Submission #1086000

#	Time	Username	Problem	Language	Result	Execution time	Memory
1086000		quanlt206	Boat (APIO16_boat)	C++17	100 / 100	1010 ms	34396 KiB

boat

#include<bits/stdc++.h>
#define X first
#define Y second
#define all(x) begin(x), end(x)
#define FOR(i, a, b) for(int i = (a); i <= (b); i++)
#define FORD(i, b, a) for(int i = (b); i >= (a); i--)
#define REP(i, a, b) for (int i = (a); i < (b); i++)
#define mxx max_element
#define mnn min_element
#define SQR(x) (1LL * (x) * (x))
#define MASK(i) (1LL << (i))
#define Point Vector
#define left Left
#define right Right
#define div Div

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef long double ld;
typedef pair<db, db> pdb;
typedef pair<ld, ld> pld;
typedef pair<int, int> pii;
typedef pair<int, pii> piii;
typedef pair<ll, ll> pll;
typedef pair<ll, pll> plll;
typedef pair<ll, int> pli;
typedef pair<ll, pii> plii;

template<class A, class B>
    bool maximize(A& x, B y) {
        if (x < y) return x = y, true; else return false;
    }
template<class A, class B>
    bool minimize(A& x, B y) {
        if (x > y) return x = y, true; else return false;
    }

/* END OF TEMPLATE */

const int N = 2e3 + 7;
const int mod = 1e9 + 7;

int n, m, a[N], b[N];

vector<int> E;

pii block[N];

int dp[2][2000][2000][2];

void add(int& x, int y) {
    if ((x+=y) >= mod) x-=mod;
}

int Ckn[N][N];

long long fact[N], inv_fact[N];

long long mul(long long a, long long b) {
    if (b == 0) return 1;
    ll tmp = mul(a, b / 2);
    tmp = tmp * tmp % mod;
    if (b & 1) tmp = tmp * a % mod;
    return tmp;
}

void buildCkn() {
    fact[0] = 1;
    for (int i = 1; i <= n; i++) fact[i] = fact[i - 1] * i % mod;
    inv_fact[n] = mul(fact[n], mod - 2);
    for (int i = n - 1; i > 0; i--) inv_fact[i] = inv_fact[i + 1] * (i + 1) % mod;
    for (int i = 1; i <= m; i++) {
        int sz = block[i].Y - block[i].X + 1;
        ll tich = 1;
        for (int j = sz; j > 0; j--) {
            tich = tich * j % mod;
            Ckn[i][sz - j + 1] = tich * inv_fact[sz - j + 1] % mod;
//            cout<<sz<<" "<<sz - j + 1<<" "<< Ckn[i][sz - j + 1]<<"\n";
            if (sz - j + 1 > n) break;
        }
    }
}

int cnt[N];

int main() {
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cin>>n;
    set<int> s;
    for (int i = 1; i <= n; i++) {
        cin>>a[i]>>b[i];
        s.insert(a[i]);
        s.insert(b[i]);
    }
    vector<int> E(s.begin(), s.end());
    for (int i = 0; i < E.size(); i++) {
        block[++m] = {E[i], E[i]};
        if (i + 1 < E.size() && E[i] + 1 <= E[i + 1] - 1) block[++m] = {E[i] + 1, E[i + 1] - 1};
    }
    buildCkn();
    for (int i = 1; i <= n; i++) {
        for (int j = 0; j <= m; j++)
            if (a[i] <= block[j].X && block[j].Y <= b[i]) cnt[j]++;
    }
    cnt[0] = n;
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= m; j++)
            if (a[i] <= block[j].X && block[j].Y <= b[i]) cnt[j]--;
        for (int j = 0; j <= m; j++)
            for (int k = 0; k <= cnt[j]; k++)
                for (int z = 0; z <= 1; z++) {
                    int& res = dp[i & 1][j][k][z];
                    res = 0;
                    if (i == 0) {
                        res = Ckn[j][k];
                        continue;
                    }
                    if (a[i] <= block[j].X && block[j].Y <= b[i]) add(res, dp[i & 1 ^ 1][j][k + 1][0]);
                    if (z == 0) add(res, dp[i & 1 ^ 1][j][k][0]);
                    if (j > 0 && k > 0) add(res, 1LL * dp[i & 1][j - 1][0][1] * Ckn[j][k] % mod); else
                    if (j > 0 && k == 0) add(res, dp[i & 1][j - 1][0][1]);
                }
    }
    cout<<dp[n & 1][m][0][0];
    return 0;
}

Compilation message (stderr)

boat.cpp: In function 'int main()':
boat.cpp:100:23: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  100 |     for (int i = 0; i < E.size(); i++) {
      |                     ~~^~~~~~~~~~
boat.cpp:102:19: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
  102 |         if (i + 1 < E.size() && E[i] + 1 <= E[i + 1] - 1) block[++m] = {E[i] + 1, E[i + 1] - 1};
      |             ~~~~~~^~~~~~~~~~
boat.cpp:122:81: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
  122 |                     if (a[i] <= block[j].X && block[j].Y <= b[i]) add(res, dp[i & 1 ^ 1][j][k + 1][0]);
      |                                                                               ~~^~~
boat.cpp:123:47: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
  123 |                     if (z == 0) add(res, dp[i & 1 ^ 1][j][k][0]);
      |                                             ~~^~~

• Subtask 1: 9 / 9
• Subtask 2: 22 / 22
• Subtask 3: 27 / 27
• Subtask 4: 42 / 42