Largest subarray having sum greater than k in C++

In this tutorial, we are going to write a program that finds the largest subarray have sum greater than k.

Let's see the steps to solve the problem.

• Initialise the array.
• Iterate over the array and store sum at each index in a vector along with the index.
• Sort the above sums based on sum and index.
• Initialise an array to store the indexes.
• Write a loop that iterates till n.
  • Update the values with min index of above indexes array and previous sums array index.
• Initialise sum to 0.
• Write a loop that iterates till n.
  • Add current element to sum.
  • If the sum is greater than k.
    • The maximum subarray length is i + 1.
  • Else the maximum subarray length is
    • Find the index from the previous sums using binary search.
    • The sum that is less than sum - k - 1 is the element index we want.

Example

Let's see the code.

 Live Demo

#include <bits/stdc++.h>
using namespace std;
bool compare(const pair<int, int>& a, const pair<int, int>& b) {
   if (a.first == b.first) {
      return a.second < b.second;
   }
   return a.first < b.first;
}
int findIndex(vector<pair<int, int> >& previousSums, int n, int val) {
   int start = 0;
   int end = n - 1;
   int mid, result = -1;
   while (start <= end) {
      mid = (start + end) / 2;
      if (previousSums[mid].first <= val) {
         result = mid;
         start = mid + 1;
      }else {
         end = mid - 1;
      }
   }
   return result;
}
int getLargestSubArray(int arr[], int n, int k) {
   int maxLength = 0;
   vector<pair<int, int> > previousSums;
   int sum = 0, minIndexes[n];
   for (int i = 0; i < n; i++) {
      sum = sum + arr[i];
      previousSums.push_back({ sum, i });
   }
   sort(previousSums.begin(), previousSums.end(), compare);
   minIndexes[0] = previousSums[0].second;
   for (int i = 1; i < n; i++) {
      minIndexes[i] = min(minIndexes[i - 1], previousSums[i].second);
   }
   sum = 0;
   for (int i = 0; i < n; i++) {
      sum = sum + arr[i];
      if (sum > k) {
         maxLength = i + 1;
      }else {
         int ind = findIndex(previousSums, n, sum - k - 1);
         if (ind != -1 && minIndexes[ind] < i) {
            maxLength = max(maxLength, i - minIndexes[ind]);
         }
      }
   }
   return maxLength;
}
int main() {
   int arr[] = { 5, 3, -3, 2, 4, 7 };
   int k = 5, n = 6;
   cout << getLargestSubArray(arr, n, k) << endl;
   return 0;
}

Output

If you run the above code, then you will get the following result.

6

Conclusion

If you have any queries in the tutorial, mention them in the comment section.