oj.uz

Submission #1076442

# Submission time Handle Problem Language Result Execution time Memory
1076442 2024-08-26T13:57:13 Z RiverFlow Boat (APIO16_boat) C++14
100 / 100
 1010 ms 7556 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[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

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 1372 KB Output is correct
2 Correct 1 ms 1372 KB Output is correct
3 Correct 2 ms 1372 KB Output is correct
4 Correct 1 ms 1372 KB Output is correct
5 Correct 1 ms 1372 KB Output is correct
6 Correct 1 ms 1372 KB Output is correct
7 Correct 1 ms 1260 KB Output is correct
8 Correct 1 ms 1372 KB Output is correct
9 Correct 1 ms 1368 KB Output is correct
10 Correct 1 ms 1372 KB Output is correct
11 Correct 1 ms 1372 KB Output is correct
12 Correct 1 ms 1372 KB Output is correct
13 Correct 1 ms 1384 KB Output is correct
14 Correct 1 ms 1372 KB Output is correct
15 Correct 1 ms 1372 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 2 ms 1368 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 1372 KB Output is correct
2 Correct 1 ms 1372 KB Output is correct
3 Correct 2 ms 1372 KB Output is correct
4 Correct 1 ms 1372 KB Output is correct
5 Correct 1 ms 1372 KB Output is correct
6 Correct 1 ms 1372 KB Output is correct
7 Correct 1 ms 1260 KB Output is correct
8 Correct 1 ms 1372 KB Output is correct
9 Correct 1 ms 1368 KB Output is correct
10 Correct 1 ms 1372 KB Output is correct
11 Correct 1 ms 1372 KB Output is correct
12 Correct 1 ms 1372 KB Output is correct
13 Correct 1 ms 1384 KB Output is correct
14 Correct 1 ms 1372 KB Output is correct
15 Correct 1 ms 1372 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 2 ms 1368 KB Output is correct
20 Correct 1 ms 1372 KB Output is correct
21 Correct 202 ms 3668 KB Output is correct
22 Correct 197 ms 3616 KB Output is correct
23 Correct 174 ms 3664 KB Output is correct
24 Correct 228 ms 3800 KB Output is correct
25 Correct 201 ms 3920 KB Output is correct
26 Correct 328 ms 4148 KB Output is correct
27 Correct 336 ms 4248 KB Output is correct
28 Correct 328 ms 4184 KB Output is correct
29 Correct 358 ms 4180 KB Output is correct
30 Correct 7 ms 4188 KB Output is correct
31 Correct 7 ms 4264 KB Output is correct
32 Correct 7 ms 4188 KB Output is correct
33 Correct 7 ms 4096 KB Output is correct
34 Correct 7 ms 4188 KB Output is correct
35 Correct 5 ms 3932 KB Output is correct
36 Correct 6 ms 4188 KB Output is correct
37 Correct 6 ms 4188 KB Output is correct
38 Correct 7 ms 4104 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 9 ms 1628 KB Output is correct
2 Correct 8 ms 1564 KB Output is correct
3 Correct 8 ms 1564 KB Output is correct
4 Correct 9 ms 1628 KB Output is correct
5 Correct 10 ms 1552 KB Output is correct
6 Correct 11 ms 1624 KB Output is correct
7 Correct 10 ms 1628 KB Output is correct
8 Correct 10 ms 1628 KB Output is correct
9 Correct 10 ms 1628 KB Output is correct
10 Correct 10 ms 1628 KB Output is correct
11 Correct 9 ms 1628 KB Output is correct
12 Correct 9 ms 1628 KB Output is correct
13 Correct 8 ms 1628 KB Output is correct
14 Correct 9 ms 1688 KB Output is correct
15 Correct 10 ms 1628 KB Output is correct
16 Correct 4 ms 1116 KB Output is correct
17 Correct 4 ms 1116 KB Output is correct
18 Correct 4 ms 1116 KB Output is correct
