Submission #1076442

#	Time	Username	Problem	Language	Result	Execution time	Memory
1076442		RiverFlow	Boat (APIO16_boat)	C++14	100 / 100	1010 ms	7556 KiB

boat

#include <bits/stdc++.h>

#define nl "\n"
#define no "NO"
#define yes "YES"
#define fi first
#define se second
#define vec vector
#define task "main"
#define _mp make_pair
#define ii pair<int, int>
#define sz(x) (int)x.size()
#define all(x) x.begin(), x.end()
#define evoid(val) return void(std::cout << val)
#define FOR(i, a, b) for(int i = (a); i <= (b); ++i)
#define FOD(i, b, a) for(int i = (b); i >= (a); --i)
#define unq(x) sort(all(x)); x.resize(unique(all(x)) - x.begin())

using namespace std;

template<typename U, typename V> bool maxi(U &a, V b) {
    if (a < b) { a = b; return 1; } return 0;
}
template<typename U, typename V> bool mini(U &a, V b) {
    if (a > b) { a = b; return 1; } return 0;
}

const int N = (int)500 + 9;
const int mod = (int)1e9 + 7;

void prepare(); void main_code();

int main() {
    ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    if (fopen(task".inp", "r")) {
        freopen(task".inp", "r", stdin);
        freopen(task".out", "w", stdout);
    }
    const bool MULTITEST = 0; prepare();
    int num_test = 1; if (MULTITEST) cin >> num_test;
    while (num_test--) { main_code(); }
}

void prepare() {};

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

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

namespace SUB1 {
int dp[N][N];
void sol() {
    dp[0][0] = 1;
    a[0] = b[0] = 0;
    FOR(i, 0, n - 1) FOR(j, 0, i) if (dp[i][j]) {
        add(dp[i + 1][j], dp[i][j]);
        if (b[i + 1] > b[j])
            add(dp[i + 1][i + 1], dp[i][j]);
    }
    int res = 0;
    FOR(i, 1, n) add(res, dp[n][i]);
    cout << res;
}
};

namespace SUB2 {
int S[N];
vector<int> dp[N];

void sol() {
    int res = 0;
    for(int i = 1; i <= n; ++i) {
        int os = 1;
        int L = b[i] - a[i] + 1;
        S[i] = L;
        dp[i].resize(L);
        for(int j = 1; j < i; ++j) {
            if (a[i] > b[j]) {
                add(os, dp[j][S[j] - 1]);
            } else if (max(a[i], a[j]) <= min(b[i], b[j])) {
                if (a[i] >= a[j]) {
                    for(int x = 0; x < L; ++x) {
                        if (x + a[i] - a[j] - 1 >= 0)
                            add(dp[i][x], dp[j][min(x + a[i] - a[j] - 1, S[j] - 1)]);
                    }
                } else {
                    for(int x = a[j] + 1; x <= b[i]; ++x) {
                        add(dp[i][x - a[i]], dp[j][min(x - a[j] - 1, S[j] - 1)]);
                    }
                }
            }
        }
        for(int x = 0; x < L; ++x) {
            add(dp[i][x], os);
            if (x > 0) add(dp[i][x], dp[i][x - 1]);
        }
        add(res, dp[i][L - 1]);
    }
    cout << res;
}
};

int Pow(int a, long long b) {
    int res = 1;
    for(; b > 0; b >>= 1, a = 1ll * a * a % mod)
        if (b & 1) res = 1ll * res * a % mod;
    return res;
}

namespace SUB3 {
const int N = 507;
int dp[N][3 * N], f[3 * N][N];
int C[3 * N][N], P[N], inv[N], F[N];

int mul(int a, int b) { return 1LL * a * b % mod; }
int comb(int k, int n) {
    return mul(P[n], mul(F[k], F[n - k]));
}

