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Submission #792598

# Submission time Handle Problem Language Result Execution time Memory
792598 2023-07-25T07:16:24 Z 이동현(#10054) Binaria (CCO23_day1problem1) C++17
0 / 25
 13 ms 23816 KB 
#include <bits/stdc++.h>
#pragma GCC optimize("O3")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#define int long long
using namespace std;

const int NS = (int)1e6 + 4, mod = (int)1e6 + 3;
int n, k;
int a[NS];
int r[NS], l[NS], chk[NS];

int pw(int x, int y){
    if(!y) return 1;
    if(y == 1) return x;
    int v = pw(x, y / 2);
    return v * v % mod * (y % 2 ? x : 1) % mod;
}

int fdr(int x){
    return (x == r[x] ? x : r[x] = fdr(r[x]));
}

int fdl(int x){
    return (x == l[x] || x == -1 ? x : l[x] = fdl(l[x]));
}

struct Fenwick{
    int n;
    vector<int> tr;
    Fenwick(int m){
        n = m + 4;
        tr.resize(n);
    }

    void push(int pos, int val){
        pos += 2;
        for(int i = pos; i < n; i += (i & -i)){
            tr[i] += val;
        }
    }

    int get(int pos){
        int rv = 0;
        pos += 2;
        for(int i = pos; i > 0; i -= (i & -i)){
            rv += tr[i];
        }

        return rv;
    }

    int get(int l, int r){
        if(l > r) return 0;
        return get(r) - get(l - 1);
    }
};

signed main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);

    iota(r, r + NS, 0);
    iota(l, l + NS, 0);
    memset(chk, -1, sizeof(chk));

    int n, k;
    cin >> n >> k;
    vector<int> a(n - k + 1);
    for(int i = 0; i < n - k + 1; ++i){
        cin >> a[i];
    }
    Fenwick tr(n);

    auto cant = [&]{
        cout << "0\n";
        exit(0);
    };

    auto nor = [&](vector<int> x)->vector<int>{
        if(x[0] > x[1]) return x;
        int nl = fdr(x[0]);
        int nr = fdl(x[1]);
        if(nl > nr){
            int nv = x[2] - tr.get(x[0], x[1]);
            if(nv) cant();
            return {nl, nr, 0};
        }
        int nv = x[2] - tr.get(x[0], nl - 1) - tr.get(nr + 1, x[1]);
        return {nl, nr, nv};
    };

    auto upd = [&](int pos, int val){
        if(val < 0 || val > 1) cant();
        chk[pos] = val;
        tr.push(pos, val);
        l[pos] = pos - 1;
        r[pos] = pos + 1;
    };

    deque<vector<int>> stk;
    stk.push_back({0, k - 1, a[0]});
    int stval = 0;
    for(int i = 1; i < n - k + 1; ++i){
        vector<int> now = nor({i, i + k - 1, a[i]});
        if(!(int)stk.size()){
            upd(now[1], now[2]);
            continue;
        }
        while((int)stk.size()){
            stk.back() = nor(stk.back());
            // cout << stk.back()[0] << ' ' << stk.back()[1] << ' ' << now[0] << ' ' << now[1] << endl;
            if(stk.back()[0] == stk.back()[1]) break;

            int sval = stk.back()[2] - tr.get(stk.back()[0], stk.back()[1]);
            int nval = now[2] - tr.get(now[0], now[1]);
            if(sval == nval) break;

            int p = -1;
            int cut = stk.back()[0];
            while(p + 1 < (int)stk.size() && (stk[p + 1] = nor(stk[p + 1]))[1] < cut){
                ++p;
            }

