QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#110976#6565. Game Show Eliminationheno239AC ✓2540ms30720kbC++1712.2kb2023-06-05 03:30:272023-06-05 03:30:30

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-06-05 03:30:30]
  • 评测
  • 测评结果:AC
  • 用时:2540ms
  • 内存:30720kb
  • [2023-06-05 03:30:27]
  • 提交

answer

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//ll mod = 1;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const int mod17 = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

using ld = long double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

template<typename T>
void chmin(T& a, T b) {
    a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
    a = max(a, b);
}
template<typename T>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
    vector<T> res;
    int ida = 0, idb = 0;
    while (ida < a.size() || idb < b.size()) {
        if (idb == b.size()) {
            res.push_back(a[ida]); ida++;
        }
        else if (ida == a.size()) {
            res.push_back(b[idb]); idb++;
        }
        else {
            if (a[ida] < b[idb]) {
                res.push_back(a[ida]); ida++;
            }
            else {
                res.push_back(b[idb]); idb++;
            }
        }
    }
    return res;
}
template<typename T>
void cinarray(vector<T>& v) {
    rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
    rep(i, v.size()) {
        if (i > 0)cout << " "; cout << v[i];
    }
    cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
    if (n < 0) {
        ll res = mod_pow(x, -n, m);
        return mod_pow(res, m - 2, m);
    }
    if (abs(x) >= m)x %= m;
    if (x < 0)x += m;
    //if (x == 0)return 0;
    ll res = 1;
    while (n) {
        if (n & 1)res = res * x % m;
        x = x * x % m; n >>= 1;
    }
    return res;
}
//mod should be <2^31
struct modint {
    int n;
    modint() :n(0) { ; }
    modint(ll m) {
        if (m < 0 || mod <= m) {
            m %= mod; if (m < 0)m += mod;
        }
        n = m;
    }
    operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
    if (n == 0)return modint(1);
    modint res = (a * a) ^ (n / 2);
    if (n % 2)res = res * a;
    return res;
}

ll inv(ll a, ll p) {
    return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 20;
modint fact[max_n], factinv[max_n];
void init_f() {
    fact[0] = modint(1);
    for (int i = 0; i < max_n - 1; i++) {
        fact[i + 1] = fact[i] * modint(i + 1);
    }
    factinv[max_n - 1] = modint(1) / fact[max_n - 1];
    for (int i = max_n - 2; i >= 0; i--) {
        factinv[i] = factinv[i + 1] * modint(i + 1);
    }
}
modint comb(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
    if (a < 0 || b < 0 || a < b)return 0;
    return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
    a = abs(a); b = abs(b);
    if (a < b)swap(a, b);
    while (b) {
        ll r = a % b; a = b; b = r;
    }
    return a;
}
template<typename T>
void addv(vector<T>& v, int loc, T val) {
    if (loc >= v.size())v.resize(loc + 1, 0);
    v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
    fill(isp + 2, isp + mn, true);
    for (int i = 2; i < mn; i++) {
        if (!isp[i])continue;
        ps.push_back(i);
        for (int j = 2 * i; j < mn; j += i) {
            isp[j] = false;
        }
    }
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    if (res == st.begin())return st.end();
    res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
    auto res = st.lower_bound(val);
    return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
    return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
    a = a + b; return a;
}
mP operator-(mP a, mP b) {
    return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
    a = a - b; return a;
}
LP operator+(LP a, LP b) {
    return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
    a = a + b; return a;
}
LP operator-(LP a, LP b) {
    return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
    a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
//int dx[4] = { 1,0,-1,0 };
//int dy[4] = { 0,1,0,-1 };

