oj.uz

Submission #655521

# Submission time Handle Problem Language Result Execution time Memory
655521 2022-11-04T16:16:39 Z jophyyjh Gondola (IOI14_gondola) C++14
100 / 100
 51 ms 6352 KB 
/**
 * Quite simple, though a little bit tedious? Just note that the gondola seq can have
 * extremely large values in [S10].
 * 
 * Time Complexity: O(n * log(n))       (Full solution)
 * Implementation 1             (Math, implementation)
*/
 
#include <bits/stdc++.h>
#include "gondola.h"

typedef long long   ll;
typedef std::vector<int>    vec;

const ll MOD = 1e9 + 9;

ll pow(ll a, int b) {
    ll res = 1;
    while (b > 0) {
        if (b % 2 == 1)
            res = res * a % MOD;
        a = a * a % MOD, b /= 2;
    }
    return res;
}


vec cyc_shift(int n, int input_seq[]) {
    int original = -1, original_pos = -1;
    for (int k = 0; k < n && original == -1; k++) {
        if (input_seq[k] <= n)
            original = input_seq[k], original_pos = k;
    }
    vec shift(n);
    int delta = (original != -1 ? original_pos + 1 - original : 0);
    for (int k = 0; k < n; k++)
         shift[k] = input_seq[(k + delta + n) % n];
    return shift;
}

int valid(int n, int input_seq[]) {
    vec shift = cyc_shift(n, input_seq);
    bool ok = true;
    std::set<int> appeared;
    for (int k = 0; k < n && ok; k++) {
        if (shift[k] <= n) {
            ok &= (shift[k] == k + 1);
        } else {
            ok &= (appeared.find(shift[k]) == appeared.end());
            appeared.emplace(shift[k]);
        }
    }
    return ok;
}

int replacement(int n, int gondola_seq[], int replacement_seq[]) {
    assert(valid(n, gondola_seq));
    vec shift = cyc_shift(n, gondola_seq);
    int repl_len = 0;
    vec count(n + 1, 0);
    memset(replacement_seq, -1, sizeof(int) * 250001);
    for (int k = 0; k < n; k++) {
        if (shift[k] > n) {
            repl_len = std::max(repl_len, shift[k] - n);
            replacement_seq[shift[k] - n - 1] = k + 1;
        }
    }
    for (int k = repl_len - 1, last = -1; k >= 0; k--) {
        if (replacement_seq[k] == -1) {
            replacement_seq[k] = replacement_seq[last];
            replacement_seq[last] = n + k + 1;
        }
        last = k;
    }
    return repl_len;
}

int countReplacement(int n, int input_seq[]) {
    if (!valid(n, input_seq))
        return 0;
    vec shift = cyc_shift(n, input_seq);
    vec top;
    int max_val = 0;
    for (int k = 0; k < n; k++) {
        if (shift[k] > n)
            top.push_back(shift[k]);
        max_val = std::max(max_val, shift[k]);
    }
    std::sort(top.begin(), top.end());
    ll comb = 1;
    for (int i = 0, m = top.size(), prev = n + 1; i < m; i++)
        comb *= pow(m - i, top[i] - prev), comb %= MOD, prev = top[i] + 1;
    bool fixed_cyc = false;
    for (int k = 0; k < n && !fixed_cyc; k++)
        fixed_cyc |= (shift[k] == k + 1);
    if (!fixed_cyc)
        comb *= ll(n), comb %= MOD;
    return int(comb);
}

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 0 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 0 ms 304 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 0 ms 308 KB Output is correct
6 Correct 4 ms 808 KB Output is correct
7 Correct 8 ms 1392 KB Output is correct
8 Correct 6 ms 1216 KB Output is correct
9 Correct 2 ms 596 KB Output is correct
10 Correct 8 ms 1412 KB Output is correct

