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Maximum sum of lengths of non-overlapping subarrays with k as the max element.

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  • Difficulty Level : Medium
  • Last Updated : 19 Jul, 2022
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Find the maximum sum of lengths of non-overlapping subarrays (contiguous elements) with k as the maximum element. 

Examples: 

Input : arr[] = {2, 1, 4, 9, 2, 3, 8, 3, 4} 
        k = 4
Output : 5
{2, 1, 4} => Length = 3
{3, 4} => Length = 2
So, 3 + 2 = 5 is the answer

Input : arr[] = {1, 2, 3, 2, 3, 4, 1} 
        k = 4
Output : 7
{1, 2, 3, 2, 3, 4, 1} => Length = 7

Input : arr = {4, 5, 7, 1, 2, 9, 8, 4, 3, 1}
        k = 4
Ans = 4
{4} => Length = 1
{4, 3, 1} => Length = 3
So, 1 + 3 = 4 is the answer

Question source : https://www.geeksforgeeks.org/amazon-interview-experience-set-376-campus-internship/

Algorithm : 

Traverse the array starting from first element
   Take a loop and keep on incrementing count 
   If element is less than equal to k
       if array element is equal to k, then mark
       a flag
   
   If flag is marked, add this count to answer
   
   Take another loop and traverse the array 
   till element is greater than k
return ans

Implementation:

C++




// CPP program to calculate max sum lengths of
// non overlapping contiguous subarrays with k as
// max element
#include <bits/stdc++.h>
using namespace std;
  
// Returns max sum of lengths with maximum element
// as k
int calculateMaxSumLength(int arr[], int n, int k)
{
    int ans = 0; // final sum of lengths
  
    // number of elements in current subarray
    int count = 0;
  
    // variable for checking if k appeared in subarray
    int flag = 0;
  
    for (int i = 0; i < n;) {
        count = 0;
        flag = 0;
  
        // count the number of elements which are
        // less than equal to k
        while (arr[i] <= k && i < n) {
            count++;
            if (arr[i] == k)
                flag = 1;
            i++;
        }
  
        // if current element appeared in current
        // subarray add count to sumLength
        if (flag == 1)
            ans += count;   
  
        // skip the array elements which are
        // greater than k
        while (arr[i] > k && i < n)
            i++;    
    }
    return ans;
}
  
// driver program
int main()
{
    int arr[] = { 4, 5, 7, 1, 2, 9, 8, 4, 3, 1 };
    int size = sizeof(arr) / sizeof(arr[0]);
    int k = 4;
    int ans = calculateMaxSumLength(arr, size, k);
    cout << "Max Length :: " << ans << endl;
    return 0;
}

Java




// A Java program to calculate max sum lengths of
// non overlapping contiguous subarrays with k as
// max element
public class GFG
{
    // Returns max sum of lengths with maximum element
    // as k
    static int calculateMaxSumLength(int arr[], int n, int k) {
        int ans = 0; // final sum of lengths
 
        // number of elements in current subarray
        int count = 0;
 
        // variable for checking if k appeared in subarray
        int flag = 0;
 
        for (int i = 0; i < n;) {
            count = 0;
            flag = 0;
 
            // count the number of elements which are
            // less than equal to k
            while (i < n && arr[i] <= k) {
                count++;
                if (arr[i] == k)
                    flag = 1;
                i++;
            }
 
            // if current element appeared in current
            // subarray add count to sumLength
            if (flag == 1)
                ans += count;
 
            // skip the array elements which are
            // greater than k
            while (i < n && arr[i] > k)
                i++;
        }
        return ans;
    }
 
    // driver program to test above method
    public static void main(String[] args) {
 
        int arr[] = { 4, 5, 7, 1, 2, 9, 8, 4, 3, 1 };
        int size = arr.length;
        int k = 4;
        int ans = calculateMaxSumLength(arr, size, k);
        System.out.println("Max Length :: " + ans);
    }
}
// This code is contributed by Sumit Ghosh

Python3




# Python program to calculate max sum lengths of non
# overlapping contiguous subarrays with k as max element
 
# Returns max sum of lengths with max elements as k
def calculateMaxSumLength(arr, n, k):
    ans = 0 # final sum of lengths
    i=0
    while i < n :
         
        # number of elements in current sub array
        count = 0
         
        # Variable for checking if k appeared in the sub array
        flag = 0
         
        # Count the number of elements which are
        # less than or equal to k
        while i < n and arr[i] <= k :
            count = count + 1
            if arr[i] == k:
                flag = 1
            i = i + 1
             
        # if current element appeared in current
        # subarray and count to sumLength
        if flag == 1:
            ans = ans + count
             
