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Submission #40681

# Submission time Handle Problem Language Result Execution time Memory
40681 2018-02-06T18:49:31 Z bogdan10bos Boat (APIO16_boat) C++14
36 / 100
 2000 ms 16208 KB 
#include <bits/stdc++.h>

using namespace std;

//#define FILE_IO

const int mod = 1e9 + 7;

int N, K;
int a[1005], b[1005], st[1005], dr[1005];
int dp[1005][4005], sum[1005][4005];  /// primele i, ultimul este in intervalul j
int fct[100005], ifct[100005], inv[100005];
int cmb[100005];
int cc[4005][1005];

class Normalize
{
public:
    map<int, int> mp;
    vector<int> ord;

    void add(int x)
    {
        if(mp.count(x)) return;
        ord.push_back(x);
        mp[x];
    }

    void normalize()
    {
        sort(ord.begin(), ord.end());
        for(int i = 0; i < ord.size(); i++)
            mp[ ord[i] ] = i;
    }

    int get(int x) { return mp[x]; }
}nrm;

int power(int x, int y)
{
    if(y <= 0)  return 1;
    int ans = power( (1LL * x * x) % mod, y >> 1 );
    if(y & 1)   ans = (1LL * x * ans) % mod;
    return ans;
}

void pre(int K)
{
    fct[0] = 1;
    for(int i = 1; i <= K; i++) fct[i] = (1LL * fct[i - 1] * i) % mod;
    ifct[K] = power(fct[K], mod - 2);
    for(int i = K - 1; i >= 0; i--) ifct[i] = (1LL * ifct[i + 1] * (i + 1)) % mod;

    for(int i = 1; i <= K; i++) inv[i] = power(i, mod - 2);
}

int C(int N, int K)
{
    if(K > N)   return 0;
    int ans = (1LL * fct[N] * ifct[K]) % mod;
    ans = (1LL * ans * ifct[N - K]) % mod;
    return ans;
}

int main()
{
    #ifdef FILE_IO
    freopen("1.in", "r", stdin);
    freopen("1.out", "w", stdout);
    #endif

    pre(1e4);

    scanf("%d", &N);
    for(int i = 1; i <= N; i++)
    {
        scanf("%d%d", &a[i], &b[i]);
        nrm.add(a[i]);
        nrm.add(b[i]);
    }
    nrm.normalize();
    for(int i = 1; i <= N; i++)
    {
        st[i] = nrm.get(a[i]);
        dr[i] = nrm.get(b[i]);
    }
    K = nrm.ord.size();

    for(int i = 2; i <= 2 * K - 1; i += 2)
    {
        int lft = nrm.ord[i / 2 - 1];
        int rgt = nrm.ord[i / 2];
        int sz = rgt - lft - 1;

        cmb[0] = 1;
        for(int k = 1; k <= N; k++)
        {
            cmb[k] = (1LL * cmb[k - 1] * (sz - k + 1)) % mod;
            cmb[k] = (1LL * cmb[k] * inv[k]) % mod;
        }

        for(int j = 1; j <= N; j++)
            for(int k = 0; k < j; k++)
                cc[i][j] = (cc[i][j] + (1LL * cmb[k + 1] * C(j - 1, k)) % mod) % mod;
    }

    for(int i = 0; i <= 2 * K - 1; i++) dp[0][i] = sum[0][i] = 1;

    int ans = 0;

    for(int i = 1; i <= N; i++)
    {
        sum[i][0] = sum[i - 1][0];
        for(int j = 1; j <= 2 * K - 1; j++)
        {
            dp[i][j] = dp[i][j - 1];
            if(j & 1)
            {
                int x = nrm.ord[j / 2];
                if(a[i] <= x && x <= b[i])
                    dp[i][j] = (dp[i][j] + sum[i - 1][j - 1]) % mod;
            }
            else
            {
                int lft = nrm.ord[j / 2 - 1];
                int rgt = nrm.ord[j / 2];
                int sz = rgt - lft - 1;

                if(a[i] <= lft && rgt <= b[i])
                {
                    cmb[0] = 1;
                    for(int k = 1; k <= i; k++)
                    {
                        cmb[k] = (1LL * cmb[k - 1] * (sz - k + 1)) % mod;
                        cmb[k] = (1LL * cmb[k] * inv[k]) % mod;
                    }

                    int cnt = 0;
                    for(int k = i; k > 0; k--)
                    {
                        if(a[k] <= lft && rgt <= b[k])
                            cnt++;

                        int ans = cc[j][cnt];

                        dp[i][j] += (1LL * dp[k - 1][j - 1] * ans) % mod;
                        dp[i][j] %= mod;
                    }
                }
            }
            sum[i][j] = (sum[i - 1][j] + dp[i][j]) % mod;
        }
        ans = (ans + dp[i][2 * K - 1]) % mod;
    }
    printf("%d\n", ans);

    return 0;
}

Compilation message

boat.cpp: In member function 'void Normalize::normalize()':
boat.cpp:32:26: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         for(int i = 0; i < ord.size(); i++)
                          ^
boat.cpp: In function 'int main()':
boat.cpp:74:20: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d", &N);
                    ^
boat.cpp:77:36: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%d%d", &a[i], &b[i]);
                                    ^

