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Submission #40683

# Submission time Handle Problem Language Result Execution time Memory
40683 2018-02-06T18:53:56 Z bogdan10bos Boat (APIO16_boat) C++14
100 / 100
 1950 ms 18356 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];
int cntall[4005];

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]);
        for(int j = 2 * st[i] + 2; j < 2 * dr[i] + 2; j += 2)  cntall[j]++;
    }
    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 <= cntall[i]; k++)
        {
            cmb[k] = (1LL * cmb[k - 1] * (sz - k + 1)) % mod;
            cmb[k] = (1LL * cmb[k] * inv[k]) % mod;
        }

        for(int j = 1; j <= cntall[i]; 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:33:26: 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:75:20: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d", &N);
                    ^
boat.cpp:78:36: 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 13 ms 8440 KB Output is correct
3 Correct 12 ms 8488 KB Output is correct
4 Correct 13 ms 8652 KB Output is correct
5 Correct 13 ms 8652 KB Output is correct
6 Correct 13 ms 8652 KB Output is correct
7 Correct 13 ms 8652 KB Output is correct
8 Correct 13 ms 8652 KB Output is correct
9 Correct 13 ms 8652 KB Output is correct
10 Correct 13 ms 8652 KB Output is correct
11 Correct 12 ms 8652 KB Output is correct
12 Correct 13 ms 8652 KB Output is correct
13 Correct 13 ms 8652 KB Output is correct
14 Correct 14 ms 8660 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 8 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
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 8440 KB Output is correct
2 Correct 13 ms 8440 KB Output is correct
3 Correct 12 ms 8488 KB Output is correct
4 Correct 13 ms 8652 KB Output is correct
5 Correct 13 ms 8652 KB Output is correct
6 Correct 13 ms 8652 KB Output is correct
7 Correct 13 ms 8652 KB Output is correct
8 Correct 13 ms 8652 KB Output is correct
9 Correct 13 ms 8652 KB Output is correct
10 Correct 13 ms 8652 KB Output is correct
11 Correct 12 ms 8652 KB Output is correct
12 Correct 13 ms 8652 KB Output is correct
13 Correct 13 ms 8652 KB Output is correct
14 Correct 14 ms 8660 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 8 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 Correct 1129 ms 16344 KB Output is correct
22 Correct 1212 ms 16548 KB Output is correct
23 Correct 1008 ms 16548 KB Output is correct
24 Correct 1101 ms 16548 KB Output is correct
25 Correct 1060 ms 16548 KB Output is correct
26 Correct 1617 ms 16548 KB Output is correct
27 Correct 1698 ms 16548 KB Output is correct
28 Correct 1625 ms 16548 KB Output is correct
29 Correct 1634 ms 16548 KB Output is correct
30 Correct 34 ms 16548 KB Output is correct
31 Correct 34 ms 16548 KB Output is correct
32 Correct 30 ms 16548 KB Output is correct
33 Correct 31 ms 16548 KB Output is correct
34 Correct 28 ms 16548 KB Output is correct
35 Correct 18 ms 16548 KB Output is correct
36 Correct 18 ms 16548 KB Output is correct
37 Correct 20 ms 16548 KB Output is correct
38 Correct 21 ms 16548 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 15 ms 16548 KB Output is correct
2 Correct 14 ms 16548 KB Output is correct
3 Correct 14 ms 16548 KB Output is correct
4 Correct 15 ms 16548 KB Output is correct
5 Correct 15 ms 16548 KB Output is correct
6 Correct 20 ms 16548 KB Output is correct
7 Correct 20 ms 16548 KB Output is correct
8 Correct 20 ms 16548 KB Output is correct
9 Correct 20 ms 16548 KB Output is correct
10 Correct 20 ms 16548 KB Output is correct
11 Correct 14 ms 16548 KB Output is correct
12 Correct 12 ms 16548 KB Output is correct
