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Submission #682043

# Submission time Handle Problem Language Result Execution time Memory
682043 2023-01-15T11:11:06 Z Cyanmond Ljetopica (COI19_ljetopica) C++17
100 / 100
 108 ms 15872 KB 
#include <bits/stdc++.h>

using i64 = long long;
constexpr i64 mod = 1000000007;

i64 add(i64 a, i64 b) {
    return (a + b) % mod;
}

void tadd(i64 &a, i64 b) {
    a = add(a, b);
}

i64 sub(i64 a, i64 b) {
    return ((a - b) % mod + mod) % mod;
}

i64 mul(i64 a, i64 b) {
    return (a * b) % mod;
}

constexpr i64 maxN = 5000;

std::array<i64, maxN> fact, inv, inv_fact, pow_2;

void init() {
    fact[0] = fact[1] = inv[1] = inv_fact[0] = inv_fact[1] = 1;
    pow_2[0] = 1, pow_2[1] = 2;
    for (int i = 2; i < maxN; ++i) {
        fact[i] = mul(fact[i - 1], i);
        inv[i] = mod - mul(inv[mod % i], mod / i);
        inv_fact[i] = mul(inv_fact[i - 1], inv[i]);

        pow_2[i] = mul(pow_2[i - 1], 2);
    }
}

i64 combination(i64 n, i64 k) {
    if (n < 0 or k < 0 or n < k) {
        return 0;
    }
    return mul(fact[n], mul(inv_fact[n - k], inv_fact[k]));
}

void minus_1(std::string &x) {
    const int n = (int)x.size();
    for (int i = n - 1; i >= 0; --i) {
        if (x[i] == '0') {
            continue;
        }
        x[i] = '0';
        for (int j = i + 1; j < n; ++j) {
            x[j] = '1';
        }
        break;
    }
}

int main() {
    init();

    int N, K;
    std::cin >> N >> K;
    std::string S;
    std::cin >> S;
    std::string A, B;
    std::cin >> A >> B;

    auto solve = [&](const std::string C) -> i64 {
        // solve for [0, C]
        
        // pre- calc
        std::vector dp(N, std::vector(K + 1, std::array<i64, 2>{{0, 0}}));
        dp[N - 1][0][S[N - 2] == 'R' ? 0 : 1] = 1;
        for (int i = N - 1; i >= 2; --i) {
            int c = S[i - 2] == 'R' ? 0 : 1;
            for (int j = 0; j <= std::min(K, N - i - 1); ++j) {
                for (int s = 0; s < 2; ++s) {
                    for (int nx = 0; nx < 2; ++nx) {
                        if (j + nx > K) {
                            continue;
                        }
                        // from dp[i][j][s] to dp[i - 1][j + nx][s]
                        
                        // nm
                        const i64 ym = combination(N - i - 1, j);

                        // default
                        tadd(dp[i - 1][j + nx][s], dp[i][j][s]);

                        // add
                        if ((j + nx + c) % 2 == (s % 2)) {
                            tadd(dp[i - 1][j + nx][s], mul(pow_2[N - i], ym));
                        }
                    }
                }
            }
        }

        auto dfs = [&](auto &&self, const int t, int count_change) -> i64 {
            if (count_change > K or (N - t - 1) < (K - count_change)) {
                return 0;
            }

            if (t == N - 1) {
                i64 ret = 0;
                for (int i = 0; i < N; ++i) {
                    if (C[i] == '1') {
                        tadd(ret, pow_2[N - i - 1]);
                    }
                }
                return ret;
            }

            if (C[t + 1] == '0') {
                // now direction
                bool now_dir = (count_change % 2) xor (S[t] == 'L');
                const int cost = now_dir ? 0 : 1;
                return self(self, t + 1, count_change + cost);
            } else {
                bool now_dir = (count_change % 2) xor (S[t] == 'L');
                const int cost = !now_dir ? 0 : 1;
                count_change += cost;
                const i64 res_right = self(self, t + 1, count_change);
                count_change -= cost;
                count_change += (1 - cost);

                // calculate the left-side cost
                const int k = K - count_change, r = N - t - 2;
                if (k < 0 or k > r) {
                    // skip
                    return res_right;
                }

