How to Convert an Array into Zigzag Array?

Last Updated on November 28, 2023 by Ankit Kochar

Welcome to the world of array manipulation! If you’ve ever found yourself pondering over the task of converting a straightforward array into a zigzag array, you’re in the right place. A zigzag array is a fascinating way to rearrange elements that adds a touch of unpredictability and order simultaneously. Whether you’re a coding enthusiast or someone looking to expand their programming skills, this guide will walk you through the steps to transform a plain array into a zigzag marvel. Get ready to zig and zag your way through the array transformation journey!

A zigzag array is an array where the elements are arranged in an alternating pattern of peaks and valleys. This pattern resembles the shape of a zigzag line. The peaks represent the local maximum values in the array, while the valleys represent the local minimum values.

Given an array of N integers, convert it into a ZigZag array by choosing any element and decrementing it by 1.

What is a Zigzag Array?

An array A is a ZigZag array if either:

1. Every even-indexed element is greater than its adjacent elements, ie. A0 > A1 A3 ...
2. OR, every odd-indexed element is greater than its adjacent elements, ie. A0 A2 A4 < ...

Print the minimum number of moves to transform the given array into a ZigZag array.

See original problem statement here

For Example

Input:

N = 3
A[] = [2, 3, 4]

Output:

2

Explanation:

We can decrease 3 to 1 to form [2, 1, 4] so that all even indexed elements are greater than the neighbours. Hence output is 2.

Solving Approach to Convert Array into Zig-Zag Fashion

1. We will solve this problem two times.
   • For the even-indexed array.
   • For the odd-indexed array.
2. Minimum of both the solutions will be our desired solution.
3. Start traversing the array, for each element find the minimum value among the element , previous element - 1 and next element - 1.
4. The difference between current element and calculated minimum value is the moves required to correctly position these three elements.
5. Similarly, keep doing it for the entire array and keep track of a sum variable.
   sum += ( A[i] - min(A[i],A[i-1]-1,A[i+1]-1) )

Code Implementation

#include <stdio.h>

int solve(int arr[],int n,int start)
{
  int res = 0;
  for(int i=start;i<n;i+=2)
  {
    int to = arr[i];
    if(i)
    // make sure current element is less than its left neighboor
    {
      if(arr[i-1]-1<to)
        to = arr[i-1]-1;
    }
    if(i+1 != n)
    // make sure current element is less than its right neighboor
    {
      if(arr[i+1]-1<to)
        to = arr[i+1]-1;
    }
    // if curr value was decreased to "to", add the difference
    res += arr[i] - to;
  }
  return res;
}

int main()
{
  int n;
  scanf("%d",&n);
  int arr[n];
  for(int i=0;i<n;i++)
    scanf("%d",&arr[i]);
  int res1 = solve(arr,n,0);
  int res2 = solve(arr,n,1);

  if(res1 < res2)
    printf("%d",res1);
  else
    printf("%d",res2);

  return 0;
}

#include <bits/stdc++.h>
using namespace std;

int solve(int arr[],int n,int start)
{
  int res = 0;
  for(int i=start;i<n;i+=2)
  {
    int to = arr[i];
    if(i){
    // make sure current element is less than its left neighboor
      to = min(to,arr[i-1]-1);
    }
    if(i+1 != n){
    // make sure current element is less than its right neighboor
      to = min(to,arr[i+1]-1);
    }
    // if curr value was decreased to "to", add the difference
    res += arr[i] - to;
  }
  return res;
}

int main()
{
  int n;cin>>n;
  int arr[n];
  for(int i=0;i<n;i++)
    cin>>arr[i];

  cout<<min(solve(arr,n,0),solve(arr,n,1));

  return 0;
}

import java.util.*;
import java.io.*;
import java.lang.Math;

public class Main {
  static int solve(int arr[],int n,int start)
  {
    int res = 0;
    for(int i=start;i<n;i+=2)
    {
      int to = arr[i];
      if(i>0)
      // make sure current element is less than its left neighboor
        to = Math.min(to,arr[i-1]-1);
      if(i+1 != n)
      // make sure current element is less than its right neighboor
        to = Math.min(to,arr[i+1]-1);
      // if curr value was decreased to "to", add the difference
      res += arr[i] - to;
    }
    return res;
  }
  public static void main(String args[]) throws IOException {

    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int arr[] = new int[n];
    for(int i=0;i<n;i++)
      arr[i] = sc.nextInt();

    System.out.println(Math.min(solve(arr,n,0),solve(arr,n,1)));
  }
}

Space Complexity: O(1)

Conclusion to Convert Array into Zig-Zag Fashion
In summary, the conversion of an array into a zigzag array introduces an unconventional organization of elements characterized by alternating peaks and valleys. This rearrangement is executed through a defined rule: elements situated at even indices surpass their neighboring elements, whereas those at odd indices are comparatively smaller. The resultant zigzag array not only presents a visually unique depiction of the data but also finds applications across diverse programming scenarios, including data compression, signal processing, and mathematical problem-solving. Proficient comprehension and application of this transformation empower programmers to harness the potential of the zigzag array, enabling exploration of innovative possibilities and optimization of algorithms or data structures.

Frequently Asked Questions to Convert Array into Zig-Zag Fashion

Below are some of the FAQs related to How to Convert Array into Zig-Zag Fashion:

Q1: What is a zigzag array, and why would I want to convert my array into one?
A1: A zigzag array is an arrangement of elements in a way that alternates between increasing and decreasing order. Converting your array into a zigzag pattern can be useful in scenarios where you want to introduce a level of unpredictability or create a unique order for the elements. It’s often employed in various algorithms and data manipulation tasks.

Q2: Is there a specific algorithm or method to convert an array into a zigzag array?
A2: Yes, there are multiple algorithms to achieve this transformation. One common approach involves iterating through the array and swapping adjacent elements based on a specified condition. Depending on whether you want to create a "peak" or "valley" zigzag, the conditions for swapping will vary. The exact implementation might differ based on the programming language you’re using.

Q3: Can I convert arrays of any size into a zigzag pattern?
A3: Yes, the process of converting an array into a zigzag array is applicable to arrays of any size. However, keep in mind that the zigzag transformation might produce different results based on the number of elements in the array. Larger arrays may exhibit more intricate zigzag patterns.

Q4: Are there any real-world applications for zigzag arrays?
A4: While the concept of zigzag arrays might seem abstract, it finds applications in various fields such as image processing, data compression, and signal processing. The alternating pattern can be leveraged to create efficient data representations or improve the performance of certain algorithms.

Q5: Can I use built-in functions in programming languages to convert an array into a zigzag array?
A5: It depends on the programming language. Some languages may have built-in functions or libraries that facilitate array manipulation, making the zigzag transformation more straightforward. However, understanding the underlying logic and implementing the transformation manually can deepen your understanding of array manipulation concepts.