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Submission #40680

# Submission time Handle Problem Language Result Execution time Memory
40680 2018-02-06T18:42:40 Z bogdan10bos Boat (APIO16_boat) C++14
36 / 100
 2000 ms 8684 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];

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 = 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 = 0;
                        for(int o = 0; o < cnt; o++)
                            ans = (ans + (1LL * cmb[o + 1] * C(cnt - 1, o)) % mod) % mod;

                        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:31:26: 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:73:20: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d", &N);
                    ^
boat.cpp:76:36: 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 13 ms 8440 KB Output is correct
2 Correct 15 ms 8544 KB Output is correct
3 Correct 13 ms 8616 KB Output is correct
4 Correct 13 ms 8616 KB Output is correct
5 Correct 13 ms 8616 KB Output is correct
6 Correct 14 ms 8632 KB Output is correct
7 Correct 14 ms 8648 KB Output is correct
8 Correct 21 ms 8684 KB Output is correct
9 Correct 13 ms 8684 KB Output is correct
10 Correct 14 ms 8684 KB Output is correct
11 Correct 17 ms 8684 KB Output is correct
12 Correct 13 ms 8684 KB Output is correct
13 Correct 14 ms 8684 KB Output is correct
14 Correct 14 ms 8684 KB Output is correct
15 Correct 13 ms 8684 KB Output is correct
16 Correct 9 ms 8684 KB Output is correct
17 Correct 9 ms 8684 KB Output is correct
18 Correct 9 ms 8684 KB Output is correct
19 Correct 9 ms 8684 KB Output is correct
20 Correct 9 ms 8684 KB Output is correct

Subtask #2
0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 8440 KB Output is correct
2 Correct 15 ms 8544 KB Output is correct
3 Correct 13 ms 8616 KB Output is correct
4 Correct 13 ms 8616 KB Output is correct
5 Correct 13 ms 8616 KB Output is correct
6 Correct 14 ms 8632 KB Output is correct
7 Correct 14 ms 8648 KB Output is correct
8 Correct 21 ms 8684 KB Output is correct
9 Correct 13 ms 8684 KB Output is correct
10 Correct 14 ms 8684 KB Output is correct
11 Correct 17 ms 8684 KB Output is correct
12 Correct 13 ms 8684 KB Output is correct
13 Correct 14 ms 8684 KB Output is correct
14 Correct 14 ms 8684 KB Output is correct
15 Correct 13 ms 8684 KB Output is correct
16 Correct 9 ms 8684 KB Output is correct
17 Correct 9 ms 8684 KB Output is correct
18 Correct 9 ms 8684 KB Output is correct
19 Correct 9 ms 8684 KB Output is correct
20 Correct 9 ms 8684 KB Output is correct
21 Execution timed out 2024 ms 8684 KB Time limit exceeded
22 Halted 0 ms 0 KB -

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 61 ms 8684 KB Output is correct
2 Correct 49 ms 8684 KB Output is correct
3 Correct 63 ms 8684 KB Output is correct
4 Correct 64 ms 8684 KB Output is correct
5 Correct 74 ms 8684 KB Output is correct
6 Correct 151 ms 8684 KB Output is correct
7 Correct 150 ms 8684 KB Output is correct
8 Correct 152 ms 8684 KB Output is correct
9 Correct 154 ms 8684 KB Output is correct
10 Correct 150 ms 8684 KB Output is correct
11 Correct 70 ms 8684 KB Output is correct
12 Correct 45 ms 8684 KB Output is correct
13 Correct 49 ms 8684 KB Output is correct
14 Correct 58 ms 8684 KB Output is correct
15 Correct 65 ms 8684 KB Output is correct
16 Correct 30 ms 8684 KB Output is correct
17 Correct 27 ms 8684 KB Output is correct
18 Correct 29 ms 8684 KB Output is correct
19 Correct 27 ms 8684 KB Output is correct
20 Correct 36 ms 8684 KB Output is correct

Subtask #4
0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 8440 KB Output is correct
2 Correct 15 ms 8544 KB Output is correct
3 Correct 13 ms 8616 KB Output is correct
4 Correct 13 ms 8616 KB Output is correct
5 Correct 13 ms 8616 KB Output is correct
6 Correct 14 ms 8632 KB Output is correct
7 Correct 14 ms 8648 KB Output is correct
8 Correct 21 ms 8684 KB Output is correct
9 Correct 13 ms 8684 KB Output is correct
10 Correct 14 ms 8684 KB Output is correct
11 Correct 17 ms 8684 KB Output is correct
12 Correct 13 ms 8684 KB Output is correct
13 Correct 14 ms 8684 KB Output is correct
14 Correct 14 ms 8684 KB Output is correct
15 Correct 13 ms 8684 KB Output is correct
16 Correct 9 ms 8684 KB Output is correct
17 Correct 9 ms 8684 KB Output is correct
18 Correct 9 ms 8684 KB Output is correct
19 Correct 9 ms 8684 KB Output is correct
20 Correct 9 ms 8684 KB Output is correct
21 Execution timed out 2024 ms 8684 KB Time limit exceeded
22 Halted 0 ms 0 KB -