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QOJ
ID | Problem | Submitter | Result | Time | Memory | Language | File size | Submit time | Judge time |
---|---|---|---|---|---|---|---|---|---|
#116506 | #4885. Triangular Cactus Paths | hos_lyric | TL | 6ms | 98768kb | C++14 | 12.1kb | 2023-06-29 13:40:03 | 2023-06-29 13:40:04 |
Judging History
answer
#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using Int = long long;
template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
static constexpr unsigned M = M_;
unsigned x;
constexpr ModInt() : x(0U) {}
constexpr ModInt(unsigned x_) : x(x_ % M) {}
constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
ModInt pow(long long e) const {
if (e < 0) return inv().pow(-e);
ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
}
ModInt inv() const {
unsigned a = M, b = x; int y = 0, z = 1;
for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
assert(a == 1U); return ModInt(y);
}
ModInt operator+() const { return *this; }
ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
explicit operator bool() const { return x; }
bool operator==(const ModInt &a) const { return (x == a.x); }
bool operator!=(const ModInt &a) const { return (x != a.x); }
friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////
constexpr unsigned MO = 998244353;
using Mint = ModInt<MO>;
constexpr int LIM_INV = 400'010;
Mint inv[LIM_INV], fac[LIM_INV], invFac[LIM_INV];
void prepare() {
inv[1] = 1;
for (int i = 2; i < LIM_INV; ++i) {
inv[i] = -((Mint::M / i) * inv[Mint::M % i]);
}
fac[0] = invFac[0] = 1;
for (int i = 1; i < LIM_INV; ++i) {
fac[i] = fac[i - 1] * i;
invFac[i] = invFac[i - 1] * inv[i];
}
}
Mint binom(Int n, Int k) {
if (n < 0) {
if (k >= 0) {
return ((k & 1) ? -1 : +1) * binom(-n + k - 1, k);
} else if (n - k >= 0) {
return (((n - k) & 1) ? -1 : +1) * binom(-k - 1, n - k);
} else {
return 0;
}
} else {
if (0 <= k && k <= n) {
assert(n < LIM_INV);
return fac[n] * invFac[k] * invFac[n - k];
} else {
return 0;
}
}
}
#ifndef LIBRA_GRAPH_GRAPH_H_
#define LIBRA_GRAPH_GRAPH_H_
#include <assert.h>
#include <ostream>
#include <utility>
#include <vector>
using std::ostream;
using std::pair;
using std::vector;
////////////////////////////////////////////////////////////////////////////////
// neighbors of u: [pt[u], pt[u + 1])
struct Graph {
int n;
vector<pair<int, int>> edges;
vector<int> pt;
vector<int> zu;
Graph() : n(0), edges() {}
explicit Graph(int n_) : n(n_), edges() {}
void ae(int u, int v) {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
edges.emplace_back(u, v);
}
void build(bool directed) {
const int edgesLen = edges.size();
pt.assign(n + 1, 0);
if (directed) {
for (int i = 0; i < edgesLen; ++i) {
++pt[edges[i].first];
}
for (int u = 0; u < n; ++u) pt[u + 1] += pt[u];
zu.resize(edgesLen);
for (int i = edgesLen; --i >= 0; ) {
zu[--pt[edges[i].first]] = edges[i].second;
}
} else {
for (int i = 0; i < edgesLen; ++i) {
++pt[edges[i].first];
++pt[edges[i].second];
}
for (int u = 0; u < n; ++u) pt[u + 1] += pt[u];
zu.resize(2 * edgesLen);
for (int i = edgesLen; --i >= 0; ) {
