Length of longest subarray in which elements greater than K are more than elements not greater than K

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Given an array arr[] of length N. The task is to find the length of the longest subarray in which elements greater than a given number K are more than elements not greater than K.
Examples:

Input : N = 5, K = 2, arr[]={ 1, 2, 3, 4, 1 }
Output : 3
The subarray [2, 3, 4] or [3, 4, 1] satisfy the given condition, and there is no subarray of
length 4 or 5 which will hold the given condition, so the answer is 3.

Input : N = 4, K = 2, arr[]={ 6, 5, 3, 4 }
Output : 4

Approach:

Idea is to use the concept of binary search over Partial Sum .
Create a new array pre[] of size n, initialized to 0.
Traverse the input array a[] of size n, and for each element a[i], do the following:
- If a[i] > k, set pre[i] to 1.
- Else, set pre[i] to -1.
Traverse the pre[] array of size n, and compute its prefix sum in place, i.e., update each pre[i] to hold the sum of all elements from pre[0] to pre[i]. You can use the following code snippet for this:

for (int i = 1; i < n; i++) 
   pre[i] = pre[i - 1] + pre[i];

Initialize lo to 1 and hi to n.
Perform binary search over the possible lengths of subarrays, i.e., while lo <= hi, do the following:
- Set mid to (lo + hi) / 2.
- Set ok to false.
- For each subarray of length mid, check if its sum is greater than 0, i.e., if pre[i] – pre[i-mid] > 0, for some index i >= mid-1 and i < n. If such a subarray exists, set ok to true and break out of the loop.
- If ok is true, update the length of the longest subarray seen so far to mid, and set lo to mid+1.
- Else, set hi to mid-1.
Return the length of the longest subarray seen so far, which is stored in the variable len.

Below is the implementation of above Approach:

C++

#include <bits/stdc++.h>
using namespace std;
// C++ implementation of above approach
 
// Function to find the length of a 
// longest subarray in which elements 
// greater than K are more than 
// elements not greater than K
int LongestSubarray(int a[], int n, int k)
{
 
    int pre[n] = { 0 };
 
    // Create a new array in which we store 1
    // if a[i] > k otherwise we store -1.
    for (int i = 0; i < n; i++) {
        if (a[i] > k)
            pre[i] = 1;
        else
            pre[i] = -1;
    }
 
    // Taking prefix sum over it
    for (int i = 1; i < n; i++) 
        pre[i] = pre[i - 1] + pre[i];
 
    // len will store maximum
    // length of subarray
    int len = 0; 
 
    int lo = 1, hi = n;
 
    while (lo <= hi) {
        int mid = (lo + hi) / 2;
 
        // This indicate there is at least one
        // subarray of length mid that has sum > 0
        bool ok = false;
 
        // Check every subarray of length mid if 
        // it has sum > 0 or not if sum > 0 then it
        // will satisfy our required condition
        for (int i = mid - 1; i < n; i++) {
 
            // x will store the sum of 
            // subarray of length mid
            int x = pre[i];
            if (i - mid >= 0)
                x -= pre[i - mid];
 
            // Satisfy our given condition
            if (x > 0) { 
                ok = true;
                break;
            }
        }
 
        // Check for higher length as we
        // get length mid
        if (ok == true) {
            len = mid;
            lo = mid + 1;
        }
        // Check for lower length as we
        // did not get length mid
        else
            hi = mid - 1;
    }
 
    return len;
}
 
// Driver code
int main()
{
    int a[] = { 2, 3, 4, 5, 3, 7 };
    int k = 3;
    int n = sizeof(a) / sizeof(a[0]);
 
    cout << LongestSubarray(a, n, k);
 
    return 0;
}

Java

// Java implementation of above approach
class GFG 
{
 
// Function to find the length of a 
// longest subarray in which elements 
// greater than K are more than 
// elements not greater than K
static int LongestSubarray(int a[], int n, int k)
{
 
    int []pre = new int[n];
 
    // Create a new array in which we store 1
    // if a[i] > k otherwise we store -1.
    for (int i = 0; i < n; i++)
    {
        if (a[i] > k)
            pre[i] = 1;
        else
            pre[i] = -1;
    }
 
    // Taking prefix sum over it
    for (int i = 1; i < n; i++) 
        pre[i] = pre[i - 1] + pre[i];
 
    // len will store maximum
    // length of subarray
    int len = 0; 
 
    int lo = 1, hi = n;
 
    while (lo <= hi)
    {
        int mid = (lo + hi) / 2;
 
        // This indicate there is at least one
        // subarray of length mid that has sum > 0
        boolean ok = false;
 
        // Check every subarray of length mid if 
        // it has sum > 0 or not if sum > 0 then it
        // will satisfy our required condition
        for (int i = mid - 1; i < n; i++)
        {
 
            // x will store the sum of 
            // subarray of length mid
            int x = pre[i];
            if (i - mid >= 0)
                x -= pre[i - mid];
 
            // Satisfy our given condition
            if (x > 0) 
            { 
                ok = true;
                break;
            }
        }
 
        // Check for higher length as we
        // get length mid
        if (ok == true) 
        {
            len = mid;
            lo = mid + 1;
        }
         
        // Check for lower length as we
        // did not get length mid
        else
            hi = mid - 1;
    }
 
    return len;
}
 
// Driver code
public static void main(String[] args)
{
    int a[] = { 2, 3, 4, 5, 3, 7 };
    int k = 3;
    int n = a.length;
 
    System.out.println(LongestSubarray(a, n, k));
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 implementation of above approach
 