13 Correct 13 ms 16548 KB Output is correct
14 Correct 13 ms 16548 KB Output is correct
15 Correct 14 ms 16548 KB Output is correct
16 Correct 10 ms 16548 KB Output is correct
17 Correct 9 ms 16548 KB Output is correct
18 Correct 9 ms 16548 KB Output is correct
19 Correct 9 ms 16548 KB Output is correct
20 Correct 12 ms 16548 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 13 ms 8440 KB Output is correct
2 Correct 13 ms 8440 KB Output is correct
3 Correct 12 ms 8488 KB Output is correct
4 Correct 13 ms 8652 KB Output is correct
5 Correct 13 ms 8652 KB Output is correct
6 Correct 13 ms 8652 KB Output is correct
7 Correct 13 ms 8652 KB Output is correct
8 Correct 13 ms 8652 KB Output is correct
9 Correct 13 ms 8652 KB Output is correct
10 Correct 13 ms 8652 KB Output is correct
11 Correct 12 ms 8652 KB Output is correct
12 Correct 13 ms 8652 KB Output is correct
13 Correct 13 ms 8652 KB Output is correct
14 Correct 14 ms 8660 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 8 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 Correct 1129 ms 16344 KB Output is correct
22 Correct 1212 ms 16548 KB Output is correct
23 Correct 1008 ms 16548 KB Output is correct
24 Correct 1101 ms 16548 KB Output is correct
25 Correct 1060 ms 16548 KB Output is correct
26 Correct 1617 ms 16548 KB Output is correct
27 Correct 1698 ms 16548 KB Output is correct
28 Correct 1625 ms 16548 KB Output is correct
29 Correct 1634 ms 16548 KB Output is correct
30 Correct 34 ms 16548 KB Output is correct
31 Correct 34 ms 16548 KB Output is correct
32 Correct 30 ms 16548 KB Output is correct
33 Correct 31 ms 16548 KB Output is correct
34 Correct 28 ms 16548 KB Output is correct
35 Correct 18 ms 16548 KB Output is correct
36 Correct 18 ms 16548 KB Output is correct
37 Correct 20 ms 16548 KB Output is correct
38 Correct 21 ms 16548 KB Output is correct
39 Correct 15 ms 16548 KB Output is correct
40 Correct 14 ms 16548 KB Output is correct
41 Correct 14 ms 16548 KB Output is correct
42 Correct 15 ms 16548 KB Output is correct
43 Correct 15 ms 16548 KB Output is correct
44 Correct 20 ms 16548 KB Output is correct
45 Correct 20 ms 16548 KB Output is correct
46 Correct 20 ms 16548 KB Output is correct
47 Correct 20 ms 16548 KB Output is correct
48 Correct 20 ms 16548 KB Output is correct
49 Correct 14 ms 16548 KB Output is correct
50 Correct 12 ms 16548 KB Output is correct
51 Correct 13 ms 16548 KB Output is correct
52 Correct 13 ms 16548 KB Output is correct
53 Correct 14 ms 16548 KB Output is correct
54 Correct 10 ms 16548 KB Output is correct
55 Correct 9 ms 16548 KB Output is correct
56 Correct 9 ms 16548 KB Output is correct
57 Correct 9 ms 16548 KB Output is correct
58 Correct 12 ms 16548 KB Output is correct
59 Correct 1184 ms 17920 KB Output is correct
60 Correct 1149 ms 17920 KB Output is correct
61 Correct 1103 ms 17920 KB Output is correct
62 Correct 1184 ms 17920 KB Output is correct
63 Correct 1147 ms 17920 KB Output is correct
64 Correct 1843 ms 18204 KB Output is correct
65 Correct 1862 ms 18356 KB Output is correct
66 Correct 1939 ms 18356 KB Output is correct
67 Correct 1909 ms 18356 KB Output is correct
68 Correct 1950 ms 18356 KB Output is correct
69 Correct 942 ms 18356 KB Output is correct
70 Correct 917 ms 18356 KB Output is correct
71 Correct 896 ms 18356 KB Output is correct
72 Correct 936 ms 18356 KB Output is correct
73 Correct 964 ms 18356 KB Output is correct
74 Correct 120 ms 18356 KB Output is correct
75 Correct 122 ms 18356 KB Output is correct
76 Correct 122 ms 18356 KB Output is correct
77 Correct 122 ms 18356 KB Output is correct
78 Correct 126 ms 18356 KB Output is correct