oj.uz

Submission #127511

# Submission time Handle Problem Language Result Execution time Memory
127511 2019-07-09T13:17:43 Z darkkcyan Kangaroo (CEOI16_kangaroo) C++14
100 / 100
 38 ms 32376 KB 
#include <bits/stdc++.h>
using namespace std;
using namespace std::placeholders;

#define llong long long 
#define xx first
#define yy second
#define len(x) ((int)x.size())
#define rep(i,n) for (int i = -1; ++ i < n; )
#define rep1(i,n) for (int i = 0; i ++ < n; )
#define all(x) x.begin(), x.end()
// #define rand __rand
// mt19937 rand(chrono::system_clock::now().time_since_epoch().count());  // or mt19937_64

#define rem ((llong)1e9+7)
#define UP 1
#define DOWN 0

namespace solution_51_points {
    // the solution is similar to the official solution, but I don't swap cs and cf.
    // I check them by hand and decrease cf if necessary.
    const int maxn = 222;
    llong dp[maxn][maxn][maxn][2];  // dp[n][cs][cf][dir]
                                    //   n - the number of cells in the garden.
                                    //   cs - the starting cell
                                    //   cf - the final cell
                                    //   dir - the current direction to move (UP or DOWN)
    llong pref_sum[maxn][maxn][maxn][2];
    // pref_sum[n][cs][cf][dir] = dp[n][1][cf][dir] + dp[n][2][cf][dir] + ... + dp[n][cs][cf][dir]
    // in other words: pref_sum[n][cs][cf][dir] = sum of dp[n][1..cs][cf][dir]

    // these 2 functions lazily calculate pref_sum and dp respectively.
    llong cal_pref_sum(int, int, int, bool);
    llong cal(int, int, int, bool);

    llong cal_pref_sum(int n, int cs, int cf, bool dir) {
        if (cs == 0) return 0;
        llong& ans = pref_sum[n][cs][cf][dir];
        if (ans == -1) ans = cal_pref_sum(n, cs - 1, cf, dir) + cal(n, cs, cf, dir);
        return ans %= rem;
    }

    llong cal(int n, int cs, int cf, bool dir) {
        llong& ans = dp[n][cs][cf][dir];
        if (ans != -1) return ans;
        if (cf == cs) return 0;
        if (n == 2) return ((dir == DOWN and cs > cf) or (dir == UP and cs < cf));
        int range_begin, range_end;
        if (dir == DOWN) {
            range_begin = 1;
            range_end = cs - 1;
        } else {
            range_begin = cs;
            range_end = n - 1;
        }

        int nxt_cf = cf - (cf > cs);
        ans = cal_pref_sum(n - 1, range_end, nxt_cf, !dir);
        ans += rem - cal_pref_sum(n - 1, range_begin - 1, nxt_cf, !dir);
        ans %= rem;
        // clog << n << ' ' << cs << ' ' << cf << ' ' << dir << ' ' << ans << endl;
        return ans;
    }

    llong solve(int n, int cs, int cf) {
        memset(dp, -1, sizeof(dp));
        memset(pref_sum, -1, sizeof pref_sum);
        return (cal(n, cf, cs, UP) + cal(n, cf, cs, DOWN)) % rem;
    }
};

namespace solution_100_points {
    const int maxn = 2020;
    llong dp[maxn][maxn];

    llong solve(int n, int cs, int cf) {
        memset(dp, 0, sizeof dp);
        dp[0][0] = 1;
        rep1(i, n) {
            if (i == cs or i == cf) {
                rep1(f, i) {
                    (dp[i][f] += dp[i - 1][f] + dp[i - 1][f - 1]) %= rem;
                }
            } else {
                int unfilled_endpoints = int(i < cs) + int(i < cf);
                //clog << i << ' ' << unfilled_endpoints << endl;
                rep1(f, i) {
                    (dp[i][f] += dp[i - 1][f + 1] * f) %= rem;
                    // (dp[i][f] += dp[i - 1][f] * (2 * f + unfilled_endpoints - 2)) %= rem;

                    int places_for_new_comp = 1;
                    if (f > 1) places_for_new_comp = f - 2 + unfilled_endpoints;
                    (dp[i][f] += dp[i - 1][f - 1] * places_for_new_comp) %= rem;
                    //clog << "place for comp" << ' ' << i << ' ' << f << ' ' << places_for_new_comp << ' ' << 2 * f + unfilled_endpoints - 2<< endl;
                }
            }