# Function to find the Length of a
# longest subarray in which elements
# greater than K are more than
# elements not greater than K
def LongestSubarray(a, n, k):
 
    pre = [0 for i in range(n)]
 
    # Create a new array in which we store 1
    # if a[i] > k otherwise we store -1.
    for i in range(n):
        if (a[i] > k):
            pre[i] = 1
        else:
            pre[i] = -1
 
    # Taking prefix sum over it
    for i in range(1, n):
        pre[i] = pre[i - 1] + pre[i]
 
    # Len will store maximum
    # Length of subarray
    Len = 0
 
    lo = 1
    hi = n
 
    while (lo <= hi):
        mid = (lo + hi) // 2
 
        # This indicate there is at least one
        # subarray of Length mid that has sum > 0
        ok = False
 
        # Check every subarray of Length mid if
        # it has sum > 0 or not if sum > 0 then it
        # will satisfy our required condition
        for i in range(mid - 1, n):
 
            # x will store the sum of
            # subarray of Length mid
            x = pre[i]
            if (i - mid >= 0):
                x -= pre[i - mid]
 
            # Satisfy our given condition
            if (x > 0):
                ok = True
                break
 
        # Check for higher Length as we
        # get Length mid
        if (ok == True):
            Len = mid
            lo = mid + 1
             
        # Check for lower Length as we
        # did not get Length mid
        else:
            hi = mid - 1
 
    return Len
 
# Driver code
a = [2, 3, 4, 5, 3, 7]
k = 3
n = len(a)
 
print(LongestSubarray(a, n, k))
 
# This code is contributed by Mohit Kumar

C#

// C# implementation of above approach
using System;
 
class GFG 
{
 
// Function to find the length of a 
// longest subarray in which elements 
// greater than K are more than 
// elements not greater than K
static int LongestSubarray(int[] a, int n, int k)
{
    int []pre = new int[n];
 
    // Create a new array in which we store 1
    // if a[i] > k otherwise we store -1.
    for (int i = 0; i < n; i++)
    {
        if (a[i] > k)
            pre[i] = 1;
        else
            pre[i] = -1;
    }
 
    // Taking prefix sum over it
    for (int i = 1; i < n; i++) 
        pre[i] = pre[i - 1] + pre[i];
 
    // len will store maximum
    // length of subarray
    int len = 0; 
 
    int lo = 1, hi = n;
 
    while (lo <= hi)
    {
        int mid = (lo + hi) / 2;
 
        // This indicate there is at least one
        // subarray of length mid that has sum > 0
        bool ok = false;
 
        // Check every subarray of length mid if 
        // it has sum > 0 or not if sum > 0 then it
        // will satisfy our required condition
        for (int i = mid - 1; i < n; i++)
        {
 
            // x will store the sum of 
            // subarray of length mid
            int x = pre[i];
            if (i - mid >= 0)
                x -= pre[i - mid];
 
            // Satisfy our given condition
            if (x > 0) 
            { 
                ok = true;
                break;
            }
        }
 
        // Check for higher length as we
        // get length mid
        if (ok == true) 
        {
            len = mid;
            lo = mid + 1;
        }
         
        // Check for lower length as we
        // did not get length mid
        else
            hi = mid - 1;
    }
    return len;
}
 
// Driver code
public static void Main()
{
    int[] a = { 2, 3, 4, 5, 3, 7 };
    int k = 3;
    int n = a.Length;
 
    Console.WriteLine(LongestSubarray(a, n, k));
}
}
 
// This code is contributed by Code_Mech

Javascript

<script>
// javascript implementation of above approach
 
// Function to find the length of a 
// longest subarray in which elements 
// greater than K are more than 
// elements not greater than K
function LongestSubarray(a , n , k)
{
 
    var pre = Array.from({length: n}, (_, i) => 0);
 
    // Create a new array in which we store 1
    // if a[i] > k otherwise we store -1.
    for (i = 0; i < n; i++)
    {
        if (a[i] > k)
            pre[i] = 1;
        else
            pre[i] = -1;
    }
 
    // Taking prefix sum over it
    for (i = 1; i < n; i++) 
        pre[i] = pre[i - 1] + pre[i];
 
    // len will store maximum
    // length of subarray
    var len = 0; 
 
    var lo = 1, hi = n;
 
    while (lo <= hi)
    {
        var mid = parseInt((lo + hi) / 2);
 
        // This indicate there is at least one
        // subarray of length mid that has sum > 0
        var ok = false;
 
        // Check every subarray of length mid if 
        // it has sum > 0 or not if sum > 0 then it
        // will satisfy our required condition
        for (i = mid - 1; i < n; i++)
        {
 
            // x will store the sum of 
            // subarray of length mid
            var x = pre[i];
            if (i - mid >= 0)
                x -= pre[i - mid];
 
            // Satisfy our given condition
            if (x > 0) 
            { 
                ok = true;
                break;
            }
        }
 
        // Check for higher length as we
        // get length mid
        if (ok == true) 
        {
            len = mid;
            lo = mid + 1;
        }
         
        // Check for lower length as we
        // did not get length mid
        else
            hi = mid - 1;
    }
 
    return len;
}
 
// Driver code
var a = [ 2, 3, 4, 5, 3, 7 ];
var k = 3;
var n = a.length;
 
document.write(LongestSubarray(a, n, k));
 
// This code is contributed by shikhasingrajput 
</script>

Output

Time Complexity: O(N*logN)
Auxiliary Space: O(N)

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