You are given an integer array deck. There is a deck of cards where every card has a unique integer. The integer on the ith card is deck[i].
You can order the deck in any order you want. Initially, all the cards start face down (unrevealed) in one deck.
You will do the following steps repeatedly until all cards are revealed:
Return an ordering of the deck that would reveal the cards in increasing order.
Note that the first entry in the answer is considered to be the top of the deck.
Example 1:
Input: deck = [17,13,11,2,3,5,7] Output: [2,13,3,11,5,17,7] Explanation: We get the deck in the order [17,13,11,2,3,5,7] (this order does not matter), and reorder it. After reordering, the deck starts as [2,13,3,11,5,17,7], where 2 is the top of the deck. We reveal 2, and move 13 to the bottom. The deck is now [3,11,5,17,7,13]. We reveal 3, and move 11 to the bottom. The deck is now [5,17,7,13,11]. We reveal 5, and move 17 to the bottom. The deck is now [7,13,11,17]. We reveal 7, and move 13 to the bottom. The deck is now [11,17,13]. We reveal 11, and move 17 to the bottom. The deck is now [13,17]. We reveal 13, and move 17 to the bottom. The deck is now [17]. We reveal 17. Since all the cards revealed are in increasing order, the answer is correct.
Example 2:
Input: deck = [1,1000] Output: [1,1000]
Constraints:
1 <= deck.length <= 10001 <= deck[i] <= 106deck are unique.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.
We 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.
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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.
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}].
Mathematical deduction does not require additional changes, this code finds the correct order for revealing cards using pattern observation and queue manipulation.
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Time Complexity: O(n log n), caused by sorting. Space Complexity: Approximates O(n) due to storage requirements.
| Approach | Complexity |
|---|---|
| Using a Queue to Simulate the 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. |
| Mathematical Induction Method | Time Complexity: O(n log n), caused by sorting. Space Complexity: Approximates O(n) due to storage requirements. |
Reveal Cards In Increasing Order - Leetcode 950 - Python • NeetCodeIO • 17,459 views views
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