| # |
Submission time |
Handle |
Problem |
Language |
Result |
Execution time |
Memory |
| 251338 |
2020-07-20T21:37:04 Z |
rqi |
Kangaroo (CEOI16_kangaroo) |
C++14 |
|
2000 ms |
32120 KB |
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str;
typedef pair<int,int> pi;
typedef pair<ll,ll> pl;
typedef pair<db,db> pd;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<db> vd;
typedef vector<str> vs;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<pd> vpd;
#define mp make_pair
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend()
#define rsz resize
#define ins insert
#define ft front()
#define bk back()
#define pf push_front
#define pb push_back
#define eb emplace_back
#define lb lower_bound
#define ub upper_bound
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)
const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
template<class T> bool ckmin(T& a, const T& b) {
return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) {
return a < b ? a = b, 1 : 0; }
int pct(int x) { return __builtin_popcount(x); }
int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x))
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0
int fstTrue(function<bool(int)> f, int lo, int hi) {
hi ++; assert(lo <= hi); // assuming f is increasing
while (lo < hi) { // find first index such that f is true
int mid = (lo+hi)/2;
f(mid) ? hi = mid : lo = mid+1;
}
return lo;
}
// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);
template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }
template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }
// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
template<class A> str ts(complex<A> c) {
stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
str res = ""; F0R(i,SZ) res += char('0'+b[i]);
return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
bool fst = 1; str res = "{";
for (const auto& x: v) {
if (!fst) res += ", ";
fst = 0; res += ts(x);
}
res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
return "("+ts(p.f)+", "+ts(p.s)+")"; }
// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) {
pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) {
pr(h); if (sizeof...(t)) pr(" "); ps(t...); }
// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
cerr << ts(h); if (sizeof...(t)) cerr << ", ";
DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "LINE(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 0
#endif
// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
unsyncIO();
// cin.exceptions(cin.failbit);
// throws exception when do smth illegal
// ex. try to read letter into int
if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
/**
* Description: pre-compute factorial mod inverses,
* assumes $MOD$ is prime and $SZ < MOD$.
* Time: O(SZ)
* Source: KACTL
* Verification: https://dmoj.ca/problem/tle17c4p5
*/
vi invs, fac, ifac;
void genFac(int SZ) {
invs.rsz(SZ), fac.rsz(SZ), ifac.rsz(SZ);
invs[1] = fac[0] = ifac[0] = 1;
FOR(i,2,SZ) invs[i] = MOD-(ll)MOD/i*invs[MOD%i]%MOD;
FOR(i,1,SZ) {
fac[i] = (ll)fac[i-1]*i%MOD;
ifac[i] = (ll)ifac[i-1]*invs[i]%MOD;
}
}
ll comb(int a, int b) {
if (a < b || b < 0) return 0;
return (ll)fac[a]*ifac[b]%MOD*ifac[a-b]%MOD;
}
/**
* Description: modular arithmetic operations
* Source:
* KACTL
* https://codeforces.com/blog/entry/63903
* https://codeforces.com/contest/1261/submission/65632855 (tourist)
* https://codeforces.com/contest/1264/submission/66344993 (ksun)
* also see https://github.com/ecnerwala/cp-book/blob/master/src/modnum.hpp (ecnerwal)
* Verification:
* https://open.kattis.com/problems/modulararithmetic
*/
#pragma once
template <int MOD, int RT> struct mint {
static const int mod = MOD;
static mint rt() { return RT; } // primitive root for FFT
int v; explicit operator int() const { return v; } // don't silently convert to int
mint() { v = 0; }
mint(ll _v) { v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
if (v < 0) v += MOD; }
friend bool operator==(const mint& a, const mint& b) {
return a.v == b.v; }
friend bool operator!=(const mint& a, const mint& b) {
return !(a == b); }
friend bool operator<(const mint& a, const mint& b) {
return a.v < b.v; }
friend void re(mint& a) { ll x; re(x); a = mint(x); }
friend str ts(mint a) { return ts(a.v); }
mint& operator+=(const mint& m) {
if ((v += m.v) >= MOD) v -= MOD;
return *this; }
mint& operator-=(const mint& m) {
if ((v -= m.v) < 0) v += MOD;
return *this; }
mint& operator*=(const mint& m) {
v = (ll)v*m.v%MOD; return *this; }
mint& operator/=(const mint& m) { return (*this) *= inv(m); }
friend mint pow(mint a, ll p) {
mint ans = 1; assert(p >= 0);
for (; p; p /= 2, a *= a) if (p&1) ans *= a;
return ans;
}
friend mint inv(const mint& a) { assert(a.v != 0);
return pow(a,MOD-2); }
mint operator-() const { return mint(-v); }
mint& operator++() { return *this += 1; }
mint& operator--() { return *this -= 1; }
friend mint operator+(mint a, const mint& b) { return a += b; }
friend mint operator-(mint a, const mint& b) { return a -= b; }
friend mint operator*(mint a, const mint& b) { return a *= b; }
friend mint operator/(mint a, const mint& b) { return a /= b; }
};
typedef mint<MOD,3> mi;
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;
vector<vmi> scmb; // small combinations
void genComb(int SZ) {
scmb.assign(SZ,vmi(SZ)); scmb[0][0] = 1;
FOR(i,1,SZ) F0R(j,i+1)
scmb[i][j] = scmb[i-1][j]+(j?scmb[i-1][j-1]:0);
}
/**
* Description: Multiply two polynomials. For xor convolution
* ignore \texttt{m}. If product of sizes is at most a certain
* threshold (ex. 10000) then it's faster to multiply directly.
