Given an array of distinct integer A, the task is to count the number of possible permutations of the given array A such that the permutations do not contain any subarray of size 2 or more from the original array.
Input: A = [ 1, 3, 9 ]
All the permutation of [ 1, 3, 9 ] are : [ 1, 3, 9 ], [ 1, 9, 3 ], [ 3, 9, 1 ], [ 3, 1, 9 ], [ 9, 1, 3 ], [ 9, 3, 1 ]
Here [ 1, 3, 9 ], [ 9, 1, 3 ] are removed as they contain sub-array [ 1, 3 ] from original list
and [ 3, 9, 1 ] removed as it contains sub-array [3, 9] from original list so,
Following are the 3 arrays that satisfy the condition : [1, 9, 3], [3, 1, 9], [9, 3, 1]
Input : A = [1, 3, 9, 12]
Naive Approach: Iterate through list of all permutations and remove those arrays which contains any sub-array [ i, i+1 ] from A.
Below is the implementation of the above approach:
Efficient Solution : After making the solution for smaller size of array, we can observe a pattern:
The following pattern generates a recurrence:
Suppose the length of array A is n, then:
count(0) = 1 count(1) = 1 count(n) = n * count(n-1) + (n-1) * count(n-2)
Below is the implementation of the approach:
Note: For the above recurrence you can check oeis.org.
- Count subarrays having total distinct elements same as original array
- Find original array from encrypted array (An array of sums of other elements)
- Find a subarray whose sum is divisible by size of the array
- Smallest subarray whose sum is multiple of array size
- Generate original array from an array that store the counts of greater elements on right
- Count Inversions of size three in a given array
- Count the number of primes in the prefix sum array of the given array
- Check in binary array the number represented by a subarray is odd or even
- Permutation of an array that has smaller values from another array
- Maximum subarray sum in array formed by repeating the given array k times
- Sort an array where a subarray of a sorted array is in reverse order
- Count the number of sub-arrays such that the average of elements present in the sub-array is greater than that not present in the sub-array
- Given an array of size n and a number k, find all elements that appear more than n/k times
- Maximize the size of array by deleting exactly k sub-arrays to make array prime
- Lexicographically smallest permutation with no digits at Original Index
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 Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.