oj.uz

Submission #1076437

# Submission time Handle Problem Language Result Execution time Memory
1076437 2024-08-26T13:53:29 Z RiverFlow Boat (APIO16_boat) C++14
58 / 100
 917 ms 8364 KB 
#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[N][3 * 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

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
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1368 KB Output is correct
2 Correct 1 ms 1372 KB Output is correct
3 Correct 1 ms 1372 KB Output is correct
4 Correct 1 ms 1368 KB Output is correct
5 Correct 1 ms 1372 KB Output is correct
6 Correct 2 ms 1372 KB Output is correct
7 Correct 1 ms 1372 KB Output is correct
8 Correct 1 ms 1372 KB Output is correct
9 Correct 1 ms 1372 KB Output is correct
10 Correct 1 ms 1368 KB Output is correct
11 Correct 1 ms 1372 KB Output is correct
12 Correct 2 ms 1372 KB Output is correct
13 Correct 1 ms 1372 KB Output is correct
14 Correct 1 ms 1372 KB Output is correct
15 Correct 1 ms 1248 KB Output is correct
16 Correct 1 ms 1372 KB Output is correct
17 Correct 1 ms 1372 KB Output is correct
18 Correct 1 ms 1372 KB Output is correct
19 Correct 1 ms 1264 KB Output is correct
20 Correct 1 ms 1372 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1368 KB Output is correct
2 Correct 1 ms 1372 KB Output is correct
3 Correct 1 ms 1372 KB Output is correct
4 Correct 1 ms 1368 KB Output is correct
5 Correct 1 ms 1372 KB Output is correct
6 Correct 2 ms 1372 KB Output is correct
7 Correct 1 ms 1372 KB Output is correct
8 Correct 1 ms 1372 KB Output is correct
9 Correct 1 ms 1372 KB Output is correct
10 Correct 1 ms 1368 KB Output is correct
11 Correct 1 ms 1372 KB Output is correct
12 Correct 2 ms 1372 KB Output is correct
13 Correct 1 ms 1372 KB Output is correct
14 Correct 1 ms 1372 KB Output is correct
15 Correct 1 ms 1248 KB Output is correct
16 Correct 1 ms 1372 KB Output is correct
17 Correct 1 ms 1372 KB Output is correct
18 Correct 1 ms 1372 KB Output is correct
19 Correct 1 ms 1264 KB Output is correct
20 Correct 1 ms 1372 KB Output is correct
21 Correct 206 ms 3792 KB Output is correct
22 Correct 208 ms 3668 KB Output is correct
23 Correct 174 ms 3668 KB Output is correct
24 Correct 220 ms 3924 KB Output is correct
25 Correct 216 ms 3920 KB Output is correct
26 Correct 323 ms 4008 KB Output is correct
27 Correct 353 ms 4180 KB Output is correct
28 Correct 328 ms 4180 KB Output is correct
29 Correct 340 ms 4176 KB Output is correct
30 Correct 7 ms 4188 KB Output is correct
31 Correct 7 ms 4188 KB Output is correct
32 Correct 7 ms 4188 KB Output is correct
33 Correct 6 ms 4188 KB Output is correct
34 Correct 7 ms 4196 KB Output is correct
35 Correct 6 ms 3928 KB Output is correct
36 Correct 6 ms 4184 KB Output is correct
37 Correct 6 ms 4188 KB Output is correct
38 Correct 8 ms 3932 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 2140 KB Output is correct
2 Correct 10 ms 2140 KB Output is correct
3 Correct 10 ms 2140 KB Output is correct
4 Correct 9 ms 2140 KB Output is correct
5 Correct 9 ms 2140 KB Output is correct
6 Correct 10 ms 2192 KB Output is correct
