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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.
1using System;
2using System.Collections.Generic;
3
4public class Solution {
5 public int[] DeckRevealedIncreasing(int[] deck) {
6 Array.Sort(deck);
7 Queue<int> index = new Queue<int>();
8 for (int i = 0; i < deck.Length; i++)
9 index.Enqueue(i);
10 int[] result = new int[deck.Length];
11 foreach (int card in deck) {
12 result[index.Dequeue()] = card;
13 if (index.Count > 0)
index.Enqueue(index.Dequeue());
}
return result;
}
}This C# solution sorts the deck and manipulates a queue to arrange the reveal order. It mimics the physical manipulation of card positions.
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.
Mathematical deduction does not require additional changes, this code finds the correct order for revealing cards using pattern observation and queue manipulation.