                // part of ancestors
                i64 sum_acs = 0;
                for (int i = 0; i <= t; ++i) {
                    if (C[i] == '1') {
                        tadd(sum_acs, pow_2[N - i - 1]);
                    }
                }
                i64 res_left = mul(sum_acs, combination(r, k));

                // part of children
                if (t != N - 2) {
                    for (int s = 0; s < 2; ++s) {
                        if (k - s < 0) {
                            continue;
                        }
                        if (k == r and s == 0) {
                            continue;
                        }
                        tadd(res_left, dp[t + 2][k - s][K % 2]);
                    }
                }

                return res_left + res_right;
            }
        };

        return dfs(dfs, 0, 0);
    };

    auto calc_ans_ot = [&]() {
        i64 answer = solve(B);
        if (std::any_of(A.begin() + 1, A.end(), [&](char x) { return x == '1'; })) {
            auto ad = A;
            minus_1(ad);
            answer = sub(answer, solve(ad));
        }
        return answer;
    };

    i64 answer = calc_ans_ot();
    for (auto &e : S) {
        e = e == 'L' ? 'R' : 'L';
    }
    tadd(answer, calc_ans_ot());

    answer = (answer % mod + mod) % mod;
    std::cout << answer << std::endl;
}

Subtask #1
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 468 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 468 KB Output is correct
8 Correct 1 ms 456 KB Output is correct

Subtask #2
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 456 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 468 KB Output is correct
5 Correct 0 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 460 KB Output is correct
11 Correct 1 ms 464 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 468 KB Output is correct

Subtask #3
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 74 ms 9564 KB Output is correct
2 Correct 55 ms 6728 KB Output is correct
3 Correct 67 ms 7652 KB Output is correct
4 Correct 94 ms 15256 KB Output is correct
5 Correct 54 ms 6412 KB Output is correct
6 Correct 93 ms 15872 KB Output is correct
7 Correct 34 ms 4208 KB Output is correct
8 Correct 63 ms 7548 KB Output is correct
9 Correct 4 ms 844 KB Output is correct
10 Correct 59 ms 6892 KB Output is correct

Subtask #4
61.0 / 61.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 468 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 468 KB Output is correct
8 Correct 1 ms 456 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 1 ms 456 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 0 ms 340 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 340 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 460 KB Output is correct
19 Correct 1 ms 464 KB Output is correct
20 Correct 1 ms 468 KB Output is correct
21 Correct 1 ms 468 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 74 ms 9564 KB Output is correct
25 Correct 55 ms 6728 KB Output is correct
26 Correct 67 ms 7652 KB Output is correct
27 Correct 94 ms 15256 KB Output is correct
28 Correct 54 ms 6412 KB Output is correct
29 Correct 93 ms 15872 KB Output is correct
30 Correct 34 ms 4208 KB Output is correct
31 Correct 63 ms 7548 KB Output is correct
32 Correct 4 ms 844 KB Output is correct
33 Correct 59 ms 6892 KB Output is correct
34 Correct 108 ms 11644 KB Output is correct
35 Correct 41 ms 4360 KB Output is correct
36 Correct 55 ms 6828 KB Output is correct
37 Correct 86 ms 14692 KB Output is correct
38 Correct 19 ms 2260 KB Output is correct
39 Correct 91 ms 12912 KB Output is correct
40 Correct 22 ms 2016 KB Output is correct
41 Correct 76 ms 8644 KB Output is correct
42 Correct 91 ms 10932 KB Output is correct
43 Correct 74 ms 10968 KB Output is correct
44 Correct 79 ms 12832 KB Output is correct
45 Correct 33 ms 3964 KB Output is correct
46 Correct 73 ms 10000 KB Output is correct
47 Correct 85 ms 10676 KB Output is correct
48 Correct 51 ms 6304 KB Output is correct
49 Correct 6 ms 864 KB Output is correct
50 Correct 88 ms 12256 KB Output is correct
51 Correct 56 ms 5792 KB Output is correct
52 Correct 53 ms 6108 KB Output is correct
53 Correct 95 ms 14840 KB Output is correct
54 Correct 38 ms 4268 KB Output is correct
55 Correct 81 ms 11860 KB Output is correct
56 Correct 90 ms 13520 KB Output is correct
57 Correct 15 ms 1828 KB Output is correct
58 Correct 78 ms 10604 KB Output is correct