            //rep(f, i + 1) clog << i << ' ' << f << ' ' << dp[i][f] << endl;
        }

        return dp[n][1];
    }
};

int main(void) {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    // using namespace solution_51_points;
    using namespace solution_100_points;

    int n, cs, cf;
    cin >> n >> cs >> cf;
    cout << solve(n, cs, cf);

    return 0;
}

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 32376 KB Output is correct
2 Correct 29 ms 32248 KB Output is correct

Subtask #2
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 32376 KB Output is correct
2 Correct 29 ms 32248 KB Output is correct
3 Correct 36 ms 32260 KB Output is correct
4 Correct 33 ms 32248 KB Output is correct
5 Correct 28 ms 32248 KB Output is correct
6 Correct 28 ms 32248 KB Output is correct
7 Correct 28 ms 32248 KB Output is correct
8 Correct 28 ms 32248 KB Output is correct
9 Correct 28 ms 32248 KB Output is correct
10 Correct 28 ms 32248 KB Output is correct
11 Correct 28 ms 32248 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 32376 KB Output is correct
2 Correct 29 ms 32248 KB Output is correct
3 Correct 36 ms 32260 KB Output is correct
4 Correct 33 ms 32248 KB Output is correct
5 Correct 28 ms 32248 KB Output is correct
6 Correct 28 ms 32248 KB Output is correct
7 Correct 28 ms 32248 KB Output is correct
8 Correct 28 ms 32248 KB Output is correct
9 Correct 28 ms 32248 KB Output is correct
10 Correct 28 ms 32248 KB Output is correct
11 Correct 28 ms 32248 KB Output is correct
12 Correct 29 ms 32248 KB Output is correct
13 Correct 28 ms 32248 KB Output is correct
14 Correct 29 ms 32248 KB Output is correct
15 Correct 29 ms 32248 KB Output is correct
16 Correct 28 ms 32248 KB Output is correct
17 Correct 29 ms 32248 KB Output is correct
18 Correct 28 ms 32248 KB Output is correct
19 Correct 28 ms 32248 KB Output is correct
20 Correct 29 ms 32248 KB Output is correct

Subtask #4
49.0 / 49.0

# Verdict Execution time Memory Grader output
1 Correct 29 ms 32376 KB Output is correct
2 Correct 29 ms 32248 KB Output is correct
3 Correct 36 ms 32260 KB Output is correct
4 Correct 33 ms 32248 KB Output is correct
5 Correct 28 ms 32248 KB Output is correct
6 Correct 28 ms 32248 KB Output is correct
7 Correct 28 ms 32248 KB Output is correct
8 Correct 28 ms 32248 KB Output is correct
9 Correct 28 ms 32248 KB Output is correct
10 Correct 28 ms 32248 KB Output is correct
11 Correct 28 ms 32248 KB Output is correct
12 Correct 29 ms 32248 KB Output is correct
13 Correct 28 ms 32248 KB Output is correct
14 Correct 29 ms 32248 KB Output is correct
15 Correct 29 ms 32248 KB Output is correct
16 Correct 28 ms 32248 KB Output is correct
17 Correct 29 ms 32248 KB Output is correct
18 Correct 28 ms 32248 KB Output is correct
19 Correct 28 ms 32248 KB Output is correct
20 Correct 29 ms 32248 KB Output is correct
21 Correct 29 ms 32248 KB Output is correct
22 Correct 30 ms 32244 KB Output is correct
23 Correct 29 ms 32248 KB Output is correct
24 Correct 38 ms 32248 KB Output is correct
25 Correct 38 ms 32248 KB Output is correct
26 Correct 38 ms 32248 KB Output is correct
27 Correct 38 ms 32248 KB Output is correct
28 Correct 34 ms 32248 KB Output is correct