Count of Range Sum in C++

Suppose we have an integer array nums, we have to find the number of range sums that lie in range [lower, upper] both inclusive. The range sum S(i, j) is defined as the sum of the elements in nums from index i to index j where i ≤ j.
So if the input is like [-3,6,-1], lower = -2 and upper = 2, then the result will be 2, as the ranges are [0,2], the sum is 2, [2,2], sum is -2.
To solve this, we will follow these steps −
Define a function mergeIt(), this will take array prefix, start, mid, end, lower, upper,
i := start, j := mid + 1
temp := end - start + 1
low := mid + 1, high := mid + 1
k := 0
Define an array arr of size: temp.
while i <= mid, do −while (low <= end and prefix[low] - prefix[i] < lower), do −increase low by 1while (high <= end and prefix[high] - prefix[i] <= upper), do −increase high by 1while (j <= end and prefix[j] < prefix[i]), do −arr[k] := prefix[j](increase j by 1)(increase k by 1)arr[k] := prefix[i](increase i by 1)(increase k by 1)count := count + high - low
while (low <= end and prefix[low] - prefix[i] < lower), do −increase low by 1
increase low by 1
while (high <= end and prefix[high] - prefix[i] <= upper), do −increase high by 1
increase high by 1
while (j <= end and prefix[j] < prefix[i]), do −arr[k] := prefix[j](increase j by 1)(increase k by 1)
arr[k] := prefix[j]
(increase j by 1)
(increase k by 1)
arr[k] := prefix[i]
(increase i by 1)
(increase k by 1)
count := count + high - low
while j <= end, do −arr[k] := prefix[j](increase k by 1)(increase j by 1)
arr[k] := prefix[j]
(increase k by 1)
(increase j by 1)
for initialize i := 0, when i < temp, update (increase i by 1), do −prefix[start] := arr[i](increase start by 1)
prefix[start] := arr[i]
(increase start by 1)
Define a function merge(), this will take prefix[], start, end, lower, upper,if start >= end, then return
if start >= end, then return
mid := start + (end - start)
call the function merge(prefix, start, mid, lower, upper)
call the function merge(prefix, mid + 1, end, lower, upper)
call the function mergeIt(prefix, start, mid, end, lower, upper)
From the main method, do the following −
n := size of nums
count := 0
Define an array prefix of size: n+1.
prefix[0] := 0
for initialize i := 1, when i <= n, update (increase i by 1), do −prefix[i] := prefix[i - 1] + nums[i - 1]
prefix[i] := prefix[i - 1] + nums[i - 1]
call the function merge(prefix, 0, n, lower, upper)
return count
Let us see the following implementation to get better understanding −
 Live Demo
#include <bits/stdc++.h>
using namespace std;
typedef long long int lli;
class Solution {
public:
   int count = 0;
   void mergeIt(lli prefix[], lli start ,lli mid, lli end, lli lower, lli upper){
      lli i = start, j = mid + 1;
      lli temp = end - start + 1;
      lli low = mid + 1, high = mid + 1;
      lli k = 0;
      lli arr[temp];
      while(i <= mid){
         while(low <= end && prefix[low] - prefix[i] < lower) low++;
         while(high <= end && prefix[high] - prefix[i] <= upper) high++;
         while(j<= end && prefix[j] < prefix[i]){
            arr[k] = prefix[j];
            j++;
            k++;
         }
         arr[k] = prefix[i];
         i++;
         k++;
         count += high - low;
      }
      while(j <= end){
         arr[k] = prefix[j];
         k++;
         j++;
      }
      for(i = 0; i < temp; i++){
         prefix[start] = arr[i];
         start++;
      }
   }
   void merge(lli prefix[], lli start, lli end, lli lower, lli upper){
      if(start >= end)return;
      lli mid = start + (end - start) / 2;
      merge(prefix, start, mid, lower, upper);
      merge(prefix, mid + 1, end, lower, upper);
      mergeIt(prefix, start, mid, end, lower, upper);
   }
   int countRangeSum(vector<int>& nums, int lower, int upper) {
      lli n = nums.size();
      count = 0;
      lli prefix[n + 1];
      prefix[0] = 0;
      for(lli i = 1; i <= n; i++){
         prefix[i] = prefix[i - 1] + nums[i - 1];
      }
      merge(prefix, 0, n, lower, upper);
      return count;
   }
};
main(){
   Solution ob;
   vector<int> v = {-3,6,-1};
   cout << (ob.countRangeSum(v, -2, 2));
}
{-3,6,-1}
-2
2
2