Subtask #3
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 304 KB Output is correct
6 Correct 5 ms 724 KB Output is correct
7 Correct 8 ms 1492 KB Output is correct
8 Correct 7 ms 1264 KB Output is correct
9 Correct 3 ms 512 KB Output is correct
10 Correct 8 ms 1344 KB Output is correct
11 Correct 0 ms 308 KB Output is correct
12 Correct 1 ms 292 KB Output is correct
13 Correct 4 ms 740 KB Output is correct
14 Correct 0 ms 312 KB Output is correct
15 Correct 10 ms 1492 KB Output is correct

Subtask #4
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1236 KB Output is correct
2 Correct 1 ms 1236 KB Output is correct
3 Correct 1 ms 1204 KB Output is correct
4 Correct 1 ms 1236 KB Output is correct
5 Correct 1 ms 1236 KB Output is correct

Subtask #5
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1208 KB Output is correct
2 Correct 1 ms 1236 KB Output is correct
3 Correct 1 ms 1236 KB Output is correct
4 Correct 1 ms 1236 KB Output is correct
5 Correct 1 ms 1236 KB Output is correct
6 Correct 1 ms 1236 KB Output is correct
7 Correct 1 ms 1236 KB Output is correct
8 Correct 1 ms 1236 KB Output is correct
9 Correct 1 ms 1236 KB Output is correct
10 Correct 1 ms 1236 KB Output is correct

Subtask #6
20.0 / 20.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 1236 KB Output is correct
2 Correct 1 ms 1236 KB Output is correct
3 Correct 1 ms 1236 KB Output is correct
4 Correct 1 ms 1208 KB Output is correct
5 Correct 1 ms 1236 KB Output is correct
6 Correct 1 ms 1204 KB Output is correct
7 Correct 1 ms 1208 KB Output is correct
8 Correct 1 ms 1236 KB Output is correct
9 Correct 1 ms 1204 KB Output is correct
10 Correct 1 ms 1236 KB Output is correct
11 Correct 11 ms 2612 KB Output is correct
12 Correct 9 ms 2756 KB Output is correct
13 Correct 20 ms 3424 KB Output is correct
14 Correct 9 ms 2544 KB Output is correct
15 Correct 27 ms 3320 KB Output is correct

Subtask #7
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 308 KB Output is correct
2 Correct 0 ms 212 KB Output is correct
3 Correct 0 ms 224 KB Output is correct

Subtask #8
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 0 ms 312 KB Output is correct
4 Correct 1 ms 212 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct

Subtask #9
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 308 KB Output is correct
4 Correct 1 ms 304 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 0 ms 308 KB Output is correct
7 Correct 0 ms 212 KB Output is correct
8 Correct 1 ms 212 KB Output is correct
9 Correct 31 ms 4028 KB Output is correct
10 Correct 23 ms 3052 KB Output is correct
11 Correct 11 ms 1676 KB Output is correct
12 Correct 12 ms 1832 KB Output is correct
13 Correct 3 ms 704 KB Output is correct

Subtask #10
10.0 / 10.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB Output is correct
2 Correct 1 ms 212 KB Output is correct
3 Correct 1 ms 212 KB Output is correct
4 Correct 1 ms 308 KB Output is correct
5 Correct 1 ms 212 KB Output is correct
6 Correct 1 ms 212 KB Output is correct
7 Correct 1 ms 308 KB Output is correct
8 Correct 0 ms 212 KB Output is correct
9 Correct 32 ms 4028 KB Output is correct
10 Correct 23 ms 3108 KB Output is correct
11 Correct 10 ms 1620 KB Output is correct
12 Correct 12 ms 1836 KB Output is correct
13 Correct 3 ms 700 KB Output is correct
14 Correct 46 ms 5760 KB Output is correct
15 Correct 51 ms 6352 KB Output is correct
16 Correct 9 ms 1336 KB Output is correct
17 Correct 38 ms 4352 KB Output is correct
18 Correct 17 ms 2548 KB Output is correct