//-----------------------------------------

using poly = vector<ld>;
poly operator*(poly a, poly b) {
    poly res;
    if (a.empty() || b.empty())return res;
    res.resize(a.size() + b.size() - 1);
    rep(i, a.size())rep(j, b.size()) {
        res[i + j] += a[i] * b[j];
    }
    return res;
}

int k;
ld coef[1 << 21][21];
bool chked[1 << 21];
ld calc_c(int i, int cc) {
    
    //cout << "?? " << i << "\n";
    if (chked[i]) {
        return coef[i][cc];
    }
    chked[i] = true;
    vector<int> vs;
    rep(j, 2*k+1)if (i & (1 << j))vs.push_back(j);
    assert(vs.size() > 1);
    ld bb = 1;
    rep(i, vs.size())bb *= k;
    rep(x, vs.size()) {
        rep(y, vs.size()) {
            if (x == y)continue;
            for (int l = vs[y] - k; l < vs[y]; l++) {
                poly p = { 1 };
                rep(i, vs.size()) {
                    if (i == y)continue;
                    if (i == x) {
                        int le = vs[i] - k;
                        int ri = vs[i];
                        if (l + 1 <= le) {
                            p.clear();
                        }
                        else if (ri <= l) {
                            poly cur = { (ld)k };
                            p = p * cur;
                        }
                        else {
                            poly cur = { (ld)-le,(ld)1 };
                            p = p * cur;
                        }
                    }
                    else {
                        int le = vs[i] - k; int ri = vs[i];
                        if (l + 1 <= le) {
                            poly cur = { (ld)k };
                            p = p * cur;
                        }
                        else if (ri <= l) {
                            p.clear();
                        }
                        else {
                            poly cur = { (ld)ri,(ld)-1 };
                            p = p * cur;
                        }
                    }
                }
                //coutarray(p);
                ld pl = 1;
                ld plp = 1;
                ld sum = 0;
                rep(i, p.size()) {
                    pl *= l;
                    plp *= l + 1;
                    ld coef = p[i] / (ld)(i + 1);
                    sum += coef * (plp - pl);
                }
                coef[i][vs[y]] += sum;
            }
        }
    }
    rep(j, vs.size()) {
        coef[i][vs[j]] /= bb;
    }
    return coef[i][cc];
}

const ld z = (1e-15);
void solve() {
    map<vector<int>, ld> mp;
    int n; cin >> n >> k;
    rep(i, (1 << (k + 1))) {
        if (i % 2 == 0)continue;
        
    }
    vector<int> cur;
    for (int i = max(0, n - 1 - k); i < n; i++) {
        cur.push_back(i);
    }
    mp[cur] = 1;
    vector<ld> ans(n);
    vector<int> nv;
    rep(_, n - 2) {
        //cout << "hello " << _ << "\n";
        int cval = n - _;
        map<vector<int>, ld> nmp;
        for (auto p : mp) {
            vector<int> v = p.first;
            ld val = p.second;
            //cout << val << " "; coutarray(v);
            if (val < z)continue;
            //cout << "? " << _ << "\n";
            assert(v.size() >= 2);
            assert(v[v.size() - 1] - v[v.size() - 2] <= k);
            //coutarray(v);
            int r = n - _ - v.size();
            int ss = 0;
            rep(i, v.size()) {
                ss |= (1 << (v.back() - v[i]));
            }
            bool curb = false;
            if (v.back() - v[v.size() - 2] == k)curb = true;
            rep(i, v.size()) {
                int loc = v.back() - v[i];
                //cout << "!? " << ss << " " << loc << "\n";
                ld nval = val * calc_c(ss, loc);
                ans[v[i]] += nval * cval;
                vector<int> nv;
                if (i + 1 == v.size()) {
                    nv = v;
                    nv.erase(nv.begin() + i);
                    if (nv.size() == 1) {
                        int las = nv.back();
                        for (int j = las - 2 * k+1; j <= las - k; j++) {
                            if (j >= 0)nv.push_back(j);
                        }
                    }
                    else {
                        int cr = v[v.size() - 2];
                        int cl = nv[nv.size() - 2];
                        Rep(j, cl, cr) {
                            if(j-k+1>=0)nv.push_back(j - k + 1);
                        }
                    }
                    sort(all(nv));
                }
                else if (i + 2 == v.size()) {
                    nv = v;
                    nv.erase(nv.begin() + i);
                    if (nv.size() == 1) {
                        for (int j = v[i] - 2 * k + 1; j <= v[i] - k; j++) {
                            if (j >= 0)nv.push_back(j);
                        }
                    }
                    else {
                        int cr = v[v.size() - 2];
                        int cl = nv[nv.size() - 2];
                        Rep(j, cl, cr) {
                            if (j - k + 1 >= 0)nv.push_back(j - k + 1);
                        }
                    }
                    sort(all(nv));
                }
                else {
                    nv = v;
                    nv.erase(nv.begin() + i);
                }
                if (nv.back() - nv[nv.size() - 2] >= k) {
                    if (!curb) {
                        ans[nv.back()] += nval;
                    }
                    nv.back() = nv[nv.size() - 2] + k;
                }
                nmp[nv] += nval;
            }
        }
        swap(mp, nmp);
        //cout << mp.size() << "\n";
    }
    //cout << "hello\n";
    for (auto p : mp) {
        vector<int> v = p.first;
        int ss = 1;
        ss |= 1 << (v[1] - v[0]);
        ld c0 = calc_c(ss, v[1] - v[0]);
        ld c1 = 1 - c0;
        ans[v[0]] += 2 * c0 * p.second + c1 * p.second;
        if (v[1] - v[0] < k) {
            ans[v[1]] += c0 * p.second + 2 * c1 * p.second;
        }
    }
    rep(i, n)cout << ans[i] << "\n";
}