        # skip the array elements which are greater than k
        while i < n and arr[i] > k :
            i = i + 1
              
    return ans
     
# Driver Program
arr = [4, 5, 7, 1, 2, 9, 8, 4, 3, 1]
size = len(arr)
k = 4
ans = calculateMaxSumLength(arr, size, k)
print ("Max Length ::",ans)
 
# Contributed by Rohit

C#




// A C# program to calculate max
// sum lengths of non overlapping
// contiguous subarrays with k as
// max element
using System;
class GFG {
     
    // Returns max sum of lengths
    // with maximum element as k
    static int calculateMaxSumLength(int []arr,
                                     int n,
                                     int k)
    {
         
        // final sum of lengths
        int ans = 0;
 
        // number of elements in
        // current subarray
        int count = 0;
 
        // variable for checking if
        // k appeared in subarray
        int flag = 0;
 
        for(int i = 0; i < n;)
        {
            count = 0;
            flag = 0;
 
            // count the number of
            // elements which are
            // less than equal to k
            while (i < n && arr[i] <= k)
            {
                count++;
                if (arr[i] == k)
                    flag = 1;
                i++;
            }
 
            // if current element
            // appeared in current
            // subarray add count
            // to sumLength
            if (flag == 1)
                ans += count;
 
            // skip the array
            // elements which are
            // greater than k
            while (i < n && arr[i] > k)
                i++;
        }
        return ans;
    }
 
    // Driver Code
    public static void Main()
    {
        int []arr = {4, 5, 7, 1, 2, 9, 8, 4, 3, 1};
        int size = arr.Length;
        int k = 4;
        int ans = calculateMaxSumLength(arr, size, k);
        Console.WriteLine("Max Length :: " + ans);
    }
}
 
// This code is contributed by anuj_67.

PHP




<?php
// PHP program to calculate max sum lengths
// of non overlapping contiguous subarrays
// with k as max element
 
// Returns max sum of lengths with maximum
// element as k
function calculateMaxSumLength(&$arr, $n, $k)
{
    $ans = 0; // final sum of lengths
 
    // number of elements in current subarray
    $count = 0;
 
    // variable for checking if k
    // appeared in subarray
    $flag = 0;
 
    for ($i = 0; $i < $n😉
    {
        $count = 0;
        $flag = 0;
 
        // count the number of elements which
        // are less than equal to k
        while ($arr[$i] <= $k && $i < $n)
        {
            $count++;
            if ($arr[$i] == $k)
                $flag = 1;
            $i++;
        }
 
        // if current element appeared in current
        // subarray add count to sumLength
        if ($flag == 1)
            $ans += $count;
 
        // skip the array elements which are
        // greater than k
        while ($arr[$i] > $k && $i < $n)
            $i++;    
    }
    return $ans;
}
 
// Driver Code
$arr = array( 4, 5, 7, 1, 2,   
              9, 8, 4, 3, 1 );
$size = sizeof($arr);
$k = 4;
$ans = calculateMaxSumLength($arr, $size, $k);
echo "Max Length :: " . $ans . "\n";
 
// This code is contributed by ita_c
?>

Javascript




<script>
// A Javascript program to calculate max sum lengths of
// non overlapping contiguous subarrays with k as
// max element
     
    // Returns max sum of lengths with maximum element
    // as k
    function calculateMaxSumLength(arr,n,k)
    {
        let ans = 0; // final sum of lengths
  
        // number of elements in current subarray
        let count = 0;
  
        // variable for checking if k appeared in subarray
        let flag = 0;
  
        for (let i = 0; i < n;) {
            count = 0;
            flag = 0;
  
            // count the number of elements which are
            // less than equal to k
            while (i < n && arr[i] <= k) {
                count++;
                if (arr[i] == k)
                    flag = 1;
                i++;
            }
  
            // if current element appeared in current
            // subarray add count to sumLength
            if (flag == 1)
                ans += count;
  
            // skip the array elements which are
            // greater than k
            while (i < n && arr[i] > k)
                i++;
        }
        return ans;
    }
     
    // driver program to test above method
    let arr=[4, 5, 7, 1, 2, 9, 8, 4, 3, 1];
    let size = arr.length;
    let k = 4;
    let ans = calculateMaxSumLength(arr, size, k);
    document.write("Max Length :: " + ans);
     
    //This code is contributed by avanitrachhadiya2155
     
</script>

Output

Max Length :: 4

Time Complexity : O(n) 

It may look like O(n2), but if you take a closer look, array is traversed only once

Another approach:

Algorithm:

