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Submission #839859

# Submission time Handle Problem Language Result Execution time Memory
839859 2023-08-30T19:04:24 Z popovicirobert Boat (APIO16_boat) C++14
100 / 100
 1603 ms 12404 KB 
#include <bits/stdc++.h>
 
using namespace std;

constexpr int MOD = (int) 1e9 + 7;

inline int logpow(int a, int b) {
    int answer = 1;
    while (b > 0) {
        if (b & 1) answer = (1LL * answer * a) % MOD;
        b >>= 1;
        a = (1LL * a * a) % MOD;
    }
    return answer;
}

inline void add(int& x, int y) {
    x += y;
    if (x >= MOD)
        x -= MOD;
}

constexpr int MAXN = 505;

int dp[2][4 * MAXN + 1][MAXN + 1];
int sp[2][4 * MAXN + 1];
 
int main() {
#ifdef HOME
    ifstream cin("input.in");
    ofstream cout("output.out");
#endif
    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    int n;
    cin >> n;
    
    vector<int> a(n + 1), b(n + 1);
    vector<int> x;

    for (int i = 1; i <= n; i++) {
        cin >> a[i] >> b[i];
        x.push_back(a[i]);
        x.push_back(b[i]);
    }

    sort(x.begin(), x.end());
    x.resize(unique(x.begin(), x.end()) - x.begin());

    vector<pair<int, int>> segs;
    segs.push_back({0, 0});

    for (int i = 0; i < (int)x.size(); i++) {
        segs.push_back({x[i], x[i]});
        if (i + 1 < (int)x.size() && x[i] + 1 <= x[i + 1] - 1) {    
            segs.push_back({x[i] + 1, x[i + 1] - 1});
        }
    }

    vector<vector<int>> comb(segs.size(), vector<int>(n + 1));
    for (int i = 0; i < (int)segs.size(); i++) {
        auto s = segs[i];
        int size = s.second - s.first + 1;

        int fact = 1, prod = 1;

        comb[i][0] = 1;
        for (int j = 1; j <= n; j++) {
            if (j > size) {
                comb[i][j] = 0;
                continue;
            }
            prod = (1LL * prod * (size - j + 1)) % MOD;
            fact = (1LL * fact * j) % MOD;
            comb[i][j] = (1LL * logpow(fact, MOD - 2) * prod) % MOD;
        }
    }

    // for (auto itr : segs) {
    //     cerr << itr.first << " " << itr.second << "    "; 
    // }
    // cerr << "\n";

    auto Comb = [&segs, &comb](int j, int k) {
        return segs[j].second - segs[j].first + 1 < k ? 0 : comb[j][k];
    };

    auto Calc = [&segs, &Comb](int i) {
        for (int j = 0; j < (int)segs.size(); j++) {
            for (int k = 1; k <= i + 1; k++) {
                int curr = dp[i & 1][j][k];
                if (curr == 0) continue;

                sp[i & 1][j] = (sp[i & 1][j] + 1LL * Comb(j, k) * curr) % MOD;
            }
        }

        for (int j = 1; j < (int)segs.size(); j++) {
            add(sp[i & 1][j], sp[i & 1][j - 1]);
        }
    };

    dp[0][0][1] = 1;
    Calc(0);

    for (int i = 1; i <= n; i++) {
        memset(sp[i & 1], 0, sizeof(sp[i & 1]));
        memset(dp[i & 1], 0, sizeof(dp[i & 1]));

        for (int j = 0; j < (int)segs.size(); j++) {
            for (int k = 1; k <= i; k++) {
                dp[i & 1][j][k] = dp[1 - i & 1][j][k];
            }
            if (a[i] <= segs[j].first && segs[j].second <= b[i]) {
                add(dp[i & 1][j][1], sp[1 - i & 1][j - 1]);
                for (int k = 1; k <= i; k++) {    
                    add(dp[i & 1][j][k], dp[1 - i & 1][j][k - 1]);
                }
            }
        }

        // for (int j = 0; j < (int)segs.size(); j++) {
        //     cerr << sp[1 - i & 1][j] << " "; 
        // }
        // cerr << "\n";

        // for (int j = 0; j < (int)segs.size(); j++) {
        //     for (int k = 1; k <= i; k++) {
        //         cerr << dp[i & 1][j][k] << " ";
        //     }
        //     cerr << "\n";
        // }
        // cerr << "\n";