void build(vector<int> val) {
    P[0] = 1;
    FOR(i, 1, n) P[i] = mul(P[i - 1], i);
    F[n] = Pow(P[n], mod - 2);
    FOD(i, n - 1, 0) F[i] = mul(F[i + 1], i + 1);
    FOR(i, 1, n) inv[i] = Pow(i, mod - 2);

    for(int i = 0; i < sz(val); ++i) {
        int k = val[i];
        // tinh c(x, k) voi x <= min(n, k)
        C[i][1] = k;
        for(int j = 2; j <= min(n, k); ++j) {
            C[i][j] = mul(C[i][j - 1], mul(inv[j], k - j + 1));
        }
        for(int d = 1; d <= n; ++d) {
            // co d option -> dien vao val
            for(int z = 1; z <= min(d, k); ++z) {
                add(f[i][d], mul(comb(z - 1, d - 1), C[i][z]));
            }
        }
    }
}
const bool DBG = 0;
void sol() {
    vector<int> mark;
    mark.push_back(0);
    for(int i = 1; i <= n; ++i) {
        mark.push_back(a[i]);
        mark.push_back(b[i]);
        mark.push_back(a[i] - 1);
    }
    unq(mark);
    if (DBG) {
        cout << "mark: "; for(int x : mark) cout << x << ' '; cout << nl;
    }
    // can tinh cac doan 1-> va mark[j]-mark[j-1]
    vector<int> val;
    val.push_back(1);
    for(int i = 1; i < sz(mark); ++i)
        val.push_back(mark[i] - mark[i - 1]);
    unq(val);
    build(val);
    if (DBG) {
        cout << "val: "; for(int x : val) cout << x << ' '; cout << nl;
        cout << nl;
    }
    int m = sz(mark) - 1;
    FOR(j, 0, m) dp[0][j] = 1;

    for(int i = 1; i <= n; ++i) {
        // dp->prefix sum;
        int L = lower_bound(all(mark), a[i]) - mark.begin();
        int R = lower_bound(all(mark), b[i]) - mark.begin();
        if (DBG) cout << "l,r: " << L << ' ' << R << nl;
        for(int j = L; j <= R; ++j) {
            // dp(i, j)
            int lr = (j == L ? mark[j] : mark[j - 1] + 1);
            int rr = mark[j];
            int id = lower_bound(all(val), rr - lr + 1) - val.begin();
            int depth = 1;
            dp[i][j] = 0;
            for(int k = i - 1; k >= 0; --k) {
                // con cai gia tri f->ta tinh duoc luon gia tri

            if (DBG) if (i == 3 and j == 3) {
                cerr << k << ' ' << " - depth: " << depth << ' ' << dp[k][j - 1] << ' ' << f[id][depth] << nl;
            }
                add(dp[i][j], mul(dp[k][j - 1], f[id][depth]));
                if (a[k] <= lr and b[k] >= rr)
                    ++depth;
            }
            if (DBG)cout << dp[i][j] << ' ';
        }
        if (DBG)cout << nl;
        for(int j = L + 1; j <= m; ++j)
            add(dp[i][j], dp[i][j - 1]);
    }
    int ans = 0;
    for(int i = 1; i <= n; ++i) {
        add(ans, dp[i][m]);
    }
    cout << ans;
}
};

void main_code() {
    cin >> n;
    long long sum = 0;
    for(int i = 1; i <= n; ++i) cin >> a[i] >> b[i], sum += b[i] - a[i] + 1;
    if (n <= 500 and sum == n) {
        return SUB1::sol(), void();
    }
    if (n <= 500 and sum <= (int)1e6 + 7) {
        return SUB2::sol(), void();
    }
    SUB3::sol();
}


/*     Let the river flows naturally     */

Compilation message (stderr)

boat.cpp: In function 'int main()':
boat.cpp:36:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   36 |         freopen(task".inp", "r", stdin);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
boat.cpp:37:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   37 |         freopen(task".out", "w", stdout);
      |         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~

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