* Time: O(N\log N)
* Source:
* KACTL
* https://cp-algorithms.com/algebra/fft.html
* https://csacademy.com/blog/fast-fourier-transform-and-variations-of-it
* maroonrk
* Verification:
* https://judge.yosupo.jp/problem/convolution_mod
* SPOJ polymul, CSA manhattan, CF Perfect Encoding
* http://codeforces.com/contest/632/problem/E
*/
template<class T> void fft(vector<T>& A, bool inv = 0) {
int n = sz(A); vector<T> B(n);
assert((T::mod-1)%n == 0); T r = pow(T::rt(),T::mod/n);
for(int b = n/2; b; b /= 2, swap(A,B)) {
T w = pow(r,b), m = 1;
for(int i = 0; i < n; i += b*2, m *= w) F0R(j,b) {
T u = A[i+j], v = A[i+j+b]*m;
B[i/2+j] = u+v; B[i/2+j+n/2] = u-v;
}
}
if (inv) { reverse(1+all(A));
T z = T(1)/T(n); trav(t,A) t *= z; }
}
template<class T> vector<T> mul(vector<T> A, vector<T> B) {
if (!min(sz(A),sz(B))) return {};
int s = sz(A)+sz(B)-1, n = 1; while (n < s) n *= 2;
bool eq = A == B; A.rsz(n), fft(A);
if (eq) B = A; // squaring poly
else B.rsz(n), fft(B);
F0R(i,n) A[i] *= B[i];
fft(A,1); A.rsz(s); return A;
}
/**
* Description: Multiply two polynomials with arbitrary $MOD.$
* Source: KACTL, https://cp-algorithms.com/algebra/fft.html, maroonrk
* Verification: see FFT
*/
template<class M, class T> vector<M> go(vector<T> x, vector<T> y) {
auto con = [](const vector<T>& v) {
vector<M> w(sz(v)); F0R(i,sz(v)) w[i] = (int)v[i];
return w; };
return mul(con(x),con(y));
}
template<class T> vector<T> MUL(const vector<T>& A, const vector<T>& B) {
using m0 = mint<(997<<20)+1,3>; // 2^20 * 997 + 1
using m1 = mint<(1003<<20)+1,6>; // 2^20 * 1003 + 1
using m2 = mint<(1005<<20)+1,7>; // 2^20 * 1005 + 1
auto c0 = go<m0>(A,B); auto c1 = go<m1>(A,B); auto c2 = go<m2>(A,B);
int n = sz(c0); vector<T> res(n);
m1 r01 = 1/m1(m0::mod); m2 r02 = 1/m2(m0::mod), r12 = 1/m2(m1::mod);
F0R(i,n) {
int a = c0[i].v, b = ((c1[i]-a)*r01).v, c = ((c2[i]-a)*r02-b)*r12.v;
res[i] = (T(c)*m1::mod+b)*m0::mod+a;
}
return res;
}
const int mx = 2005;
mi sing[mx][mx]; //length i, did a right jump and ended at position j (1-indexed)
mi stot[mx]; //sum of sing[i]
mi comps[mx][mx]; //# of ways to have i components that size sum to j
mi rightnums[mx]; //total size of special component
mi rights[mx]; // for each component #, ways
mi lefts[mx]; // for each component #, ways
int main() {
setIO();
genFac(5005);
int N, cs, cf;
cin >> N >> cs >> cf;
if(cs > cf) swap(cs, cf);
sing[1][1] = 1;
for(int i = 2; i <= N; i++){
for(int j = i; j >= 1; j--){
sing[i][j]+=sing[i][j+1];
sing[i][j]+=sing[i-1][j];
}
for(int j = 1; j <= i/2; j++){
swap(sing[i][j], sing[i][i+1-j]); //treat it like a right jump
}
}
for(int i = 2; i <= N; i+=2){
for(int j = 1; j <= i/2; j++){
swap(sing[i][j], sing[i][i+1-j]); //swap even ones back
}
}
for(int i = 1; i <= N; i++){
for(int j = 1; j <= i; j++){
stot[i]+=sing[i][j];
}
}
vmi p(N+1, mi(0));
for(int i = 1; i <= N; i+=2){ //odd components only
p[i] = stot[i]/mi(fac[i]); //happens to be tan(x)
}
vmi curp = p;
//dbg(curp);
for(int i = 1; i <= N; i++){
for(int j = 1; j <= N; j++){
comps[i][j] = curp[j]*mi(fac[j]);
}
curp = MUL(curp, p);
curp.rsz(N+1);
}
if(cs-1 == 0){
lefts[0] = 1;
}
else{
for(int i = 1; i <= N; i++){
lefts[i]+=comps[i][cs-1];
}
}
for(int i = 1; i <= N; i++){ //size
for(int j = 1; j <= N; j++){ //ending spot
if(i-j > N-cf) continue;
if(j-1 > cf-cs-1) continue;
//if(i == 1) dbg(i, j, sing[i][j]*mi(comb(N-cf, i-j))*mi(comb(cf-cs-1, j-1)));
rightnums[i]+=sing[i][j]*mi(comb(N-cf, i-j))*mi(comb(cf-cs-1, j-1));
}
}
// for(int i = 1; i <= N; i++){
// dbg(i, rightnums[i]);
// }
rights[1] = sing[N-cs][cf-cs];
//dbg(rights[1]);
for(int i = 1; i <= N; i++){
for(int j = 1; j <= N; j++){
if(N-cs-j < 0) continue;
rights[i+1]+=comps[i][N-cs-j]*rightnums[j];
}
}
// for(int i = 1; i <= N; i++){
