Length of the longest ZigZag Subsequence of the given Array

Last Updated : 24 Jan, 2024

Given an array arr[] of integers, if the differences between consecutive numbers alternate between positive and negative. More formally, if arr[i] - arr[i-1] has a different sign for all i from 1 to n-1, the subsequence is considered a zig-zag subsequence. Find out the length of the longest Zig-Zag subsequence of the given array.

Examples:

Input: arr[] = {1, 7, 4, 9, 2, 5}
Output: 6
Explanation: The entire sequence is a zig-zag sequence.

Input: arr[] = {1, 17, 5, 10, 13, 15, 10, 5, 16, 8}
Output: 7
Explanation: The zig-zag subsequence is [1, 17, 10, 13, 10, 16, 8].

Approach: To solve the problem follow the below idea:

We can solve this problem using Dynamic Programming.

Follow the steps to solve the problem:

Create two arrays, up and down, both of the same length as the input array. The up[i] array will store the length of the longest zig-zag subsequence ending at index i and having the last difference as positive. Similarly, the down[i] array will store the length of the longest zig-zag subsequence ending at index i and having the last difference as negative.
Initialize both up and down arrays with values of 1 since any single element is a valid zig-zag subsequence of length 1.
For each index i from 1 to n-1, compare the current element arr[i] with the previous element arr[i-1]. If arr[i] is greater, update up[i] using the maximum of up[i] and down[i-1] + 1, since the last difference is negative and now you have a positive difference.
If arr[i] is smaller, update down[i] using the maximum of down[i] and up[i-1] + 1, since the last difference is positive and now you have a negative difference.
The maximum value between up and down arrays at index n-1 will be the answer.

Below is the implementation of the above idea:

C++14

// C++ program to find longest Zig-Zag // subsequence in an array #include <algorithm> #include <iostream> #include <vector> using namespace std;  int longestZigZag(vector<int>& arr) {     int n = arr.size();     vector<int> up(n, 1);     vector<int> down(n, 1);      for (int i = 1; i < n; i++) {         for (int j = 0; j < i; j++) {             if (arr[i] > arr[j]) {                  // up[i] array will store the                 // length of the longest zig-zag                 // subsequence ending at index i                 up[i] = max(up[i], down[j] + 1);             }             else if (arr[i] < arr[j]) {                  // down[i] array will store the                 // length of the longest zig-zag                 // subsequence ending at index i                 down[i] = max(down[i], up[j] + 1);             }         }     }      return max(up[n - 1], down[n - 1]); }  // Drivers code int main() {     vector<int> arr         = { 1, 17, 5, 10, 13, 15, 10, 5, 16, 8 };      // Function Call     cout << longestZigZag(arr) << endl;      return 0; }

Java

// Java program to find longest // Zig-Zag subsequence in an array public class GFG {     // Function to return longest     // Zig-Zag subsequence length     public static int longestZigZag(int[] arr) {         int n = arr.length;         int[] up = new int[n];         int[] down = new int[n];                  //initialize both up and down arrays with values of 1         for (int i = 0; i < n; i++) {             up[i] = 1;             down[i] = 1;         }          for (int i = 1; i < n; i++) {             for (int j = 0; j < i; j++) {                 if (arr[i] > arr[j]) {                     // up[i] array will store the length of the longest zig-zag subsequence ending at index i                     up[i] = Math.max(up[i], down[j] + 1);                 } else if (arr[i] < arr[j]) {                     // down[i] array will store the length of the longest zig-zag subsequence ending at index i                     down[i] = Math.max(down[i], up[j] + 1);                 }             }         }          return Math.max(up[n - 1], down[n - 1]);     }      public static void main(String[] args) {         int[] arr = {1, 7, 4, 9, 2, 5};         System.out.println(longestZigZag(arr));       } }  // This code is contributed by spbabaraheem

Python3

# Python3 program to find longest # Zig-Zag subsequence in an array def longestZigZag(arr):     n = len(arr)     up = [1] * n     down = [1] * n      for i in range(1, n):         for j in range(i):             if arr[i] > arr[j]:                 # up[i] array will store the length of the longest zig-zag subsequence ending at index i                 up[i] = max(up[i], down[j] + 1)             elif arr[i] < arr[j]:                 # down[i] array will store the length of the longest zig-zag subsequence ending at index i                 down[i] = max(down[i], up[j] + 1)      return max(up[-1], down[-1])  # Example usage arr = [1, 7, 4, 9, 2, 5] print(longestZigZag(arr))    # This code is contributed by spbabaraheem

// C# program to find longest // Zig-Zag subsequence in an array using System; using System.Collections.Generic;  public class Program {     // Function to return longest     // Zig-Zag subsequence length     public static int LongestZigZag(int[] arr)     {         int n = arr.Length;         int[] up = new int[n];         int[] down = new int[n];                  //initialize both up and down arrays with values of 1         for (int i = 0; i < n; i++) {           up[i] = 1;           down[i] = 1;         }                for (int i = 1; i < n; i++)         {             for (int j = 0; j < i; j++)             {                 // up[i] array will store the length of the longest zig-zag subsequence ending at index i                 if (arr[i] > arr[j])                 {                     up[i] = Math.Max(up[i], down[j] + 1);                 }                 else if (arr[i] < arr[j])                 {                     // down[i] array will store the length of the longest zig-zag subsequence ending at index i                     down[i] = Math.Max(down[i], up[j] + 1);                 }             }         }          return Math.Max(up[n - 1], down[n - 1]);     }      public static void Main()     {         int[] arr = { 1, 17, 5, 10, 13, 15, 10, 5, 16, 8 };          // Function Call         Console.WriteLine(LongestZigZag(arr));     } } // This code is contributed by Rohit Singh

JavaScript

function longestZigZag(arr) {     let n = arr.length;     let up = Array(n).fill(1);     let down = Array(n).fill(1);      for (let i = 1; i < n; i++) {         for (let j = 0; j < i; j++) {             if (arr[i] > arr[j]) {                 up[i] = Math.max(up[i], down[j] + 1);             } else if (arr[i] < arr[j]) {                 down[i] = Math.max(down[i], up[j] + 1);             }         }     }      return Math.max(up[n - 1], down[n - 1]); }  // Driver code let arr = [1, 17, 5, 10, 13, 15, 10, 5, 16, 8];  // Function call console.log(longestZigZag(arr));