Traverse the array from first element to last element
    if the element is less than k increment the count
    if the element is equals to k 
        if k is not found
            increment the count and mark flag as 1
        if k is found
            add the value of count to ans and mark count as 1
    if the element is greater than k
            if k is present in the subarray add the value of count to ans and
            assign value of count and flag variables as 0
finally check again if k value is found in subarray or not
    if k is found return sum of answer and count
    if not return ans

Implementation:

C++




// C++ program to find Maximum sum of lengths of
// non-overlapping subarrays with k as the max element.
#include <bits/stdc++.h>
using namespace std;
// Below function calculates the Maximum sum of lengths of
// non-overlapping subarrays with k as the max element.
int calculateMaxSumLength(int arr[], int n, int k)
{
    // maximum sum of lengths
    int ans = 0;
    // number of elements in current subarray
    int count = 0;
    // flag variable for checking if k is present
    // in current subarray or not
    int flag = 0;
    for (int i = 0; i < n; i++) {
        // increment the count if element in arr is less
        // than k
        if (arr[i] < k) {
            count++;
        }
        // if the element is equals to k
        else if (arr[i] == k) {
            if (flag == 0) {
                count++;
                flag = 1;
            }
            // if flag is 1, we can say k is already present
            // in that subarray. So, add the value of count
            // to ans variable and make the count value as 1
            // because we found the k
            else {
                ans += count;
                count = 1;
            }
        }
        // if element in arr is greater than k
        else {
            // if k is present in the subarray
            // add the value of count to ans variable
            if (flag == 1) {
                ans += count;
            }
            // assign value of count and flag variables as 0
            count = 0;
            flag = 0;
        }
    }
    // Check again if k value is found in subarray
    // if k is found, return sum of values of variables ans
    // and count if k is not found, return value of variable
    // ans.
    if (flag == 1) {
        return ans + count;
    }
    return ans;
}
// driver program
int main()
{
    int arr[] = { 4, 5, 7, 1, 2, 9, 8, 4, 3, 1 };
    int size = sizeof(arr) / sizeof(arr[0]);
    int k = 4;
    int ans = calculateMaxSumLength(arr, size, k);
    cout << "Max Length :: " << ans << endl;
    return 0;
}
// Contributed by Ravi Teja Kuchipudi

Java




// JAVA program to find Maximum sum of lengths of
// non-overlapping subarrays with k as the max element.
class GFG {
    // Below function calculates the Maximum sum of lengths
    // of non-overlapping subarrays with k as the max
    // element.
    static int calculateMaxSumLength(int arr[], int n,
                                     int k)
    {
        // maximum sum of lengths
        int ans = 0;
        // number of elements in current subarray
        int count = 0;
        // flag variable for checking if k is present
        // in current subarray or not
        int flag = 0;
        for (int i = 0; i < n; i++) {
            // increment the count if element in arr is less
            // than k
            if (arr[i] < k) {
                count++;
            }
            // if the element is equals to k
            else if (arr[i] == k) {
                // if flag is equals to 0 then make flag
                // variable value as 1 and increment the
                // count.
                if (flag == 0) {
                    count++;
                    flag = 1;
                }
                // if flag is 1, we can say k is already
                // present in that subarray. So, add the
                // value of count to ans variable and make
                // the count value as 1 because we found the
                // k
                else {
                    ans += count;
                    count = 1;
                }
            }
            // if element in arr is greater than k
            else {
                // if k is present in the subarray
                // add the value of count to ans variable
                if (flag == 1) {
                    ans += count;
                }
                // assign value of count and flag variables
                // as 0
                count = 0;
                flag = 0;
            }
        }
        // Check again if k value is found in subarray
        // if k is found, return sum of values of variables
        // ans and count if k is not found, return value of
        // variable ans.
        if (flag == 1) {
            return ans + count;
        }
        return ans;
    }
    // driver program to test above method
    public static void main(String[] args)
    {
        int arr[] = { 4, 5, 7, 1, 2, 9, 8, 4, 3, 1 };
        int size = arr.length;
        int k = 4;
        int ans = calculateMaxSumLength(arr, size, k);
        System.out.println("Max Length :: " + ans);
    }
}
// Contributed by Ravi Teja Kuchipudi

Python3




# program to find Maximum sum of lengths of
# non-overlapping subarrays with k as the max element.
 
 
def calculateMaxSumLength(arr, n, k):
    # maximum sum of lengths
    ans = 0
    # number of elements in current subarray
    count = 0
    # flag variable for checking if k is present in current subarray or not
    flag = 0
 
    for i in range(n):
        # increment the count if element in arr is less than k
        if arr[i] < k:
            count = count+1
        # if the element is equals to k
        elif arr[i] == k:
            # if flag is equals to 0 then make flag variable value as 1 and
            # increment the count.
            if flag == 0:
                count = count + 1
                flag = 1
            # if flag is 1, we can say k is already present in that subarray.
            # So, add the value of count to ans variable and
            # make the count value as 1 because we found the k
            else:
                ans = ans + count
                count = 1
        # if element in arr is greater than k
        else:
            # if k is present in the subarray
            # add the value of count to ans variable
            if flag == 1:
                ans = ans + count
            # assign value of count and flag variables as 0
            count = 0
            flag = 0
    # Check again if k value is found in subarray
    # if k is found, return sum of values of variables ans and count
    # if k is not found, return value of variable ans.
    if flag == 1:
        return ans + count
    return ans
 