signed main() {
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(10);
    //init_f();
    //init();
    //while(true)
    //expr();
    //int t; cin >> t; rep(i, t)
    solve();
    return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 5ms
memory: 13652kb

input:

3 2

output:

2.1093750000
2.6250000000
1.2656250000

result:

ok 3 numbers

Test #2:

score: 0
Accepted
time: 2540ms
memory: 30720kb

input:

1000 10

output:

2.9272933165
3.5373161568
4.2811822032
5.1312206600
6.0539327788
7.0191885096
8.0057023988
9.0012910300
10.0001652073
10.9999999996
11.9999999996
12.9999999996
13.9999999995
14.9999999995
15.9999999995
16.9999999994
17.9999999994
18.9999999994
19.9999999993
20.9999999993
21.9999999993
22.9999999992
...

result:

ok 1000 numbers

Test #3:

score: 0
Accepted
time: 217ms
memory: 16608kb

input:

300 8

output:

2.7512630513
3.3900737270
4.1750068651
5.0660215194
6.0201465578
7.0045578589
8.0005725930
9.0000000000
10.0000000000
11.0000000000
12.0000000000
12.9999999999
13.9999999999
14.9999999999
15.9999999999
16.9999999999
17.9999999999
18.9999999999
19.9999999999
20.9999999999
21.9999999999
22.9999999999
...

result:

ok 300 numbers

Test #4:

score: 0
Accepted
time: 11ms
memory: 12968kb

input:

1000 3

output:

2.2302561681
3.0347656711
4.0000000000
5.0000000000
6.0000000000
7.0000000000
8.0000000000
9.0000000000
10.0000000000
11.0000000000
12.0000000000
13.0000000000
14.0000000000
15.0000000000
16.0000000000
17.0000000000
18.0000000000
19.0000000000
20.0000000000
21.0000000000
22.0000000000
23.0000000000
...

result:

ok 1000 numbers

Test #5:

score: 0
Accepted
time: 3ms
memory: 13452kb

input:

7 10

output:

2.9815864384
3.4936049601
3.9653422649
4.3196770586
4.5087248562
4.4988808477
4.2321835741

result:

ok 7 numbers

Test #6:

score: 0
Accepted
time: 911ms
memory: 20404kb

input:

993 9

output:

2.8411212285
3.4643592446
4.2273243674
5.0969425981
6.0352816657
7.0105742427
8.0023873941
9.0003025183
9.9999999999
10.9999999999
11.9999999999
12.9999999998
13.9999999998
14.9999999998
15.9999999998
16.9999999998
17.9999999998
18.9999999998
19.9999999998
20.9999999998
21.9999999997
22.9999999997
2...

result:

ok 993 numbers