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Maximum sum subarray of size K with sum less than X
  • Difficulty Level : Basic
  • Last Updated : 13 Nov, 2020

Given an array arr[] and two integers K and X, the task is to find the maximum sum among all subarrays of size K with the sum less than X.

Examples:

Input: arr[] = {20, 2, 3, 10, 5}, K = 3, X = 20
Output: 18
Explanation: Subarray of size 3 having maximum sum less than 20 is {3, 10, 5}. Therefore, required output is 18.

Input: arr[] = {-5, 8, 7, 2, 10, 1, 20, -4, 6, 9}, K = 5, X = 30
Output: 29
Explanation: Subarray of size 5having maximum sum less than 30 is {2, 10, 1, 20, -4}. Therefore, required output is 29.

Naive Approach: The simplest approach to solve the problem is to generate all subarrays of size K and check if its sum is less than X or not. Print the maximum sum obtained among all such subarrays.



Time Complexity: O(N * K)
Auxiliary Space: O(1)

Efficient Approach: Follow the steps below to solve the problem using Sliding Window technique:

  1. Initialize a variable sum_K to store the sum of first K array elements.
  2. If sum_K is less than X, then initialize Max_Sum with sum_K.
  3. Traverse the array from (K + 1)th index and perform the following: 
    1. In each iteration, subtract the first element of the previous K length subarray and add the current element to sum_K.
    2. If sum_K is less than X, then compare sum_K with Max_Sum and update Max_Sum accordingly.
  4. Finally, print Max_Sum.

Below is the implementation of the above approach:

C++

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// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate maximum sum
// among all subarrays of size K
// with the sum less than X
void maxSumSubarr(int A[], int N,
                  int K, int X)
{
 
    // Initialize sum_K to 0
    int sum_K = 0;
 
    // Calculate sum of first K elements
    for (int i = 0; i < K; i++) {
 
        sum_K += A[i];
    }
 
    int Max_Sum = 0;
 
    // If sum_K is less than X
    if (sum_K < X) {
 
        // Initialize MaxSum with sum_K
        Max_Sum = sum_K;
    }
 
    // Iterate over the array from
    // (K + 1)-th index
    for (int i = K; i < N; i++) {
 
        // Subtract the first element
        // from the previous K elements
        // and add the next element
        sum_K -= (A[i - K] - A[i]);
 
        // If sum_K is less than X
        if (sum_K < X) {
 
            // Update the Max_Sum
            Max_Sum = max(Max_Sum, sum_K);
        }
    }
 
    cout << Max_Sum << endl;
}
 
// Driver Code
int main()
{
    int arr[] = { -5, 8, 7, 2, 10,
                  1, 20, -4, 6, 9 };
    int K = 5;
    int X = 30;
 
    // Size of Array
    int N = sizeof(arr)
            / sizeof(arr[0]);
 
    // Function Call
    maxSumSubarr(arr, N, K, X);
 
    return 0;
}

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Java

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// Java program for the above approach
import java.io.*;
 
class GFG{
     
// Function to calculate maximum sum
// among all subarrays of size K
// with the sum less than X
private static void maxSumSubarr(int A[], int N,
                                 int K, int X)
{
     
    // Initialize sum_K to 0
    int sum_K = 0;
     
    // Calculate sum of first K elements
    for(int i = 0; i < K; i++)
    {
        sum_K += A[i];
    }
     
    int Max_Sum = 0;
     
    // If sum_K is less than X
    if (sum_K < X)
    {
         
        // Initialize MaxSum with sum_K
        Max_Sum = sum_K;
    }
     
    // Iterate over the array from
    // (K + 1)-th index
    for(int i = K; i < N; i++)
    {
         
        // Subtract the first element
        // from the previous K elements
        // and add the next element
        sum_K -= (A[i - K] - A[i]);
         
        // If sum_K is less than X
        if (sum_K < X)
        {
             
            // Update the Max_Sum
            Max_Sum = Math.max(Max_Sum, sum_K);
        }
    }
     
    System.out.println(Max_Sum);
}
  
// Driver Code
public static void main (String[] args)
{
    int arr[] = { -5, 8, 7, 2, 10,
                  1, 20, -4, 6, 9 };
    int K = 5;
    int X = 30;
     
    // Size of Array
    int N = arr.length;
     
    // Function Call
    maxSumSubarr(arr, N, K, X);
}
}
 
// This code is contributed by jithin

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Python3

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# Python3 program for the above approach
  
# Function to calculate maximum sum
# among all subarrays of size K
# with the sum less than X
def maxSumSubarr(A, N, K, X):
     
    # Initialize sum_K to 0
    sum_K = 0
  
    # Calculate sum of first K elements
    for i in range(0, K):
        sum_K += A[i]
     
    Max_Sum = 0
  
    # If sum_K is less than X
    if (sum_K < X):
  
        # Initialize MaxSum with sum_K
        Max_Sum = sum_K
     
    # Iterate over the array from
    # (K + 1)-th index
    for i in range(K, N):
  
        # Subtract the first element
        # from the previous K elements
        # and add the next element
        sum_K -= (A[i - K] - A[i])
  
        # If sum_K is less than X
        if (sum_K < X):
             
            # Update the Max_Sum
            Max_Sum = max(Max_Sum, sum_K)
         
    print(Max_Sum)
 
# Driver Code
arr = [ -5, 8, 7, 2, 10,
         1, 20, -4, 6, 9 ]
K = 5
X = 30
  
# Size of Array
N = len(arr)
  
# Function Call
maxSumSubarr(arr, N, K, X)
 
# This code is contributed by sanjoy_62

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C#

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// C# program for the above approach
using System;
 
class GFG{
     
// Function to calculate maximum sum
// among all subarrays of size K
// with the sum less than X
private static void maxSumSubarr(int []A, int N,
                                 int K, int X)
{
     
    // Initialize sum_K to 0
    int sum_K = 0;
     
    // Calculate sum of first K elements
    for(int i = 0; i < K; i++)
    {
        sum_K += A[i];
    }
     
    int Max_Sum = 0;
     
    // If sum_K is less than X
    if (sum_K < X)
    {
         
        // Initialize MaxSum with sum_K
        Max_Sum = sum_K;
    }
     
    // Iterate over the array from
    // (K + 1)-th index
    for(int i = K; i < N; i++)
    {
         
        // Subtract the first element
        // from the previous K elements
        // and add the next element
        sum_K -= (A[i - K] - A[i]);
         
        // If sum_K is less than X
        if (sum_K < X)
        {
             
            // Update the Max_Sum
            Max_Sum = Math.Max(Max_Sum, sum_K);
        }
    }
    Console.WriteLine(Max_Sum);
}
  
// Driver Code
public static void Main(String[] args)
{
    int []arr = { -5, 8, 7, 2, 10,
                   1, 20, -4, 6, 9 };
    int K = 5;
    int X = 30;
     
    // Size of Array
    int N = arr.Length;
     
    // Function Call
    maxSumSubarr(arr, N, K, X);
}
}
 
// This code is contributed by Amit Katiyar

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Output: 

29























 

Time Complexity: O(N)
Auxiliary Space: O(1)

 

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