        Calc(i);
    }

    cout << (sp[n & 1][(int)segs.size() - 1] + MOD - 1) % MOD;
 
    return 0;
}

Compilation message

boat.cpp: In function 'int main()':
boat.cpp:113:40: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
  113 |                 dp[i & 1][j][k] = dp[1 - i & 1][j][k];
      |                                      ~~^~~
boat.cpp:116:43: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
  116 |                 add(dp[i & 1][j][1], sp[1 - i & 1][j - 1]);
      |                                         ~~^~~
boat.cpp:118:47: warning: suggest parentheses around '-' in operand of '&' [-Wparentheses]
  118 |                     add(dp[i & 1][j][k], dp[1 - i & 1][j][k - 1]);
      |                                             ~~^~~

Subtask #1
9.0 / 9.0

# Verdict Execution time Memory Grader output
1 Correct 242 ms 10332 KB Output is correct
2 Correct 237 ms 10332 KB Output is correct
3 Correct 234 ms 10332 KB Output is correct
4 Correct 241 ms 10340 KB Output is correct
5 Correct 238 ms 10408 KB Output is correct
6 Correct 231 ms 10224 KB Output is correct
7 Correct 243 ms 10316 KB Output is correct
8 Correct 231 ms 10316 KB Output is correct
9 Correct 235 ms 10452 KB Output is correct
10 Correct 239 ms 10336 KB Output is correct
11 Correct 238 ms 10316 KB Output is correct
12 Correct 232 ms 10336 KB Output is correct
13 Correct 230 ms 10316 KB Output is correct
14 Correct 239 ms 10336 KB Output is correct
15 Correct 234 ms 10332 KB Output is correct
16 Correct 74 ms 8660 KB Output is correct
17 Correct 78 ms 8660 KB Output is correct
18 Correct 80 ms 8660 KB Output is correct
19 Correct 79 ms 8716 KB Output is correct
20 Correct 84 ms 8704 KB Output is correct

Subtask #2
22.0 / 22.0

# Verdict Execution time Memory Grader output
1 Correct 242 ms 10332 KB Output is correct
2 Correct 237 ms 10332 KB Output is correct
3 Correct 234 ms 10332 KB Output is correct
4 Correct 241 ms 10340 KB Output is correct
5 Correct 238 ms 10408 KB Output is correct
6 Correct 231 ms 10224 KB Output is correct
7 Correct 243 ms 10316 KB Output is correct
8 Correct 231 ms 10316 KB Output is correct
9 Correct 235 ms 10452 KB Output is correct
10 Correct 239 ms 10336 KB Output is correct
11 Correct 238 ms 10316 KB Output is correct
12 Correct 232 ms 10336 KB Output is correct
13 Correct 230 ms 10316 KB Output is correct
14 Correct 239 ms 10336 KB Output is correct
15 Correct 234 ms 10332 KB Output is correct
16 Correct 74 ms 8660 KB Output is correct
17 Correct 78 ms 8660 KB Output is correct
18 Correct 80 ms 8660 KB Output is correct
19 Correct 79 ms 8716 KB Output is correct
20 Correct 84 ms 8704 KB Output is correct
21 Correct 838 ms 11680 KB Output is correct
22 Correct 860 ms 11604 KB Output is correct
23 Correct 796 ms 11656 KB Output is correct
24 Correct 822 ms 11704 KB Output is correct
25 Correct 836 ms 11632 KB Output is correct
26 Correct 1120 ms 11488 KB Output is correct
27 Correct 1111 ms 11512 KB Output is correct
28 Correct 1092 ms 11636 KB Output is correct
29 Correct 1109 ms 11600 KB Output is correct
30 Correct 368 ms 11996 KB Output is correct
31 Correct 410 ms 11980 KB Output is correct
32 Correct 371 ms 12108 KB Output is correct
33 Correct 373 ms 12056 KB Output is correct
34 Correct 367 ms 12028 KB Output is correct
35 Correct 236 ms 10316 KB Output is correct
36 Correct 237 ms 10316 KB Output is correct
37 Correct 240 ms 10348 KB Output is correct
38 Correct 252 ms 10340 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 21 ms 8480 KB Output is correct
2 Correct 19 ms 8440 KB Output is correct
3 Correct 21 ms 8404 KB Output is correct
4 Correct 23 ms 8520 KB Output is correct
5 Correct 23 ms 8532 KB Output is correct
6 Correct 31 ms 8512 KB Output is correct
7 Correct 26 ms 8404 KB Output is correct
8 Correct 28 ms 8404 KB Output is correct
9 Correct 25 ms 8404 KB Output is correct
10 Correct 29 ms 8516 KB Output is correct
11 Correct 23 ms 8448 KB Output is correct
12 Correct 30 ms 8404 KB Output is correct
13 Correct 23 ms 8404 KB Output is correct
14 Correct 22 ms 8404 KB Output is correct
15 Correct 23 ms 8532 KB Output is correct
16 Correct 15 ms 8404 KB Output is correct
17 Correct 19 ms 8404 KB Output is correct
18 Correct 17 ms 8404 KB Output is correct
19 Correct 17 ms 8532 KB Output is correct
20 Correct 15 ms 8404 KB Output is correct

