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,

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

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Improved By : vt_m

Practice Tags :

Arrays

Dynamic Programming