Submission #1125683

#	Time	Username	Problem	Language	Result	Execution time	Memory
1125683		tintingyn21	Binaria (CCO23_day1problem1)	C++20	0 / 25	20 ms	16712 KiB

Main

// author : daohuyenchi



#ifdef LOCAL
    #include "D:\C++ Submit\debug.h"
#else
    #define debug(...)
#endif



#include <bits/stdc++.h>

using namespace std;

#define ull unsigned long long
#define db double
#define i32 int32_t  
#define i64 int64_t 
#define ll long long
// 
#define fi first
#define se second


//                                      #define int long long    // consider carefully


//
#define pii pair <int, int>
#define pll pair <ll, ll>
#define PAIR make_pair 
#define TUP make_tuple
//                                      TIME IS LIMITED ...  
#define  rep(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define repd(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define repv(v, H) for(auto &v: H)
//                                      REFLECT ON THE PAST ...
#define RESET(c, x) memset(c, x, sizeof(c))
#define MASK(i) (1LL << (i))
#define BIT(mask, i) (((mask) >> (i)) & 1LL)
#define ONBIT(mask, i) ((mask) | (1LL << (i)))
#define OFFBIT(mask, i) ((mask) &~ (1LL << (i)))
#define COUNTBIT __builtin_popcountll
//                                      30 / 1 / 2024 ? love is zero... start from zero 
#define vi vector <int>
#define vll vector <ll>
#define Lower lower_bound
#define Upper upper_bound
#define all(v) (v).begin(), (v).end()
#define special(H) (H).resize(distance(H.begin(), unique(all(H))))
//                                      
#define sp ' ' 
#define nl '\n'
#define EL { cerr << '\n'; }
#define yes "YES"
#define no "NO"
#define Log2(n) (63 - __builtin_clzll(n))
#define left __left__
#define right __right__ 
#define lps(id) ((id) << 1)
#define rps(id) ((id) << 1 | 1)

//____________________________________________________________________


template <class X, class Y> bool maximize(X &a, const Y &b) 
{ if(a < b) return a = b, true; else return false; }

template <class X, class Y> bool minimize(X &a, const Y &b) 
{ if(a > b) return a = b, true; else return false; }

template <class... T>
void print(T&&... n) 
{ using exp = int[]; exp{ 0, (cerr << n << sp, 0)... }; cerr << nl; }

template <class T, class... C>
void assign(int n, T v, C&&... a) 
{ using e = int[]; e { (a.assign(n, v), 0)...}; }

template <class... C>
void resize(int n, C&&... a) 
{ using e = int[]; e { (a.resize(n), 0)...}; }

template <class T>
using vector2d = vector<vector<T>>;
template <class T>
using vector3d = vector<vector2d<T>>;

template <class T> int ssize(T &a) { return (int) a.size(); }


//____________________________________________________________________


mt19937 rng(chrono::steady_clock().now().time_since_epoch().count());

const long long MOD      = 1e6 + 3;
// const int MOD[2] = {1000000009, 998244353};

template<class X> void modmize(X &x, long long cur_Mod = MOD) {
    if(x >= cur_Mod) x -= cur_Mod;
    if(x < 0) x += cur_Mod;
}

int mod_plus(int A, int B) { modmize(A += B); return A; }

const long long oo      = 1e18 + 7;
const long long LINF    = 1e18 + 7;
const int IINF          = 2e9;
const int nmax          = 2e5 + 10;
const int MAX           = 1e6;
const int base          = 311;
const double eps        = 1e-6;
const int block         = 500;
static const double PI  = acos(-1.0);

//____________________________________________________________________


int n, k;
int x[nmax], a[nmax];


struct DSU {
    vector<int> parent;

    void Init(int _n) {
        parent.assign(_n + 1, -1);
        return;
    }

    void Reset(int _n = 0) {
        for (int i = 1; i <= _n; ++i) {
            parent[i] = -1;
        }
    }

    int Find(int u) {
        return (parent[u] < 0 ? u : parent[u] = Find(parent[u]));
    }

    int Son(int u) {
        u = Find(u);
        return - parent[u];
    }

    bool Merge(int u, int v) {
        u = Find(u);
        v = Find(v);
        if(u == v) return false;
        if(parent[u] > parent[v]) swap(u, v);
        parent[u] += parent[v];
        parent[v] = u;
        return true;
    }
} dsu;


int64_t Pow(ll a, ll b) {
    ll cur = 1;
    for(; b > 0; b >>= 1) {
        if(b & 1LL) cur = cur * a % MOD;
        a = a * a % MOD;
    }
    return cur;
}
        
struct combinatorics {
    vector<ll> fac, ifac;

    void init(int _n) {
        fac.assign(_n + 5, 0);
        ifac.assign(_n + 5, 0);
        fac[0] = 1;
        for (int i = 1; i <= _n; ++i) {
            fac[i] = fac[i - 1] * i % MOD;
        }

        ifac[_n] = Pow(fac[_n], MOD - 2);
        for (int i = _n - 1; i >= 0; --i) {
            ifac[i] = ifac[i + 1] * (i + 1) % MOD;
        }
    }