7 Correct 10 ms 2140 KB Output is correct
8 Correct 10 ms 2024 KB Output is correct
9 Correct 10 ms 2080 KB Output is correct
10 Correct 9 ms 2140 KB Output is correct
11 Correct 10 ms 2140 KB Output is correct
12 Correct 9 ms 2068 KB Output is correct
13 Correct 8 ms 2024 KB Output is correct
14 Correct 8 ms 2136 KB Output is correct
15 Correct 8 ms 2140 KB Output is correct
16 Correct 4 ms 1372 KB Output is correct
17 Correct 4 ms 1372 KB Output is correct
18 Correct 4 ms 1372 KB Output is correct
19 Correct 4 ms 1372 KB Output is correct
20 Correct 4 ms 1372 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1368 KB Output is correct
2 Correct 1 ms 1372 KB Output is correct
3 Correct 1 ms 1372 KB Output is correct
4 Correct 1 ms 1368 KB Output is correct
5 Correct 1 ms 1372 KB Output is correct
6 Correct 2 ms 1372 KB Output is correct
7 Correct 1 ms 1372 KB Output is correct
8 Correct 1 ms 1372 KB Output is correct
9 Correct 1 ms 1372 KB Output is correct
10 Correct 1 ms 1368 KB Output is correct
11 Correct 1 ms 1372 KB Output is correct
12 Correct 2 ms 1372 KB Output is correct
13 Correct 1 ms 1372 KB Output is correct
14 Correct 1 ms 1372 KB Output is correct
15 Correct 1 ms 1248 KB Output is correct
16 Correct 1 ms 1372 KB Output is correct
17 Correct 1 ms 1372 KB Output is correct
18 Correct 1 ms 1372 KB Output is correct
19 Correct 1 ms 1264 KB Output is correct
20 Correct 1 ms 1372 KB Output is correct
21 Correct 206 ms 3792 KB Output is correct
22 Correct 208 ms 3668 KB Output is correct
23 Correct 174 ms 3668 KB Output is correct
24 Correct 220 ms 3924 KB Output is correct
25 Correct 216 ms 3920 KB Output is correct
26 Correct 323 ms 4008 KB Output is correct
27 Correct 353 ms 4180 KB Output is correct
28 Correct 328 ms 4180 KB Output is correct
29 Correct 340 ms 4176 KB Output is correct
30 Correct 7 ms 4188 KB Output is correct
31 Correct 7 ms 4188 KB Output is correct
32 Correct 7 ms 4188 KB Output is correct
33 Correct 6 ms 4188 KB Output is correct
34 Correct 7 ms 4196 KB Output is correct
35 Correct 6 ms 3928 KB Output is correct
36 Correct 6 ms 4184 KB Output is correct
37 Correct 6 ms 4188 KB Output is correct
38 Correct 8 ms 3932 KB Output is correct
39 Correct 9 ms 2140 KB Output is correct
40 Correct 10 ms 2140 KB Output is correct
41 Correct 10 ms 2140 KB Output is correct
42 Correct 9 ms 2140 KB Output is correct
43 Correct 9 ms 2140 KB Output is correct
44 Correct 10 ms 2192 KB Output is correct
45 Correct 10 ms 2140 KB Output is correct
46 Correct 10 ms 2024 KB Output is correct
47 Correct 10 ms 2080 KB Output is correct
48 Correct 9 ms 2140 KB Output is correct
49 Correct 10 ms 2140 KB Output is correct
50 Correct 9 ms 2068 KB Output is correct
51 Correct 8 ms 2024 KB Output is correct
52 Correct 8 ms 2136 KB Output is correct
53 Correct 8 ms 2140 KB Output is correct
54 Correct 4 ms 1372 KB Output is correct
55 Correct 4 ms 1372 KB Output is correct
56 Correct 4 ms 1372 KB Output is correct
57 Correct 4 ms 1372 KB Output is correct
58 Correct 4 ms 1372 KB Output is correct
59 Incorrect 917 ms 8364 KB Output isn't correct
60 Halted 0 ms 0 KB -