 
# Driver Program
arr = [4, 5, 7, 1, 2, 9, 8, 4, 3, 1]
size = len(arr)
k = 4
ans = calculateMaxSumLength(arr, size, k)
print("Max Length ::", ans)
 
# Contributed by Ravi Teja Kuchipudi

C#




// C# program to find Maximum sum of lengths of
// non-overlapping subarrays with k as the max element.
using System;
class GFG
{
    // Returns max sum of lengths
    // with maximum element as k
    static int calculateMaxSumLength(int[] arr, int n, int k)
    {
        // maximum sum of lengths
        int ans = 0;
        // number of elements in current subarray
        int count = 0;
        // flag variable for checking if k is present
        // in current subarray or not
        int flag = 0;
        for (int i = 0; i < n; i++)
        {
            // increment the count if element in arr is less
            // than k
            if (arr[i] < k)
            {
                count++;
            }
            // if the element is equals to k
            else if (arr[i] == k)
            {
                // if flag is equals to 0 then make flag
                // variable value as 1 and increment the
                // count.
                if (flag == 0)
                {
                    count++;
                    flag = 1;
                }
                // if flag is 1, we can say k is already
                // present in that subarray. So, add the
                // value of count to ans variable and make
                // the count value as 1 because we found the
                // k
                else
                {
                    ans += count;
                    count = 1;
                }
            }
            // if element in arr is greater than k
            else
            {
                // if k is present in the subarray
                // add the value of count to ans variable
                if (flag == 1)
                {
                    ans += count;
                }
                // assign value of count and flag variables
                // as 0
                count = 0;
                flag = 0;
            }
        }
        // Check again if k value is found in subarray
        // if k is found, return sum of values of variables
        // ans and count if k is not found, return value of
        // variable ans.
        if (flag == 1)
        {
            return ans + count;
        }
        return ans;
    }
 
    // Driver Code
    public static void Main()
    {
        int []arr = {4, 5, 7, 1, 2, 9, 8, 4, 3, 1};
        int size = arr.Length;
        int k = 4;
        int ans = calculateMaxSumLength(arr, size, k);
        Console.WriteLine("Max Length :: " + ans);
    }
}
 
// This code is contributed by kothavvsaakash

Javascript




<script>
 
// JavaScript program to find Maximum sum of lengths of
// non-overlapping subarrays with k as the max element.
 
// Below function calculates the Maximum sum of lengths of
// non-overlapping subarrays with k as the max element.
function calculateMaxSumLength(arr, n, k)
{
    // maximum sum of lengths
    let ans = 0;
     
    // number of elements in current subarray
    let count = 0;
     
    // flag variable for checking if k is present
    // in current subarray or not
    let flag = 0;
    for (let i = 0; i < n; i++)
    {
     
        // increment the count if element in arr is less
        // than k
        if (arr[i] < k) {
            count++;
        }
         
        // if the element is equals to k
        else if (arr[i] == k) {
            if (flag == 0) {
                count++;
                flag = 1;
            }
             
            // if flag is 1, we can say k is already present
            // in that subarray. So, add the value of count
            // to ans variable and make the count value as 1
            // because we found the k
            else {
                ans += count;
                count = 1;
            }
        }
         
        // if element in arr is greater than k
        else
        {
         
            // if k is present in the subarray
            // add the value of count to ans variable
            if (flag == 1)
            {
                ans += count;
            }
             
            // assign value of count and flag variables as 0
            count = 0;
            flag = 0;
        }
    }
     
    // Check again if k value is found in subarray
    // if k is found, return sum of values of variables ans
    // and count if k is not found, return value of variable
    // ans.
    if (flag == 1) {
        return ans + count;
    }
    return ans;
}
 
// driver program
let arr = [ 4, 5, 7, 1, 2, 9, 8, 4, 3, 1 ];
let size = arr.length;
let k = 4;
let ans = calculateMaxSumLength(arr, size, k);
document.write("Max Length :: ",ans,"</br>");
 
// This code is contributed by shinjanpatra
 
</script>

Output

Max Length :: 4

Time Complexity : O(n) 


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