19 Correct 4 ms 1116 KB Output is correct
20 Correct 5 ms 1116 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1372 KB Output is correct
2 Correct 1 ms 1372 KB Output is correct
3 Correct 2 ms 1372 KB Output is correct
4 Correct 1 ms 1372 KB Output is correct
5 Correct 1 ms 1372 KB Output is correct
6 Correct 1 ms 1372 KB Output is correct
7 Correct 1 ms 1260 KB Output is correct
8 Correct 1 ms 1372 KB Output is correct
9 Correct 1 ms 1368 KB Output is correct
10 Correct 1 ms 1372 KB Output is correct
11 Correct 1 ms 1372 KB Output is correct
12 Correct 1 ms 1372 KB Output is correct
13 Correct 1 ms 1384 KB Output is correct
14 Correct 1 ms 1372 KB Output is correct
15 Correct 1 ms 1372 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 2 ms 1368 KB Output is correct
20 Correct 1 ms 1372 KB Output is correct
21 Correct 202 ms 3668 KB Output is correct
22 Correct 197 ms 3616 KB Output is correct
23 Correct 174 ms 3664 KB Output is correct
24 Correct 228 ms 3800 KB Output is correct
25 Correct 201 ms 3920 KB Output is correct
26 Correct 328 ms 4148 KB Output is correct
27 Correct 336 ms 4248 KB Output is correct
28 Correct 328 ms 4184 KB Output is correct
29 Correct 358 ms 4180 KB Output is correct
30 Correct 7 ms 4188 KB Output is correct
31 Correct 7 ms 4264 KB Output is correct
32 Correct 7 ms 4188 KB Output is correct
33 Correct 7 ms 4096 KB Output is correct
34 Correct 7 ms 4188 KB Output is correct
35 Correct 5 ms 3932 KB Output is correct
36 Correct 6 ms 4188 KB Output is correct
37 Correct 6 ms 4188 KB Output is correct
38 Correct 7 ms 4104 KB Output is correct
39 Correct 9 ms 1628 KB Output is correct
40 Correct 8 ms 1564 KB Output is correct
41 Correct 8 ms 1564 KB Output is correct
42 Correct 9 ms 1628 KB Output is correct
43 Correct 10 ms 1552 KB Output is correct
44 Correct 11 ms 1624 KB Output is correct
45 Correct 10 ms 1628 KB Output is correct
46 Correct 10 ms 1628 KB Output is correct
47 Correct 10 ms 1628 KB Output is correct
48 Correct 10 ms 1628 KB Output is correct
49 Correct 9 ms 1628 KB Output is correct
50 Correct 9 ms 1628 KB Output is correct
51 Correct 8 ms 1628 KB Output is correct
52 Correct 9 ms 1688 KB Output is correct
53 Correct 10 ms 1628 KB Output is correct
54 Correct 4 ms 1116 KB Output is correct
55 Correct 4 ms 1116 KB Output is correct
56 Correct 4 ms 1116 KB Output is correct
57 Correct 4 ms 1116 KB Output is correct
58 Correct 5 ms 1116 KB Output is correct
59 Correct 916 ms 7248 KB Output is correct
60 Correct 931 ms 7180 KB Output is correct
61 Correct 908 ms 7364 KB Output is correct
62 Correct 912 ms 7240 KB Output is correct
63 Correct 905 ms 7292 KB Output is correct
64 Correct 1010 ms 7336 KB Output is correct
65 Correct 984 ms 7252 KB Output is correct
66 Correct 983 ms 7248 KB Output is correct
67 Correct 984 ms 7508 KB Output is correct
68 Correct 972 ms 7252 KB Output is correct
69 Correct 853 ms 7376 KB Output is correct
70 Correct 851 ms 7292 KB Output is correct
71 Correct 858 ms 7556 KB Output is correct
72 Correct 880 ms 7276 KB Output is correct
73 Correct 863 ms 7344 KB Output is correct
74 Correct 98 ms 3156 KB Output is correct
75 Correct 97 ms 3120 KB Output is correct
76 Correct 100 ms 3032 KB Output is correct
77 Correct 98 ms 3084 KB Output is correct
78 Correct 115 ms 3156 KB Output is correct