oj.uz

Submission #622281

# Submission time Handle Problem Language Result Execution time Memory
622281 2022-08-04T05:48:41 Z jophyyjh Lottery (CEOI18_lot) C++14
65 / 100
 78 ms 21376 KB 
/**
 * Notes during contest.
 * 
 * ------ A ------
 * Looks like a dp.
 * 
 * ------ B ------
 * I think i've seen sth similar on luogu. First, let's assume that d >= 0 and i'll
 * use the words "increase" & "decrease". If we wanna increase an interval by d, we
 * can greedily increase a suffix (instead of just an interval in the middle). If we
 * are to decrease an interval by d, we can greedily decrease a prefix. The two cases
 * are symmetric, so we can assume that one always increase a suffix by 0 <= d <= x.
 * And, if we're increasing a suffix, why don't we just do d=x? The rest is quite
 * straight-forward.
 * 
 * ------ C ------
 * For k_j = 0, we have to find the num of times each interval appeared. This can be
 * effectively done with str hashing. [S3] solved. [S1] is just brute-force: we can
 * do a O(n^2) for loop, iterating over all pairs of starting pos, naively comparing
 * the dist. of 2 substr. [S2] is a O(n^2) comparison between pairs of VALUES and
 * apply a difference array.
 * We're only looking for the num of mismatches. Let's compress the values (a_i:
 * 10^9 -> 10^4).
 * 
 * Time Complexity 1: O()
 * Time Complexity 2: O(n * log(n))
 * Time Complexity 3: O(n^2 + q) ([S1-2]), O(n)    (non-deterministic hashing)
 * Implementation 1         (Just for partials, [S1-2], [S3]. [S3] not finished)
*/
 
#include <bits/stdc++.h>
 
typedef int64_t     int_t;
typedef std::vector<int>    vec;
 
const int INF = 0x3f3f3f3f;
 
int_t pow(int_t a, int_t b, int_t mod) {
    int_t res = 1;
    while (b > 0) {
        if (b % 2 == 1)
            res = res * a % mod;
        a = a * a % mod, b /= 2;
    }
    return res;
}
 
struct RH {     // rolling hash
    std::vector<std::vector<int_t>> _p;
    std::vector<std::vector<int_t>> hash;
    RH(std::vector<std::vector<int_t>> params, const vec& values) {
        int sets = params.size(), n = values.size();
        hash.assign(sets, std::vector<int_t>(n + 1));
        _p = params;
        for (int i = 0; i < sets; i++) {
            int_t p = params[i][0], m = params[i][1];
            hash[i][0] = 0;
            for (int k = 0; k < n; k++) {
                hash[i][k + 1] = hash[i][k] * m % p + int_t(values[k]) % p;
                hash[i][k + 1] = (hash[i][k + 1] % p + p) % p;
            }
        }
    }
    inline std::vector<int_t> find_hash(int s, int l) {
        std::vector<int_t> ans;
        for (int i = 0; i < int(_p.size()); i++) {
            int_t p = _p[i][0], m = _p[i][1];
            int_t val = hash[i][s + l] - hash[i][s] * pow(m, l, p) % p;
            val = (val % p + p) % p;
            ans.push_back(val);
        }
        return ans;
    }
};
 
 
int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(NULL);
 
    int n, l;
    std::cin >> n >> l;
    vec values(n);
    for (int k = 0; k < n; k++)
        std::cin >> values[k];
        
 
    if (n <= 2000) {
        // Mismatch at i, j add 1 to the dist of (s, s+d)   (d = j-i)
        // 1 <= i-s+1 <= l, so max(i-l+1,0) <= s <= i.
        // Note that (l+1) means invalid.
        std::vector<vec> dist(n, vec(n, l + 1));
        for (int d = 1; d < n; d++) {
            vec diff(n + 1, 0);
            for (int i = 0; i + d < n; i++) {
                int j = i + d;
                if (values[i] != values[j])
                    diff[std::max(i - l + 1, 0)]++, diff[i + 1]--;
            }
            for (int i = 0, prefix = 0; i + d + l <= n; i++) {
                prefix += diff[i];
                dist[i][i + d] = prefix;
            }
        }
        for (int i = 0; i < n; i++) {
            dist[i][i] = l + 1;
            for (int j = i + 1; j < n; j++)
                dist[j][i] = dist[i][j];
        }
        std::vector<vec> pre(n, vec(l + 2, 0));
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++)
                pre[i][dist[i][j]]++;
            for (int j = 1; j <= l + 1; j++)
                pre[i][j] += pre[i][j - 1];
        }
        int q;
        std::cin >> q;
        for (int _ = 0; _ < q; _++) {
            int sim;
            std::cin >> sim;
            for (int i = 0; i + l - 1 < n; i++)
                std::cout << pre[i][sim] << ' ';
            std::cout << '\n';
        }
    } else {    // [S3] assumes q=1 and k1=0
        // 3 is a primitive root of 998244353. Idk about 5
        RH hash({{998244353, 3}, {int_t(1e9) + 7, 5}}, values);
        std::map<std::vector<int_t>, int> count;
        for (int i = 0; i + l - 1 < n; i++) {
            std::vector<int_t> h = hash.find_hash(i, l);
            for (int_t a : h)
                std::cerr << a << ' ';
            std::cerr << std::endl;
        }
        for (int i = 0; i + l - 1 < n; i++)
            count[hash.find_hash(i, l)]++;
        for (int i = 0; i + l - 1 < n; i++)
            std::cout << count[hash.find_hash(i, l)] - 1 << ' ';
        std::cout << '\n';
    }
}

