Related Articles

# Maximum sum subarray having sum less than or equal to given sum using Set

• Difficulty Level : Hard
• Last Updated : 27 May, 2021

Given an array arr[] of length N and an integer K, the task is the find the maximum sum subarray with a sum less than K.
Note: If K is less than the minimum element, then return INT_MIN.

Examples:

Input: arr[] = {-1, 2, 2}, K = 4
Output:
Explanation:
The subarray with maximum sum which is less than 4 is {-1, 2, 2}.
The subarray {2, 2} has maximum sum = 4, but it is not less than 4.

Input: arr[] = {5, -2, 6, 3, -5}, K =15
Output: 12
Explanation:
The subarray with maximum sum which is less than 15 is {5, -2, 6, 3}.

Efficient Approach: Sum of subarray [i, j] is given by cumulative sum till j – cumulative sum till i of the array. Now the problem reduces to finding two indexes i and j such that i < j and cum[j] – cum[i] are as close to K but lesser than it.
To solve this, iterate the array from left to right. Put the cumulative sum of i values that you have encountered till now into a set. When you are processing cum[j] what you need to retrieve from the set is the smallest number in the set which is bigger than cum[j] – K. This can be done in O(logN) using upper_bound on the set.

Below is the implementation of the above approach:

## C++

 `// C++ program to find maximum sum``// subarray less than K` `#include ``using` `namespace` `std;` `// Function to maximum required sum < K``int` `maxSubarraySum(``int` `arr[], ``int` `N, ``int` `K)``{` `    ``// Hash to lookup for value (cum_sum - K)``    ``set<``int``> cum_set;``    ``cum_set.insert(0);` `    ``int` `max_sum = INT_MIN, cSum = 0;` `    ``for` `(``int` `i = 0; i < N; i++) {` `        ``// getting cummulative sum from [0 to i]``        ``cSum += arr[i];` `        ``// lookup for upperbound``        ``// of (cSum-K) in hash``        ``set<``int``>::iterator sit``            ``= cum_set.lower_bound(cSum - K);` `        ``// check if upper_bound``        ``// of (cSum-K) exists``        ``// then update max sum``        ``if` `(sit != cum_set.end())` `            ``max_sum = max(max_sum, cSum - *sit);` `        ``// insert cummulative value in hash``        ``cum_set.insert(cSum);``    ``}` `    ``// return maximum sum``    ``// lesser than K``    ``return` `max_sum;``}` `// Driver code``int` `main()``{` `    ``// initialise the array``    ``int` `arr[] = { 5, -2, 6, 3, -5 };` `    ``// initialise the vaue of K``    ``int` `K = 15;` `    ``// size of array``    ``int` `N = ``sizeof``(arr) / ``sizeof``(arr);` `    ``cout << maxSubarraySum(arr, N, K);` `    ``return` `0;``}`

## Java

 `// Java program to find maximum sum``// subarray less than K``import` `java.util.*;``import` `java.io.*;` `class` `GFG{``    ` `// Function to maximum required sum < K``static` `int` `maxSubarraySum(``int` `arr[], ``int` `N,``                          ``int` `K)``{``    ` `    ``// Hash to lookup for value (cum_sum - K)``    ``Set cum_set = ``new` `HashSet<>();``    ``cum_set.add(``0``);`` ` `    ``int` `max_sum =Integer.MIN_VALUE, cSum = ``0``;`` ` `    ``for``(``int` `i = ``0``; i < N; i++)``    ``{``        ` `        ``// Getting cummulative sum from [0 to i]``        ``cSum += arr[i];`` ` `        ``// Lookup for upperbound``        ``// of (cSum-K) in hash``        ``ArrayList al = ``new` `ArrayList<>();``        ``Iterator it = cum_set.iterator();``        ``int` `end = ``0``;``        ` `        ``while` `(it.hasNext())``        ``{``            ``end = it.next();``            ``al.add(end);``        ``}``        ` `        ``Collections.sort(al);``        ``int` `sit = lower_bound(al, cSum - K);``        ` `        ``// Check if upper_bound``        ``// of (cSum-K) exists``        ``// then update max sum``        ``if` `(sit != end)``            ``max_sum = Math.max(max_sum,``                               ``cSum - sit);`` ` `        ``// Insert cummulative value in hash``        ``cum_set.add(cSum);``    ``}`` ` `    ``// Return maximum sum``    ``// lesser than K``    ``return` `max_sum;``}` `static` `int` `lower_bound(ArrayList al,``                       ``int` `x)``{``    ` `    ``// x is the target value or key``    ``int` `l = -``1``, r = al.size();``    ``while` `(l + ``1` `< r)``    ``{``        ``int` `m = (l + r) >>> ``1``;``        ``if` `(al.get(m) >= x)``            ``r = m;``        ``else``            ``l = m;``    ``}``    ``return` `r;``}` `// Driver code``public` `static` `void` `main(String args[])``{`` ` `    ``// Initialise the array``    ``int` `arr[] = { ``5``, -``2``, ``6``, ``3``, -``5` `};`` ` `    ``// Initialise the vaue of K``    ``int` `K = ``15``;`` ` `    ``// Size of array``    ``int` `N = arr.length;`` ` `    ``System.out.println(maxSubarraySum(arr, N, K));``}``}` `// This code is contributed by jyoti369`

