Write a function rotate(ar[], d, n) that rotates arr[] of size n by d elements.
Rotation of the above array by 2 will make array
Algorithm :
Initialize A = arr[0..d-1] and B = arr[d..n-1]
1) Do following until size of A is equal to size of B
a) If A is shorter, divide B into Bl and Br such that Br is of same
length as A. Swap A and Br to change ABlBr into BrBlA. Now A
is at its final place, so recur on pieces of B.
b) If A is longer, divide A into Al and Ar such that Al is of same
length as B Swap Al and B to change AlArB into BArAl. Now B
is at its final place, so recur on pieces of A.
2) Finally when A and B are of equal size, block swap them.
Recursive Implementation:
Python3
# Wrapper over the recursive function leftRotateRec() # It left rotates arr by d. def leftRotate(arr, d, n): leftRotateRec(arr, 0, d, n); def leftRotateRec(arr, i, d, n): ''' * Return If number of elements to be rotated is zero or equal to array size ''' if (d == 0 or d == n): return; ''' * If number of elements to be rotated is exactly half of array size ''' if (n - d == d): swap(arr, i, n - d + i, d); return; ''' If A is shorter ''' if (d < n - d): swap(arr, i, n - d + i, d); leftRotateRec(arr, i, d, n - d); ''' If B is shorter ''' else: swap(arr, i, d, n - d); ''' This is tricky ''' leftRotateRec(arr, n - d + i, 2 * d - n, d); ''' UTILITY FUNCTIONS '''''' function to print an array '''def printArray(arr, size): for i in range(size): print(arr[i], end = " "); print(); ''' * This function swaps d elements starting at * index fi with d elements starting at index si '''def swap(arr, fi, si, d): for i in range(d): temp = arr[fi + i]; arr[fi + i] = arr[si + i]; arr[si + i] = temp; # Driver Code if __name__ == '__main__': arr = [1, 2, 3, 4, 5, 6, 7]; leftRotate(arr, 2, 7); printArray(arr, 7); # This code is contributed by Rohit_ranjan |
Output:
3 5 4 6 7 1 2
Time Complexity: O(N), where N represents the size of the given array.
Auxiliary Space: O(1), no extra space is required, so it is a constant.
Iterative Implementation:
Here is iterative implementation of the same algorithm. Same utility function swap() is used here.
Time Complexity: O(n)
Please see following posts for other methods of array rotation:
https://www.geeksforgeeks.org/array-rotation/
https://www.geeksforgeeks.org/program-for-array-rotation-continued-reversal-algorithm/
Please write comments if you find any bug in the above programs/algorithms or want to share any additional information about the block swap algorithm.
Please refer complete article on Block swap algorithm for array rotation for more details!
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