Python Program For Converting Array Into Zig-Zag Fashion

Given an array of DISTINCT elements, rearrange the elements of array in zig-zag fashion in O(n) time. The converted array should be in form a < b > c < d > e < f. 

Example:

Input: arr[] = {4, 3, 7, 8, 6, 2, 1} 
Output: arr[] = {3, 7, 4, 8, 2, 6, 1}

Input: arr[] = {1, 4, 3, 2} 
Output: arr[] = {1, 4, 2, 3}

A Simple Solution is to first sort the array. After sorting, exclude the first element, swap the remaining elements in pairs. (i.e. keep arr[0] as it is, swap arr[1] and arr[2], swap arr[3] and arr[4], and so on). 
Time complexity: O(N log N) since we need to sort the array first.

We can convert in O(n) time using an efficient approach. The idea is to use a modified one pass of bubble sort.

• Maintain a flag for representing which order(i.e. < or >) currently we need.
• If the current two elements are not in that order then swap those elements otherwise not.

Let us see the main logic using three consecutive elements A, B, C.

Suppose we are processing B and C currently and the current relation is '<', but we have B > C. Since current relation is '<' previous relation must be '>' i.e., A must be greater than B. So, the relation is A > B and B > C. We can deduce A > C. So if we swap B and C then the relation is A > C and C < B. Finally we get the desired order A C B 
Refer this for more explanation.

Below image is a dry run of the above approach:

Below is the implementation of above approach:

# Python program to sort an array 
# in Zig-Zag form 

# Program for zig-zag conversion 
# of array 
def zigZag(arr, n): 

    # Flag true indicates relation "<" 
    # is expected, else ">" is expected. 
    # The first expected relation is "<" 
    flag = True

    for i in range(n - 1): 

        # "<" relation expected 
        if flag is True: 

            # If we have a situation like 
            # A > B > C, we get A > B < C 
            # by swapping B and C 
            if arr[i] > arr[i + 1]: 
                arr[i], arr[i + 1] = arr[i + 1], arr[i] 

            # ">" relation expected 
        else: 

            # If we have a situation like 
            # A < B < C, we get A < C > B  
            # by swapping B and C     
            if arr[i] < arr[i + 1]: 
                arr[i], arr[i + 1] = arr[i + 1], arr[i] 
        flag = bool(1 - flag) 
    print(arr) 

# Driver code
arr = [4, 3, 7, 8, 6, 2, 1] 
n = len(arr) 
zigZag(arr, n) 
# This code is contributed by Pratik Chhajer 

Output: 

3  7  4  8  2  6  1 

Time complexity: O(n) 
Auxiliary Space: O(1) 
 

kartik

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