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 694 ms 11520 KB Output is correct
2 Correct 685 ms 11520 KB Output is correct
3 Correct 688 ms 11524 KB Output is correct
4 Correct 720 ms 11668 KB Output is correct
5 Correct 709 ms 11688 KB Output is correct
6 Correct 700 ms 11780 KB Output is correct
7 Correct 712 ms 11832 KB Output is correct
8 Correct 710 ms 11832 KB Output is correct
9 Correct 703 ms 11832 KB Output is correct
10 Correct 723 ms 11868 KB Output is correct
11 Correct 712 ms 11868 KB Output is correct
12 Correct 688 ms 11868 KB Output is correct
13 Correct 699 ms 11868 KB Output is correct
14 Correct 686 ms 11868 KB Output is correct
15 Correct 739 ms 11868 KB Output is correct
16 Correct 125 ms 11868 KB Output is correct
17 Correct 140 ms 11868 KB Output is correct
18 Correct 135 ms 11868 KB Output is correct
19 Correct 153 ms 11868 KB Output is correct
20 Correct 134 ms 11868 KB Output is correct

Subtask #2
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 694 ms 11520 KB Output is correct
2 Correct 685 ms 11520 KB Output is correct
3 Correct 688 ms 11524 KB Output is correct
4 Correct 720 ms 11668 KB Output is correct
5 Correct 709 ms 11688 KB Output is correct
6 Correct 700 ms 11780 KB Output is correct
7 Correct 712 ms 11832 KB Output is correct
8 Correct 710 ms 11832 KB Output is correct
9 Correct 703 ms 11832 KB Output is correct
10 Correct 723 ms 11868 KB Output is correct
11 Correct 712 ms 11868 KB Output is correct
12 Correct 688 ms 11868 KB Output is correct
13 Correct 699 ms 11868 KB Output is correct
14 Correct 686 ms 11868 KB Output is correct
15 Correct 739 ms 11868 KB Output is correct
16 Correct 125 ms 11868 KB Output is correct
17 Correct 140 ms 11868 KB Output is correct
18 Correct 135 ms 11868 KB Output is correct
19 Correct 153 ms 11868 KB Output is correct
20 Correct 134 ms 11868 KB Output is correct
21 Execution timed out 2062 ms 16208 KB Time limit exceeded
22 Halted 0 ms 0 KB -

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 16208 KB Output is correct
2 Correct 24 ms 16208 KB Output is correct
3 Correct 24 ms 16208 KB Output is correct
4 Correct 27 ms 16208 KB Output is correct
5 Correct 26 ms 16208 KB Output is correct
6 Correct 29 ms 16208 KB Output is correct
7 Correct 30 ms 16208 KB Output is correct
8 Correct 27 ms 16208 KB Output is correct
9 Correct 27 ms 16208 KB Output is correct
10 Correct 28 ms 16208 KB Output is correct
11 Correct 23 ms 16208 KB Output is correct
12 Correct 22 ms 16208 KB Output is correct
13 Correct 24 ms 16208 KB Output is correct
14 Correct 23 ms 16208 KB Output is correct
15 Correct 27 ms 16208 KB Output is correct
16 Correct 15 ms 16208 KB Output is correct
17 Correct 14 ms 16208 KB Output is correct
18 Correct 13 ms 16208 KB Output is correct
19 Correct 14 ms 16208 KB Output is correct
20 Correct 14 ms 16208 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 694 ms 11520 KB Output is correct
2 Correct 685 ms 11520 KB Output is correct
3 Correct 688 ms 11524 KB Output is correct
4 Correct 720 ms 11668 KB Output is correct
5 Correct 709 ms 11688 KB Output is correct
6 Correct 700 ms 11780 KB Output is correct
7 Correct 712 ms 11832 KB Output is correct
8 Correct 710 ms 11832 KB Output is correct
9 Correct 703 ms 11832 KB Output is correct
10 Correct 723 ms 11868 KB Output is correct
11 Correct 712 ms 11868 KB Output is correct
12 Correct 688 ms 11868 KB Output is correct
13 Correct 699 ms 11868 KB Output is correct
14 Correct 686 ms 11868 KB Output is correct
15 Correct 739 ms 11868 KB Output is correct
16 Correct 125 ms 11868 KB Output is correct
17 Correct 140 ms 11868 KB Output is correct
18 Correct 135 ms 11868 KB Output is correct
19 Correct 153 ms 11868 KB Output is correct
20 Correct 134 ms 11868 KB Output is correct
21 Execution timed out 2062 ms 16208 KB Time limit exceeded
22 Halted 0 ms 0 KB -