Longest alternating (positive and negative) subarray starting at every index

A subarray is called alternating if any two consecutive numbers in it have opposite signs (i.e. one of them should be negative, whereas the other should be positive).

Given an array of n integers. For each index i, we need to find the length if the longest alternating subarray starting at i.

Examples:

Input : a[] = {1, -5, 1, -5}
Output : For index 0, {1, -5, 1, -5} = 4
             index 1, {-5, 1, -5} = 3
             index 2, {1, -5} = 2
             index 3, {-5} = 1.
      
Input :a[] = {-5, -1, -1, 2, -2, -3}
Output : index 0 = 1,
         index 1 = 1,
         index 2 = 3,
         index 3 = 2,
         index 4 = 1,
         index 5 = 1,



A Naive approach is to use two loops in which we traverse the whole array starting from every index i (0 to n-1) and calculate the length of the alternating subarray.
Time Complexity: O(n2).

Efficient Approach:
Observe that when a[i] and a[i+1] have opposite signs, count[i] will be 1 more than count[i+1]. Otherwise when they have same sign count[i] will be 1.

We use Dynamic Programming here.

C++

// CPP program to find longest alternating
// subarray starting from every index.
#include <bits/stdc++.h>
using namespace std;
  
void longestAlternating(int arr[], int n)
{
    int count[n];
  
    // Fill count[] from end. 
    count[n - 1] = 1;
    for (int i = n - 2; i >= 0; i--) {
        if (arr[i] * arr[i + 1] < 0)
            count[i] = count[i + 1] + 1;
        else
            count[i] = 1;
    }
  
    // Print result
    for (int i = 0; i < n; i++)
        cout << count[i] << " ";
}
  
// Driver code
int main()
{
    int a[] = { -5, -1, -1, 2, -2, -3 };
    int n = sizeof(a) / sizeof(a[0]);
    longestAlternating(a, n);
    return 0;
}

Java

// Java program to find longest alternating
// subarray starting from every index.
import java.util.*;
  
class Longest{
      
    public static void longestAlternating(int arr[], 
                                             int n)
    {
        int[] count = new int[n];
  
        // Fill count[] from end. 
        count[n - 1] = 1;
        for (int i = n - 2; i >= 0; i--) {
            if (arr[i] * arr[i + 1] < 0)
                count[i] = count[i + 1] + 1;
            else
                count[i] = 1;
        }
  
        // Print result
        for (int i = 0; i < n; i++)
            System.out.print(count[i] + " ");
    }
      
    // driver program
    public static void main(String[] args)
    {
        int a[] = { -5, -1, -1, 2, -2, -3 };
        int n = 6;
        longestAlternating(a, n);
    }
}
  
// This code is contributed by rishabh_jain

Python3

# Python3 program to find longest alternating
# subarray starting from every index.
  
def longestAlternating(arr, n) :
    count = [None] * n
  
    # Fill count[] from end. 
    count[n - 1] = 1
    i = n - 2
      
    while i >= 0 :
        if (arr[i] * arr[i + 1] < 0) :
            count[i] = count[i + 1] + 1
        else :
            count[i] = 1;
        i = i - 1
  
    i = 0
      
    # Print result
    while i < n :
        print (count[i], end = " ")
        i = i + 1
  
# Driver Code
a = [ -5, -1, -1, 2, -2, -3 ]
n = len(a)
longestAlternating(a, n);
  
  
# This code is contributed by rishabh_jain 

C#

//C# program to find longest alternating
// subarray starting from every index.
using System;
  
class Longest
{
      
    public static void longestAlternating(int []arr, 
                                            int n)
    {
        int[] count = new int[n];
  
        // Fill count[] from end. 
        count[n - 1] = 1;
        for (int i = n - 2; i >= 0; i--) 
        {
            if (arr[i] * arr[i + 1] < 0)
                count[i] = count[i + 1] + 1;
            else
                count[i] = 1;
        }
  
        // Print result
        for (int i = 0; i < n; i++)
            Console.Write(count[i] + " ");
    }
      
    // Driver program
    public static void Main()
    {
        int []a = { -5, -1, -1, 2, -2, -3 };
        int n = 6;
        longestAlternating(a, n);
    }
}
  
// This code is contributed by vt_m

PHP

<?php
// PHP program to find longest alternating
// subarray starting from every index.
  
function longestAlternating( $arr, $n)
{
    $count = array();
  
    // Fill count[] from end. 
    $count[$n - 1] = 1;
    for ( $i = $n - 2; $i >= 0; $i--) 
    {
        if ($arr[$i] * $arr[$i + 1] < 0)
            $count[$i] = $count[$i + 1] + 1;
        else
            $count[$i] = 1;
    }
  
    // Print result
    for ( $i = 0; $i < $n; $i++)
        echo $count[$i] , " ";
}
  
    // Driver code
    $a = array( -5, -1, -1, 2, -2, -3 );
    $n =count($a);
    longestAlternating($a, $n);
  
// This code is contributed by anuj_67.
?>


Output:

1 1 3 2 1 1


My Personal Notes arrow_drop_up

Recommended Posts:


Harsha_Mogali
Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. 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.



Improved By : vt_m

Article Tags :
Arrays
Dynamic Programming
Practice Tags :
Arrays
Dynamic Programming



Be the First to upvote.


1.7

Based on 10 vote(s)
Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.