Submission #251346

#	Time	Username	Problem	Language	Result	Execution time	Memory
251346		rqi	Kangaroo (CEOI16_kangaroo)	C++14	100 / 100	114 ms	31992 KiB

kangaroo

#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);
    }*/

    comps[1][1] = 1;
    for(int n = 1; n <= N; n++){
        for(int k = 1; k <= N; k++){
            if(n == 1 && k == 1) continue;
            comps[k][n] = k*(comps[k-1][n-1]+comps[k+1][n-1]);
        }
    }

    // for(int i = 1; i <= 15; i++){
    //     for(int j = 1; j <= 15; j++){
    //         cout << int(comps[i][j]) << " ";
    //     }
    //     cout << "\n";
    // }

    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 (stderr)

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); }
                         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 6 / 6
• Subtask 2: 30 / 30
• Subtask 3: 15 / 15
• Subtask 4: 49 / 49