    // n choose k
    ll ncr(int n, int k) {
        if (k > n) return 0;
        if (k == 0 && n == 0) return 1;
        if (k == 0) return 1;
        if (n == 0) return 0;
        return fac[n] * ifac[k] % MOD * ifac[n - k] % MOD;
    }

    // n permutation k 
    ll npr(int n, int k) {
        if (k > n) return 0;
        return fac[n] * ifac[n - k] % MOD;
    }

    //             (k, n) = 0 if k > n
    //             (k, n) = n * nf[k] * (k - 1, n - 1)
    //       sigma (i, n) = 2 ^ n              :i = 0 -> n
    //       sigma (k, i) = (k + 1, n + 1)     :i = 0 -> n
    //  sigma (i, n + i)  = (m, n + m + 1)     :i = 0 -> m
    // sigma {(i, n) ^ 2} = (n, 2n)            :i = 0 -> n
    // sigma {k * (k, n)} = n * 2 ^ (n - 1)    :i = 1 -> n
    // x[1] + x[2] + .. + x[n]  = m (x[i] >= 0) => (n - 1, m + n - 1)
    // x[1] + x[2] + .. + x[n] <= m (x[i] >= 0) => (n, m + n)
    // cell(u, v) -> cell(x, y) => (x - u, x + y - u - v) 

    // choose len elements in n elements (not need to be diifer) = ncr(n - 1 + len, len) 

    //  the number of regular bracket strings of length 2⋅n is equal to (1 / (n + 1)) * ncr(2 * n, n)
    
} C;


void tintingyn() 
{

    cin >> n >> k;
    rep (i, k, n) {
        cin >> x[i];
    }

    C.init(1e6);

    dsu.Init(n);
    memset(a, -1, sizeof a);
    rep (i, n - k + 1, n - 1) {
        if (x[i] != x[i + 1]) {
            if (abs(x[i] - x[i + 1]) > 1) {
                cout << 0 << nl;
                exit(0);
            }
            if (x[i + 1] > x[i]) a[i + 1] = 1, a[i - k + 1] = 0;
            else a[i + 1] = 0, a[i - k + 1] = 1;
        }
        else {
            dsu.Merge(i + 1, i - k + 1);
        }
    }

    vector2d < int > List;
    assign(n + 2, vector < int > (), List);
    rep (i, 1, n) {
        List[dsu.Find(i)].push_back(i);
    }    

    rep (i, 1, n) {
        if (dsu.Find(i) == i) {
            int ok = -1;
            repv (v, List[i]) {
                if (ok == -1) {
                    if (a[v] != -1) ok = a[v];
                }
                else {
                    if (ok != a[v]) {
                        cout << 0 << nl;
                        exit(0);
                    }
                }
            }
            if (ok != -1) {
                repv (v, List[i]) {
                    a[v] = ok;
                }
            }
            else {

            }
        }
    }

    
    int cnt = 0;
    int sum = x[k];
    vector < bool > vis(n + 2, 0);
    rep (i, 1, k) {
        int p = dsu.Find(i);
        if (a[p] != -1) sum -= a[p];
        else cnt++;
        vis[p] = 1;
    }

    ll ans = C.ncr(cnt, sum);
    // rep (i, k + 1, n) {
    //     int p = dsu.Find(i);
    //     if (vis[p] == 0) {
    //         vis[p] = 1;
    //         ans = ans * Pow(2, dsu.Son(p)) % MOD;
    //     }
    // }

    cout << ans << nl;

}

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

    //________________________________________________________________

    #define TASK "2"
    if(fopen(TASK".inp", "r")) 
    { freopen(TASK".inp", "r", stdin); freopen(TASK".out", "w", stdout); }

    //________________________________________________________________
    
    //  CODE FROM HERE ...! 





    int num_test = 1; 
    // cin >> num_test;

    while(num_test--) {

        tintingyn();

    }


    cerr << '\n' << "Time elapsed: " << (1.0 * clock() / CLOCKS_PER_SEC) << " s\n" << nl;

    return 0;
}

Compilation message (stderr)

Main.cpp: In function 'int main()':
Main.cpp:312:14: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  312 |     { freopen(TASK".inp", "r", stdin); freopen(TASK".out", "w", stdout); }
      |       ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:312:47: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
  312 |     { freopen(TASK".inp", "r", stdin); freopen(TASK".out", "w", stdout); }
      |                                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

• Subtask 1: 0 / 3
• Subtask 2: 0 / 3
• Subtask 3: 0 / 4
• Subtask 4: 0 / 4
• Subtask 5: 0 / 4
• Subtask 6: 0 / 7