            // cout << p << endl;

            if(stk.back()[0] == now[0]){
                upd(now[1], nval - sval);
                p = -1;
            }
            else if(sval > nval){
                upd(stk.back()[0], sval - nval);
                upd(now[1], 0);
            }
            else{
                upd(now[1], nval - sval);
                upd(stk.back()[0], 0);
            }

            for(int j = p; j >= 0; --j){
                stk[j] = nor(stk[j]);
                stk[j + 1] = nor(stk[j + 1]);
                upd(stk[j][0], stk[j][2] - tr.get(stk[j][0], stk[j][1]) - (stk[j + 1][2] - tr.get(stk[j + 1][0], stk[j + 1][1])));
                ++stval;
            }
            for(int j = 0; j <= p; ++j) stk.pop_front();

            now = nor(now);
            stk.pop_back();
        }

        while((int)stk.size()){
            stk.back() = nor(stk.back());
            if(stk.back()[0] < stk.back()[1]) break;
            upd(stk.back()[1], stk.back()[2]);
            stk.pop_back();
        }

        if(now[0] < now[1]){
            stk.push_back(now);
        }
        else if(now[0] == now[1]){
            upd(now[1], now[2]);
        }
    }

    if(!(int)stk.size()){
        cout << "1\n";
        return 0;
    }

    int ac = 0, oc = a[stval];
    for(int i = stval; i < stval + k; ++i){
        ac += (chk[i] == -1);
        oc -= (chk[i] == 1);
    }

    int ans = 1;
    for(int i = oc + 1; i <= ac; ++i){
        (ans *= i) %= mod;
    }
    for(int i = 2; i <= ac - oc; ++i){
        (ans *= pw(i, mod - 2)) %= mod;
    }

    auto naive = [&]{
        vector<vector<int>> ran(n - k + 1);
        for(int i = 0; i < n - k + 1; ++i){
            ran[i] = {i, i + k - 1, a[i]};
        }
        while(true){
            int f = 0;
            for(int i = 0; i + 1 < (int)ran.size(); ++i){
                ran[i] = nor(ran[i]);
                // cout << i << ' ' << ran[i + 1][0] << ' ' << ran[i + 1][1] << ' ' << ran[i + 1][2] << endl;
                ran[i + 1] = nor(ran[i + 1]);
                int sval = ran[i][2] - tr.get(ran[i][0], ran[i][1]);
                int nval = ran[i + 1][2] - tr.get(ran[i + 1][0], ran[i + 1][1]);
                if(ran[i][0] > ran[i][1] || ran[i + 1][0] > ran[i + 1][1]) continue;
                if(ran[i][0] == ran[i + 1][0] && ran[i][1] == ran[i + 1][1]){
                    if(sval != nval) cant();
                    continue;
                }
                if(ran[i][0] < ran[i + 1][0] && ran[i][1] < ran[i + 1][1] && sval == nval){
                    continue;
                }

                f = 1;
                // cout << i << ' ' << sval << ' ' << nval << endl;

                if(ran[i][0] == ran[i + 1][0]){
                    upd(ran[i + 1][1], nval - sval);
                }
                else if(ran[i][1] == ran[i + 1][1]){
                    upd(ran[i][0], sval - nval);
                }
                else{
                    if(sval > nval){
                        upd(ran[i][0], sval - nval);
                        upd(ran[i + 1][1], 0);
                    }
                    else{
                        upd(ran[i + 1][1], nval - sval);
                        upd(ran[i][0], 0);
                    }
                }
            }
            if(!f) break;
        }

        // cout << "HI" << endl;

        int stval = 0;
        while(stval < n - k + 1){
            ran[stval] = nor(ran[stval]);
            if(ran[stval][0] <= ran[stval][1]) break;
            ++stval;
        }
        if(stval == n - k + 1){
            return 1ll;
        }
        int ac = 0, oc = a[stval];
        for(int i = stval; i < stval + k; ++i){
            ac += (chk[i] == -1);
            oc -= (chk[i] == 1);
        }

        int ans = 1;
        for(int i = oc + 1; i <= ac; ++i){
            (ans *= i) %= mod;
        }
        for(int i = 2; i <= ac - oc; ++i){
            (ans *= pw(i, mod - 2)) %= mod;
        }