Subtask #1
25.0 / 25.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 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 836 KB Output is correct
9 Correct 2 ms 836 KB Output is correct
10 Correct 2 ms 724 KB Output is correct
11 Correct 2 ms 724 KB Output is correct
12 Correct 2 ms 708 KB Output is correct

Subtask #2
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 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 836 KB Output is correct
9 Correct 2 ms 836 KB Output is correct
10 Correct 2 ms 724 KB Output is correct
11 Correct 2 ms 724 KB Output is correct
12 Correct 2 ms 708 KB Output is correct
13 Correct 38 ms 16076 KB Output is correct
14 Correct 45 ms 21376 KB Output is correct
15 Correct 42 ms 21316 KB Output is correct
16 Correct 46 ms 17892 KB Output is correct
17 Correct 42 ms 18824 KB Output is correct
18 Correct 40 ms 18784 KB Output is correct

Subtask #3
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 61 ms 636 KB Output is correct
2 Correct 70 ms 672 KB Output is correct
3 Correct 64 ms 672 KB Output is correct
4 Correct 72 ms 988 KB Output is correct
5 Correct 40 ms 1144 KB Output is correct
6 Correct 72 ms 1652 KB Output is correct
7 Correct 36 ms 736 KB Output is correct
8 Correct 50 ms 748 KB Output is correct
9 Correct 70 ms 868 KB Output is correct
10 Correct 78 ms 916 KB Output is correct
11 Correct 17 ms 596 KB Output is correct
12 Correct 58 ms 1324 KB Output is correct
13 Correct 53 ms 1344 KB Output is correct
14 Correct 45 ms 1280 KB Output is correct

Subtask #4
0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 61 ms 636 KB Output is correct
2 Correct 70 ms 672 KB Output is correct
3 Correct 64 ms 672 KB Output is correct
4 Correct 72 ms 988 KB Output is correct
5 Correct 40 ms 1144 KB Output is correct
6 Correct 72 ms 1652 KB Output is correct
7 Correct 36 ms 736 KB Output is correct
8 Correct 50 ms 748 KB Output is correct
9 Correct 70 ms 868 KB Output is correct
10 Correct 78 ms 916 KB Output is correct
11 Correct 17 ms 596 KB Output is correct
12 Correct 58 ms 1324 KB Output is correct
13 Correct 53 ms 1344 KB Output is correct
14 Correct 45 ms 1280 KB Output is correct
15 Incorrect 75 ms 1780 KB Output isn't correct
16 Halted 0 ms 0 KB -

Subtask #5
0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 1 ms 340 KB Output is correct
4 Correct 1 ms 340 KB Output is correct
5 Correct 1 ms 324 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 836 KB Output is correct
9 Correct 2 ms 836 KB Output is correct
10 Correct 2 ms 724 KB Output is correct
11 Correct 2 ms 724 KB Output is correct
12 Correct 2 ms 708 KB Output is correct
13 Correct 38 ms 16076 KB Output is correct
14 Correct 45 ms 21376 KB Output is correct
15 Correct 42 ms 21316 KB Output is correct
16 Correct 46 ms 17892 KB Output is correct
17 Correct 42 ms 18824 KB Output is correct
18 Correct 40 ms 18784 KB Output is correct
19 Correct 61 ms 636 KB Output is correct
20 Correct 70 ms 672 KB Output is correct
21 Correct 64 ms 672 KB Output is correct
22 Correct 72 ms 988 KB Output is correct
23 Correct 40 ms 1144 KB Output is correct
24 Correct 72 ms 1652 KB Output is correct
25 Correct 36 ms 736 KB Output is correct
26 Correct 50 ms 748 KB Output is correct
27 Correct 70 ms 868 KB Output is correct
28 Correct 78 ms 916 KB Output is correct
29 Correct 17 ms 596 KB Output is correct
30 Correct 58 ms 1324 KB Output is correct
31 Correct 53 ms 1344 KB Output is correct
32 Correct 45 ms 1280 KB Output is correct
33 Incorrect 75 ms 1780 KB Output isn't correct
34 Halted 0 ms 0 KB -