Given a pack of 2^N cards (0 … 2^N – 1), shuffle it in N steps. At step k (0 < k < N) we divide the deck into 2k equal-sized decks. Each one of those decks is reordered by having all the cards that lie on even positions first, followed by all cards that lie on odd positions (the order is preserved in each one of the two subsequences). Now, we are given a key (index). We have to answer the card on that position (0-based indexing). Examples:
Input : N = 3 (Size = 2^N), Key = 3 Output : 6 Explanation : Pack : 0 1 2 3 4 5 6 7 Shuffle 1 : 0 2 4 6|1 3 5 7 Shuffle 2 : 0 4|2 6|1 5|3 7 Card at index 3 : 6
Method 1 : We can simply simulate the whole process and find the exact order of the cards after all the N shuffles are done.
Time Complexity : O(N * 2^N)
Method 2 :
Let us try to find the binary representation of Key and the final answer and try to spot some observations based on it.
Let N = 3
Below is the table :
It is clearly visible that the answer is the reverse of binary representation of Key.
This article is contributed by Rohit. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
- Best way to answer If an Interviewer asks about Salary Expectation to you as a Fresher
- Range query for count of set bits
- Sum of Bitwise OR of all pairs in a given array
- Maximum subset sum such that no two elements in set have same digit in them
- Count pairs of elements such that number of set bits in their AND is B[i]
- Number of 0s and 1s at prime positions in the given array
- Find uncommon characters of the two strings | Set 2
- Fibonacci Power
- Find N distinct numbers whose bitwise Or is equal to K
- Find a sub matrix with maximum XOR
- Nikhil Kumar - Geek on the top | "Never follow the crowd, be the face of it"
- Multiply a number by 15 without using * and / operators
- Blog | Programming Guidelines
- Queries for bitwise OR in the given matrix