const int u = edges[i].first, v = edges[i].second;
zu[--pt[u]] = v;
zu[--pt[v]] = u;
}
}
}
inline int deg(int u) const {
return pt[u + 1] - pt[u];
}
inline int operator[](int j) const {
return zu[j];
}
friend ostream &operator<<(ostream &os, const Graph &g) {
os << "Graph(n=" << g.n << ";";
for (int u = 0; u < g.n; ++u) {
os << " " << u << ":[";
for (int j = g.pt[u]; j < g.pt[u + 1]; ++j) {
if (j != g.pt[u]) os << ",";
os << g[j];
}
os << "]";
}
os << ")";
return os;
}
};
////////////////////////////////////////////////////////////////////////////////
#endif // LIBRA_GRAPH_GRAPH_H_
// gg: bipartite graph between {vertex} and {biconnected component}
// (gg.n - n) biconnected components
// isolated point: not regarded as biconnected component (==> isolated in gg)
// f: DFS forest
struct Biconnected {
int n;
Graph g, f, gg;
Biconnected() : n(0), stackLen(0), zeit(0) {}
explicit Biconnected(int n_) : n(n_), g(n_), stackLen(0), zeit(0) {}
void ae(int u, int v) {
g.ae(u, v);
}
int stackLen;
vector<int> stack;
vector<int> par, rs;
int zeit;
vector<int> dis, fin, low;
vector<int> cntPar;
void dfs(int u) {
stack[stackLen++] = u;
dis[u] = low[u] = zeit++;
for (int j = g.pt[u]; j < g.pt[u + 1]; ++j) {
const int v = g[j];
if (par[u] == v && !cntPar[u]++) continue;
if (~dis[v]) {
if (low[u] > dis[v]) low[u] = dis[v];
} else {
f.ae(u, v);
par[v] = u;
rs[v] = rs[u];
dfs(v);
if (low[u] > low[v]) low[u] = low[v];
if (dis[u] <= low[v]) {
const int x = gg.n++;
for (; ; ) {
const int w = stack[--stackLen];
gg.ae(w, x);
if (w == v) break;
}
gg.ae(u, x);
}
}
}
fin[u] = zeit;
}
void build() {
g.build(false);
f = Graph(n);
gg = Graph(n);
stack.resize(n);
par.assign(n, -1);
rs.assign(n, -1);
zeit = 0;
dis.assign(n, -1);
fin.assign(n, -1);
low.assign(n, -1);
cntPar.assign(n, 0);
for (int u = 0; u < n; ++u) if (!~dis[u]) {
stackLen = 0;
rs[u] = u;
dfs(u);
}
f.build(true);
gg.build(false);
}
// Returns true iff u is an articulation point
// <=> # of connected components increases when u is removed.
inline bool isArt(int u) const {
return (gg.deg(u) >= 2);
}
// Returns w s.t. w is a child of u and a descendant of v in the DFS forest.
// Returns -1 instead if v is not a proper descendant of u
// O(log(deg(u))) time
int dive(int u, int v) const {
if (dis[u] < dis[v] && dis[v] < fin[u]) {
int j0 = f.pt[u], j1 = f.pt[u + 1];
for (; j0 + 1 < j1; ) {
const int j = (j0 + j1) / 2;
((dis[f[j]] <= dis[v]) ? j0 : j1) = j;
}
return f[j0];
} else {
return -1;
}
}
// Returns true iff there exists a v-w path when u is removed.
// O(log(deg(u))) time
bool isStillReachable(int u, int v, int w) const {
assert(0 <= u); assert(u < n);
assert(0 <= v); assert(v < n);
assert(0 <= w); assert(w < n);
assert(u != v);
assert(u != w);
if (rs[v] != rs[w]) return false;
if (rs[u] != rs[v]) return true;
const int vv = dive(u, v);
const int ww = dive(u, w);
if (~vv) {
if (~ww) {
return (vv == ww || (dis[u] > low[vv] && dis[u] > low[ww]));
} else {
return (dis[u] > low[vv]);
}
} else {
if (~ww) {
return (dis[u] > low[ww]);
} else {
return true;
}
}
}
};
////////////////////////////////////////////////////////////////////////////////
