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This approach involves using a queue to simulate the process of revealing cards in increasing order. The given deck is first sorted to achieve this order. We then place the lowest cards at the positions where they will eventually be revealed.
The process is as follows:
The card is placed at the index dequeued first, and after checking if there are still indices left, the second index is enqueued to the queue for the recycling process.
Time Complexity: O(n log n), where n is the number of cards, because we sort the deck first. Space Complexity: O(n), since we use a deque to manage the card indices.
1from collections import deque
2
3def deckRevealedIncreasing(deck):
4 deck.sort()
5 n = len(deck)
6 index = dequeWe use a deque to simulate the revealing process according to the problem's steps. By sorting the deck, we prepare to place the smallest card first and follow the steps iteratively to position each card correctly.
Consider using a mathematical pattern to determine the correct order of cards. Start by handling small cases and rebalance the reordering according to the general steps defined. This approach focuses on finding the sequence by mathematical induction, considering the card's positions multiplication pattern to simulate the reveal process. Given the position pos[i], the card is added during the iteration, assume it follows a position pattern according to pos[i - 2 ^ {k-t}].
Time Complexity: O(n log n), caused by sorting. Space Complexity: Approximates O(n) due to storage requirements.
#include <deque>
#include <algorithm>
std::vector<int> deckRevealedIncreasing(std::vector<int>& deck) {
std::sort(deck.begin(), deck.end());
std::deque<int> index;
for (int i = 0; i < deck.size(); ++i) index.push_back(i);
std::vector<int> result(deck.size());
for (int card : deck) {
result[index.front()] = card;
index.pop_front();
if (!index.empty()) {
index.push_back(index.front());
index.pop_front();
}
}
return result;
}Through deduction, this C++ program matches the card indexes with their positions via mathematical observation on sequential cards.