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Reveal Cards In Increasing Order

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:

  1. Take the top card of the deck, reveal it, and take it out of the deck.
  2. If there are still cards in the deck then put the next top card of the deck at the bottom of the deck.
  3. If there are still unrevealed cards, go back to step 1. Otherwise, stop.

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 <= 1000
  • 1 <= deck[i] <= 106
  • All the values of deck are unique.

Solution Explanation

This problem requires us to arrange a deck of cards such that when we reveal cards following the given rules (reveal top card, move next card to bottom, repeat), the revealed cards are in increasing order. The most efficient approach utilizes a deque (double-ended queue) to simulate the card revealing process.

Algorithm:

  1. Sort the deck: First, we sort the input deck in descending order. This is because we want the largest card to be revealed last, the second largest second to last, and so on.

  2. Use a deque: A deque is ideal for efficiently adding and removing elements from both ends. We'll use it to represent the deck of cards.

  3. Iterate and simulate: We iterate through the sorted deck. For each card:

    • If the deque is not empty, we move the last element (card) to the beginning. This simulates moving the next card to the bottom of the deck.
    • Then, we add the current card (from the sorted deck) to the front of the deque. This simulates revealing the card.

  4. Convert to list: Finally, we convert the deque back into a list and return it. This list represents the reordered deck that will reveal cards in increasing order.

Time Complexity Analysis:

  • Sorting the deck takes O(N log N) time, where N is the number of cards.
  • Iterating through the sorted deck and manipulating the deque takes O(N) time.
  • Therefore, the overall time complexity is dominated by the sorting step, resulting in O(N log N).

Space Complexity Analysis:

  • The space used by the deque is proportional to the number of cards, so it's O(N).
  • The sorted array also takes O(N) space (in-place sorting is possible but not shown in the examples for simplicity).
  • Thus, the overall space complexity is O(N).

Code Explanation (Python3):

from collections import deque
 
class Solution:
    def deckRevealedIncreasing(self, deck: List[int]) -> List[int]:
        q = deque()  # Initialize a deque
        for v in sorted(deck, reverse=True): #Iterate through the sorted deck (descending)
            if q:  #If deque is not empty, move the last element to the front
                q.appendleft(q.pop()) 
            q.appendleft(v) #Add the current card to the front
        return list(q) # Convert deque to list and return

The Java, C++, and Go code examples follow the same algorithm, only differing in syntax and data structure implementations. The core logic remains consistent across all languages.