Subtask #4
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 242 ms 10332 KB Output is correct
2 Correct 237 ms 10332 KB Output is correct
3 Correct 234 ms 10332 KB Output is correct
4 Correct 241 ms 10340 KB Output is correct
5 Correct 238 ms 10408 KB Output is correct
6 Correct 231 ms 10224 KB Output is correct
7 Correct 243 ms 10316 KB Output is correct
8 Correct 231 ms 10316 KB Output is correct
9 Correct 235 ms 10452 KB Output is correct
10 Correct 239 ms 10336 KB Output is correct
11 Correct 238 ms 10316 KB Output is correct
12 Correct 232 ms 10336 KB Output is correct
13 Correct 230 ms 10316 KB Output is correct
14 Correct 239 ms 10336 KB Output is correct
15 Correct 234 ms 10332 KB Output is correct
16 Correct 74 ms 8660 KB Output is correct
17 Correct 78 ms 8660 KB Output is correct
18 Correct 80 ms 8660 KB Output is correct
19 Correct 79 ms 8716 KB Output is correct
20 Correct 84 ms 8704 KB Output is correct
21 Correct 838 ms 11680 KB Output is correct
22 Correct 860 ms 11604 KB Output is correct
23 Correct 796 ms 11656 KB Output is correct
24 Correct 822 ms 11704 KB Output is correct
25 Correct 836 ms 11632 KB Output is correct
26 Correct 1120 ms 11488 KB Output is correct
27 Correct 1111 ms 11512 KB Output is correct
28 Correct 1092 ms 11636 KB Output is correct
29 Correct 1109 ms 11600 KB Output is correct
30 Correct 368 ms 11996 KB Output is correct
31 Correct 410 ms 11980 KB Output is correct
32 Correct 371 ms 12108 KB Output is correct
33 Correct 373 ms 12056 KB Output is correct
34 Correct 367 ms 12028 KB Output is correct
35 Correct 236 ms 10316 KB Output is correct
36 Correct 237 ms 10316 KB Output is correct
37 Correct 240 ms 10348 KB Output is correct
38 Correct 252 ms 10340 KB Output is correct
39 Correct 21 ms 8480 KB Output is correct
40 Correct 19 ms 8440 KB Output is correct
41 Correct 21 ms 8404 KB Output is correct
42 Correct 23 ms 8520 KB Output is correct
43 Correct 23 ms 8532 KB Output is correct
44 Correct 31 ms 8512 KB Output is correct
45 Correct 26 ms 8404 KB Output is correct
46 Correct 28 ms 8404 KB Output is correct
47 Correct 25 ms 8404 KB Output is correct
48 Correct 29 ms 8516 KB Output is correct
49 Correct 23 ms 8448 KB Output is correct
50 Correct 30 ms 8404 KB Output is correct
51 Correct 23 ms 8404 KB Output is correct
52 Correct 22 ms 8404 KB Output is correct
53 Correct 23 ms 8532 KB Output is correct
54 Correct 15 ms 8404 KB Output is correct
55 Correct 19 ms 8404 KB Output is correct
56 Correct 17 ms 8404 KB Output is correct
57 Correct 17 ms 8532 KB Output is correct
58 Correct 15 ms 8404 KB Output is correct
59 Correct 1097 ms 12236 KB Output is correct
60 Correct 1127 ms 12276 KB Output is correct
61 Correct 1040 ms 12344 KB Output is correct
62 Correct 1165 ms 12268 KB Output is correct
63 Correct 1109 ms 12348 KB Output is correct
64 Correct 1603 ms 12348 KB Output is correct
65 Correct 1561 ms 12352 KB Output is correct
66 Correct 1569 ms 12364 KB Output is correct
67 Correct 1477 ms 12356 KB Output is correct
68 Correct 1494 ms 12348 KB Output is correct
69 Correct 1090 ms 12404 KB Output is correct
70 Correct 1112 ms 12344 KB Output is correct
71 Correct 1119 ms 12356 KB Output is correct
72 Correct 1127 ms 12348 KB Output is correct
73 Correct 1142 ms 12236 KB Output is correct
74 Correct 148 ms 8660 KB Output is correct
75 Correct 146 ms 8660 KB Output is correct
76 Correct 149 ms 8660 KB Output is correct
77 Correct 148 ms 8744 KB Output is correct
78 Correct 148 ms 8660 KB Output is correct