]; map<int,int> ew[maxn]; int cnt; namespace cactus { struct E { int to, nxt; } e[maxn * 2]; int head[maxn], ecnt; void adde(int u, int v) { e[++ecnt] = {v, head[u]}; head[u] = ecnt; } int tot, dfn[maxn], fa[maxn]; bool ring[maxn]; void clear(int n) { cnt = ecnt = tot = 0; for (int i = 1; i <= n; i++) { head[i] = dfn[i] = ans[i] = 0; } } void dfs(int u, int f) { dfn[u] = ++tot; for (int i = head[u]; i; i = e[i].nxt) { int v = e[i].to; if (v == f) continue; if (!dfn[v]) { fa[v] = u; ring[u] = false; dfs(v, u); if (!ring[u]) { edge[u].push_back(v); edge[v].push_back(u); } } else if (dfn[v] < dfn[u]) { cnt++; int rt = cnt + n; bcc[cnt].clear(); edge[rt].push_back(v); edge[v].push_back(rt); bcc[cnt].push_back(v); for (int x = u; x != v; x = fa[x]) { ring[x] = true; bcc[cnt].push_back(x); edge[rt].push_back(x); edge[x].push_back(rt); } ring[v] = true; } } } void build() { dfs(1, 0); } } void dp(int id) { vector<int>& ring = bcc[id]; int sz = (int)ring.size(); vector<int> w(sz, 0), pre(sz, 0), suf(sz, 0); for (int i = 0; i + 1 < sz; i++) { w[i] = ew[ring[i]][ring[i + 1]]; } w[sz - 1] = ew[ring[0]][ring[sz - 1]]; pre[0] = w[0]; suf[sz - 1] = w[sz - 1]; for (int i = 1; i < sz; i++) { pre[i] = mul(pre[i - 1], w[i]); } for (int i = sz - 2; i >= 0; i--) { suf[i] = mul(suf[i + 1], w[i]); } int p = ans[ring[0]]; for (int i = 1; i < sz; i++) { int u = ring[i]; ans[u] = mul(sub(1, pre[i - 1]), sub(1, suf[i])); ans[u] = mul(p, sub(1, ans[u])); } } void dfs(int u, int f) { // dbg(u, f); if (u > n) dp(u - n); for (int v: edge[u]) { if (v == f) continue; if (u <= n && v <= n) { ans[v] = mul(ans[u], ew[u][v]); } dfs(v, u); } } int main() { int T, kase = 0; scanf("%d", &T); while (T--) { scanf("%d%d", &n, &m); cactus::clear(n); for (int i = 1; i <= n; i++) ew[i].clear(); for (int i = 1; i <= 2 * n; i++) edge[i].clear(); for (int i = 1, u, v, a, b; i <= m; i++) { scanf("%d%d%d%d", &u, &v, &a, &b); int w = mul(a, inv(b)); cactus::adde(u, v); cactus::adde(v, u); ew[u][v] = w; ew[v][u] = w; } cactus::build(); ans[1] = 1; dfs(1, 0); int res = 0; for (int i = 1; i <= n; i++) res = add(res, ans[i]); printf("Case #%d: %d\n", ++kase, res); } return 0; }
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