int N, M;
vector<int> A, B;
Biconnected C;
constexpr int E = 19;
constexpr int MAX_N = 400'010;
int dep[MAX_N];
int ppar[E][MAX_N];
int sum2[E][MAX_N];
int sum3[E][MAX_N];
void dfs(int u, int p) {
dep[u] = (~p) ? (dep[p] + 1) : 0;
ppar[0][u] = p;
for (int j = C.gg.pt[u]; j < C.gg.pt[u + 1]; ++j) {
const int v = C.gg[j];
if (p != v) {
dfs(v, u);
}
}
}
int lca(int u, int v) {
for (int e = E; --e >= 0; ) {
if (dep[u] - (1 << e) >= dep[v]) {
u = ppar[e][u];
}
if (dep[v] - (1 << e) >= dep[u]) {
v = ppar[e][v];
}
}
for (int e = E; --e >= 0; ) {
if (ppar[e][u] != ppar[e][v]) {
u = ppar[e][u];
v = ppar[e][v];
}
}
if (u != v) {
u = ppar[0][u];
v = ppar[0][v];
}
return u;
}
int main() {
prepare();
for (; ~scanf("%d%d", &N, &M); ) {
A.resize(M);
B.resize(M);
for (int i = 0; i < M; ++i) {
scanf("%d%d", &A[i], &B[i]);
--A[i];
--B[i];
}
C = Biconnected(N);
for (int i = 0; i < M; ++i) {
C.ae(A[i], B[i]);
}
C.build();
cerr<<"gg = "<<C.gg<<endl;
fill(dep, dep + C.gg.n, -1);
for (int u = 0; u < C.gg.n; ++u) if (!~dep[u]) {
dfs(u, -1);
}
fill(sum2[0], sum2[0] + C.gg.n, 0);
for (int u = N; u < C.gg.n; ++u) {
((C.gg.deg(u) == 2) ? sum2 : sum3)[0][u] = 1;
}
for (int e = 0; e < E - 1; ++e) {
for (int u = 0; u < C.gg.n; ++u) {
const int p = ppar[e][u];
if (~p) {
ppar[e + 1][u] = ppar[e][p];
sum2[e + 1][u] = sum2[e][u] + sum2[e][p];
sum3[e + 1][u] = sum3[e][u] + sum3[e][p];
} else {
ppar[e + 1][u] = -1;
sum2[e + 1][u] = sum2[e][u];
sum3[e + 1][u] = sum3[e][u];
}
}
}
int Q;
scanf("%d", &Q);
for (; Q--; ) {
int S, T, K;
scanf("%d%d%d", &S, &T, &K);
--S;
--T;
int s2 = 0, s3 = 0;
auto add = [&](int u, int d) -> void {
for (int e = E; --e >= 0; ) if (d >> e & 1) {
s2 += sum2[e][u];
s3 += sum3[e][u];
u = ppar[e][u];
}
};
const int l = lca(S, T);
add(S, dep[S] - dep[l]);
add(T, dep[T] - dep[l]);
if (l >= N) {
++((C.gg.deg(l) == 2) ? s2 : s3);
}
cerr<<"s2 = "<<s2<<", s3 = "<<s3<<endl;
Mint ans = 0;
if (s2 + s3 <= K && K <= s2 + 2 * s3) {
ans = binom(s3, K - (s2 + s3));
}
printf("%u\n", ans.x);
}
}
return 0;
}
Details
Tip: Click on the bar to expand more detailed information
Test #1:
score: 100
Accepted
time: 6ms
memory: 97472kb
input:
8 10 1 2 2 3 3 1 3 4 4 5 5 6 6 4 4 7 7 8 8 4 6 1 1 0 1 1 1 1 4 3 6 2 4 5 7 4 3 4 2
output:
1 0 1 2 1 0
result:
ok 6 numbers
Test #2:
score: 0
Accepted
time: 1ms
memory: 98768kb
input:
2 1 1 2 8 1 1 0 1 1 1 1 2 0 1 2 1 2 1 0 2 1 1 2 2 0 2 2 1
output:
1 0 0 1 0 1 1 0
result:
ok 8 numbers
Test #3:
score: -100
Time Limit Exceeded
input:
50 70 41 24 9 15 29 19 21 11 1 14 5 27 34 48 10 32 34 49 46 3 22 33 34 39 16 30 22 45 7 16 25 30 43 17 22 44 5 25 41 49 29 32 39 25 10 4 45 27 13 38 29 7 3 35 14 30 50 2 8 11 13 35 18 26 34 40 38 36 7 19 12 3 25 26 30 42 21 8 12 46 44 33 14 31 47 2 25 46 20 19 49 24 15 43 18 25 13 36 27 22 4 32 30 3...
output:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 4 0 0 15 5 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 2 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 0 0 0 0 3 0 6 0 0 0 0 7 0 6 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0...