// dbg(i, lefts[i], rights[i]);
// }
mi ans = 0;
for(int i = 1; i <= N; i++){
ans+=rights[i]*lefts[i-1];
ans+=rights[i]*lefts[i];
}
ps(ans);
// you should actually read the stuff at the bottom
}
/* stuff you should look for
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* WRITE STUFF DOWN
*/
Compilation message
kangaroo.cpp:176:9: warning: #pragma once in main file
#pragma once
^~~~
kangaroo.cpp: In function 'void setIn(std::__cxx11::string)':
kangaroo.cpp:128:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~
kangaroo.cpp: In function 'void setOut(std::__cxx11::string)':
kangaroo.cpp:129:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 2 |
Correct |
17 ms |
31872 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 2 |
Correct |
17 ms |
31872 KB |
Output is correct |
| 3 |
Correct |
19 ms |
31864 KB |
Output is correct |
| 4 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 5 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 6 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 7 |
Correct |
18 ms |
31860 KB |
Output is correct |
| 8 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 9 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 10 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 11 |
Correct |
18 ms |
31872 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 2 |
Correct |
17 ms |
31872 KB |
Output is correct |
| 3 |
Correct |
19 ms |
31864 KB |
Output is correct |
| 4 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 5 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 6 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 7 |
Correct |
18 ms |
31860 KB |
Output is correct |
| 8 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 9 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 10 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 11 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 12 |
Correct |
44 ms |
31960 KB |
Output is correct |
| 13 |
Correct |
41 ms |
31872 KB |
Output is correct |
| 14 |
Correct |
41 ms |
31872 KB |
Output is correct |
| 15 |
Correct |
45 ms |
31872 KB |
Output is correct |
| 16 |
Correct |
46 ms |
32000 KB |
Output is correct |
| 17 |
Correct |
43 ms |
31872 KB |
Output is correct |
| 18 |
Correct |
41 ms |
31968 KB |
Output is correct |
| 19 |
Correct |
42 ms |
31872 KB |
Output is correct |
| 20 |
Correct |
44 ms |
31872 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 2 |
Correct |
17 ms |
31872 KB |
Output is correct |
| 3 |
Correct |
19 ms |
31864 KB |
Output is correct |
| 4 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 5 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 6 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 7 |
Correct |
18 ms |
31860 KB |
Output is correct |
| 8 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 9 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 10 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 11 |
Correct |
18 ms |
31872 KB |
Output is correct |
| 12 |
Correct |
44 ms |
31960 KB |
Output is correct |
| 13 |
Correct |
41 ms |
31872 KB |
Output is correct |
| 14 |
Correct |
41 ms |
31872 KB |
Output is correct |
| 15 |
Correct |
45 ms |
31872 KB |
Output is correct |
| 16 |
Correct |
46 ms |
32000 KB |
Output is correct |
| 17 |
Correct |
43 ms |
31872 KB |
Output is correct |
| 18 |
Correct |
41 ms |
31968 KB |
Output is correct |
| 19 |
Correct |
42 ms |
31872 KB |
Output is correct |
| 20 |
Correct |
44 ms |
31872 KB |
Output is correct |
| 21 |
Correct |
391 ms |
32120 KB |
Output is correct |
| 22 |
Correct |
406 ms |
32024 KB |
Output is correct |
| 23 |
Correct |
433 ms |
32120 KB |
Output is correct |
| 24 |
Execution timed out |
2080 ms |
31992 KB |
Time limit exceeded |
| 25 |
Halted |
0 ms |
0 KB |
- |
