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

Given an array arr[] of length N and an integer K, the task is the find the maximum sum subarray with sum less than K.

Note: If K is less than minimum element, then return INT_MIN.

Examples:

Input: arr[] = {-1, 2, 2}, K = 4
Output: 3
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}.

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

Efficient Approach: Sum of subarray [i, j] is given by cumulative sum till j – cumulative sum till i of 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++ 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.upper_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[0]); ` ` `  `    ``cout << maxSubarraySum(arr, N, K); ` ` `  `    ``return` `0; ` `} `

 `# python3 program to find maximum sum ` `# subarray less than K ` `import` `sys,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 ``=` `5` `        ``if` `x ``in` `cum_set: ` `            ``max_sum ``=` `max``(max_sum,cSum ``-` `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 `

Output:
```12
```

Time Complexity: O(N*Log(N))

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Improved By : SURENDRA_GANGWAR