        return ans;
    };

    tr = Fenwick(n);
    iota(r, r + NS, 0);
    iota(l, l + NS, 0);
    memset(chk, -1, sizeof(chk));
    assert(ans == naive());
    cout << ans << '\n';
    
    return 0;
}

Subtask #1
0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 23764 KB Output is correct
2 Correct 12 ms 23732 KB Output is correct
3 Correct 11 ms 23764 KB Output is correct
4 Correct 9 ms 23720 KB Output is correct
5 Correct 11 ms 23808 KB Output is correct
6 Correct 12 ms 23808 KB Output is correct
7 Correct 12 ms 23800 KB Output is correct
8 Correct 12 ms 23764 KB Output is correct
9 Correct 12 ms 23816 KB Output is correct
10 Incorrect 11 ms 23760 KB Output isn't correct
11 Halted 0 ms 0 KB -

Subtask #2
0 / 3.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 23764 KB Output is correct
2 Correct 12 ms 23732 KB Output is correct
3 Correct 11 ms 23764 KB Output is correct
4 Correct 9 ms 23720 KB Output is correct
5 Correct 11 ms 23808 KB Output is correct
6 Correct 12 ms 23808 KB Output is correct
7 Correct 12 ms 23800 KB Output is correct
8 Correct 12 ms 23764 KB Output is correct
9 Correct 12 ms 23816 KB Output is correct
10 Incorrect 11 ms 23760 KB Output isn't correct
11 Halted 0 ms 0 KB -

Subtask #3
0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 23764 KB Output is correct
2 Correct 12 ms 23732 KB Output is correct
3 Correct 11 ms 23764 KB Output is correct
4 Correct 9 ms 23720 KB Output is correct
5 Correct 11 ms 23808 KB Output is correct
6 Correct 12 ms 23808 KB Output is correct
7 Correct 12 ms 23800 KB Output is correct
8 Correct 12 ms 23764 KB Output is correct
9 Correct 12 ms 23816 KB Output is correct
10 Incorrect 11 ms 23760 KB Output isn't correct
11 Halted 0 ms 0 KB -

Subtask #4
0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 23764 KB Output is correct
2 Correct 12 ms 23732 KB Output is correct
3 Correct 11 ms 23764 KB Output is correct
4 Correct 9 ms 23720 KB Output is correct
5 Correct 11 ms 23808 KB Output is correct
6 Correct 12 ms 23808 KB Output is correct
7 Correct 12 ms 23800 KB Output is correct
8 Correct 12 ms 23764 KB Output is correct
9 Correct 12 ms 23816 KB Output is correct
10 Incorrect 11 ms 23760 KB Output isn't correct
11 Halted 0 ms 0 KB -

Subtask #5
0 / 4.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 23764 KB Output is correct
2 Correct 12 ms 23732 KB Output is correct
3 Correct 11 ms 23764 KB Output is correct
4 Correct 9 ms 23720 KB Output is correct
5 Correct 11 ms 23808 KB Output is correct
6 Correct 12 ms 23808 KB Output is correct
7 Correct 12 ms 23800 KB Output is correct
8 Correct 12 ms 23764 KB Output is correct
9 Correct 12 ms 23816 KB Output is correct
10 Incorrect 11 ms 23760 KB Output isn't correct
11 Halted 0 ms 0 KB -

Subtask #6
0 / 7.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 23764 KB Output is correct
2 Correct 12 ms 23732 KB Output is correct
3 Correct 11 ms 23764 KB Output is correct
4 Correct 9 ms 23720 KB Output is correct
5 Correct 11 ms 23808 KB Output is correct
6 Correct 12 ms 23808 KB Output is correct
7 Correct 12 ms 23800 KB Output is correct
8 Correct 12 ms 23764 KB Output is correct
9 Correct 12 ms 23816 KB Output is correct
10 Incorrect 11 ms 23760 KB Output isn't correct
11 Halted 0 ms 0 KB -