Submission #655521

#	Time	Username	Problem	Language	Result	Execution time	Memory
655521		jophyyjh	Gondola (IOI14_gondola)	C++14	100 / 100	51 ms	6352 KiB

gondola

/**
 * 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 / 5
• Subtask 2: 5 / 5
• Subtask 3: 10 / 10
• Subtask 4: 5 / 5
• Subtask 5: 10 / 10
• Subtask 6: 20 / 20
• Subtask 7: 5 / 5
• Subtask 8: 15 / 15
• Subtask 9: 15 / 15
• Subtask 10: 10 / 10