Find all subarray index ranges in given Array with set bit sum equal to X

Given an array arr (1-based indexing) of length N and an integer X, the task is to find and print all index ranges having a set bit sum equal to X in the array.

Examples:

Input: A[] = {1 4 3 5 7}, X = 4
Output:  (1, 3), (3, 4)
Explanation: In the above array subarray having set bit sum equal to X (= 4). 
Starting from index 1 to 3. {1 4 3}  = (001) + (100) + (011) = 4  and 
other one is from 3 to 4 {3, 5} = (011) + (101) = 4.

Input: arr[] = {5, 3, 0,  4, 10}, X = 7
Output:  (1 5)
Explanation: In the above array  subarrays having set bit sum equal to X(= 7) start from 1 to 5 only.

Approach: The problem is solved using two pointer approach. 

• Write a function countSetBit to count the number of set bits.
  • Initialize a counter c=0, to store the individual count for every number in the array.
  • Iterate over the array and check for every set bit and increase the counter.
  • replace every number with the count of a number of set bits
• Write a function to print a range of subarrays PrintIndex
     Run a loop using two pointers i and j and check for the sum as follow:
  • If the current index sum is less than X then, add the value at arr[j] in currsum
  • else if the sum is equal to X push back the start and end index of the array and increment the counter i.
  • else decrement the counter, subtract the value at arr[i] from currsum.
  • Repeat the same for all elements.
    

Below is the implementation of the above method :

(1 3) (3 4)

Time Complexity: O(N * d) where d is the count of bits in an array element
Auxiliary Space: O(N)

Another Approach:

1. The code defines a function called countSetBit that takes an integer x and returns the number of set bits in its binary representation.
2. The code also defines another function called printSubarraysWithSetBitSumX that takes a vector of integers arr and an integer X. This function prints all the subarrays of arr whose sum of set bits is equal to X.
3. Inside the printSubarraysWithSetBitSumX function, the code initializes some variables: n is the size of the input vector arr, i and j are two pointers initially set to 0, and currSum is the current sum of set bits.
4. The code enters a while loop with a condition of j < n. This loop iterates through all the elements of the input vector arr.
5. Inside the while loop, the code adds the count of set bits of the current element to the currSum variable and increments j by 1.
6. The code then enters another while loop with a condition of currSum > X. This loop removes the set bit count of the element pointed by i from the currSum variable and increments i by 1 until the currSum becomes less than or equal to X.
7. If the currSum is equal to X after the above while loop, the code prints the indices of the subarray whose sum of set bits is equal to X.
8. The while loop in step 4 continues until j reaches the end of the input vector arr.
9. Finally, the main function creates a vector arr containing integers {1, 4, 3, 5, 7} and sets X to 4. It then calls the printSubarraysWithSetBitSumX function with these arguments, which prints "(1, 3) (3, 4)" to the console.

Below is the implementation of the above approach:

(1, 3) (3, 4) 

Time complexity: O(n*logx)
Auxiliary Space: O(n)