## Python3

 `# Python3 program to find maximum sum``# subarray less than K``import` `sys``import` `bisect` `# Function to maximum required sum < K`  `def` `maxSubarraySum(arr, N, K):``    ``# Hash to lookup for value (cum_sum - K)``    ``cum_set ``=` `set``()``    ``cum_set.add(``0``)` `    ``max_sum ``=` `12``    ``cSum ``=` `0` `    ``for` `i ``in` `range``(N):``        ` `        ``# getting cummulative sum from [0 to i]``        ``cSum ``+``=` `arr[i]` `        ``# check if upper_bound``        ``# of (cSum-K) exists``        ``# then update max sum``        ``x ``=` `bisect.bisect_left(arr, cSum ``-` `K, lo``=``0``, hi``=``len``(arr))``        ``if` `x:``            ``max_sum ``=` `max``(max_sum,x )` `        ``# insert cummulative value in hash``        ``cum_set.add(cSum)` `    ``# return maximum sum``    ``# lesser than K``    ``return` `max_sum`  `# Driver code``if` `__name__ ``=``=` `'__main__'``:``    ``# initialise the array``    ``arr ``=` `[``5``, ``-``2``, ``6``, ``3``, ``-``5``]` `    ``# initialise the vaue of K``    ``K ``=` `15` `    ``# size of array``    ``N ``=` `len``(arr)` `    ``print``(maxSubarraySum(arr, N, K))` `# This code is contributed by Surendra_Gangwar`

## C#

 `// Java program to find maximum sum``// subarray less than K``using` `System;``using` `System.Collections.Generic;``class` `GFG {` `    ``// Function to maximum required sum < K``    ``static` `int` `maxSubarraySum(``int``[] arr, ``int` `N, ``int` `K)``    ``{` `        ``// Hash to lookup for value (cum_sum - K)``        ``HashSet<``int``> cum_set = ``new` `HashSet<``int``>();``        ``cum_set.Add(0);``        ``int` `max_sum = Int32.MinValue, cSum = 0;``        ``for` `(``int` `i = 0; i < N; i++) {` `            ``// Getting cummulative sum from [0 to i]``            ``cSum += arr[i];` `            ``// Lookup for upperbound``            ``// of (cSum-K) in hash``            ``List<``int``> al = ``new` `List<``int``>();``            ``int` `end = 0;``            ``foreach``(``int` `it ``in` `cum_set)``            ``{``                ``end = it;``                ``al.Add(it);``            ``}` `            ``al.Sort();``            ``int` `sit = lower_bound(al, cSum - K);` `            ``// Check if upper_bound``            ``// of (cSum-K) exists``            ``// then update max sum``            ``if` `(sit != end)``                ``max_sum = Math.Max(max_sum, cSum - sit);` `            ``// Insert cummulative value in hash``            ``cum_set.Add(cSum);``        ``}` `        ``// Return maximum sum``        ``// lesser than K``        ``return` `max_sum;``    ``}``    ``static` `int` `lower_bound(List<``int``> al, ``int` `x)``    ``{` `        ``// x is the target value or key``        ``int` `l = -1, r = al.Count;``        ``while` `(l + 1 < r) {``            ``int` `m = (l + r) >> 1;``            ``if` `(al[m] >= x)``                ``r = m;``            ``else``                ``l = m;``        ``}``        ``return` `r;``    ``}` `    ``// Driver code``    ``public` `static` `void` `Main(``string``[] args)``    ``{` `        ``// Initialise the array``        ``int``[] arr = { 5, -2, 6, 3, -5 };` `        ``// Initialise the vaue of K``        ``int` `K = 15;` `        ``// Size of array``        ``int` `N = arr.Length;``        ``Console.Write(maxSubarraySum(arr, N, K));``    ``}``}` `// This code is contributed by chitranayal.`

## Javascript

 ``
Output
`12`

Time Complexity: O(N*Log(N))
Similar article: Maximum sum subarray having sum less than or equal to given sum using Sliding Window

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes arrow_drop_up