# Range query for count of set bits

Given an array of positive integer and q query which contains two integers, L & R. Task is to find the number of set bits for a given range.

Prerequisite : Bitwise Hacks

Examples :

```Input :  Arr[] = { 1, 5, 6, 10, 9, 4 }
Query : 2
L  &  R
1     5
2     4
Output : 9
6

Input : Arr[] = { 1, 10, 5, 2, 8, 11, 15 }
Query : 2
L  &  R
2     4
1     5
Output :  4
9
```

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

Simple solution to this problem is to run a loop from L to R and count number of set bits in a Range. This solution take O(nlog(s)) ( where s is bits size ) for each query.

Efficient solution is based on the fact that if we store count of all set bits of numbers in an array “BitCounts”, then we answer each query in O(1) time. So, start traversing the elements of array and count set bits for each element and store in array. Now, find cumulative sum of this array. This array will help in answering queries.

```BitCount[] that will store the count of set bits
in a number.

Run a Loop from 0 to 31 "for 32 bits size integer "
-> mark elements with i'th bit set

Run an inner Loop from 0 to size of Array "Arr"
-> Check whether the current bit is set or not
-> if it's set then mark it.
long  temp = arr[j] >> i;
if (temp %2 != 0)
BitCount[j] += 1
```

Below is implementation of above idea.

## C++

 `// c++ program to Range query for ` `// Count number of set bits ` `#include ` `using` `namespace` `std; ` ` `  `// 2-D array that will stored the count ` `// of bits set in element of array ` `int` `BitCount = { 0 }; ` ` `  `// Function store the set bit ` `// count in BitCount Array ` `void` `fillSetBitsMatrix(``int` `arr[], ``int` `n) ` `{ ` ` `  `    ``// traverse over all bits ` `    ``for` `(``int` `i = 0; i < 32; i++) { ` ` `  `        ``// mark elements with i'th bit set ` `        ``for` `(``int` `j = 0; j < n; j++) { ` ` `  `            ``// Check whether the current bit is ` `            ``// set or not if it's set then mark it. ` `            ``long` `temp = arr[j] >> i; ` `            ``if` `(temp % 2 != 0) ` `                ``BitCount[j] += 1; ` `        ``} ` `    ``} ` ` `  `    ``// store cumulative sum of bits ` `    ``for` `(``int` `i = 1; i < n; i++) ` `        ``BitCount[i] += BitCount[i - 1]; ` `} ` ` `  `// Function to process queries ` `void` `Query(``int` `Q[], ``int` `q) ` `{ ` `    ``for` `(``int` `i = 0; i < q; i++) ` `        ``cout << (BitCount[Q[i]] -  ` `                 ``BitCount[Q[i] - 1]) << endl; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `Arr[] = { 1, 5, 6, 10, 9, 4, 67 }; ` `    ``int` `n = ``sizeof``(Arr) / ``sizeof``(Arr); ` ` `  `    ``fillSetBitsMatrix(Arr, n); ` ` `  `    ``int` `q = 2; ` `    ``int` `Q = { { 1, 5 }, { 2, 6 } }; ` ` `  `    ``Query(Q, q); ` ` `  `    ``return` `0; ` `} `

## Java

 `// java program to Range query for ` `// Count number of set bits ` `import` `java.io.*; ` ` `  `class` `GFG { ` ` `  `    ``// 2-D array that will stored the count ` `    ``// of bits set in element of array ` `    ``static` `int` `BitCount[] = ``new` `int``[``10000``]; ` `     `  `    ``// Function store the set bit ` `    ``// count in BitCount Array ` `    ``static` `void` `fillSetBitsMatrix(``int` `arr[], ``int` `n) ` `    ``{ ` `     `  `        ``// traverse over all bits ` `        ``for` `(``int` `i = ``0``; i < ``32``; i++) { ` `     `  `            ``// mark elements with i'th bit set ` `            ``for` `(``int` `j = ``0``; j < n; j++) { ` `     `  `                ``// Check whether the current  ` `                ``// bit is set or not if it's  ` `                ``// set then mark it. ` `                ``long` `temp = arr[j] >> i; ` `                ``if` `(temp % ``2` `!= ``0``) ` `                    ``BitCount[j] += ``1``; ` `            ``} ` `        ``} ` `     `  `        ``// store cumulative sum of bits ` `        ``for` `(``int` `i = ``1``; i < n; i++) ` `            ``BitCount[i] += BitCount[i - ``1``]; ` `    ``} ` `     `  `    ``// Function to process queries ` `    ``static` `void` `Query(``int` `Q[][], ``int` `q) ` `    ``{ ` `        ``for` `(``int` `i = ``0``; i < q; i++) ` `            ``System.out.println( (BitCount[Q[i][``1``]] ` `                        ``- BitCount[Q[i][``0``] - ``1``])); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `main (String[] args) ` `    ``{ ` `        ``int` `Arr[] = { ``1``, ``5``, ``6``, ``10``, ``9``, ``4``, ``67` `}; ` `        ``int` `n = Arr.length; ` `     `  `        ``fillSetBitsMatrix(Arr, n); ` `     `  `        ``int` `q = ``2``; ` `        ``int` `Q[][] = { { ``1``, ``5` `}, { ``2``, ``6` `} }; ` `     `  `        ``Query(Q, q); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

## Python3

 `# Python program to Range query for ` `# Count number of set bits ` ` `  `# 2-D array that will stored the count ` `# of bits set in element of array ` `BitCount ``=` `[``0``] ``*` `10000` ` `  `# Function store the set bit ` `# count in BitCount Array ` `def` `fillSetBitsmatrix(arr: ``list``, n: ``int``): ` `    ``global` `BitCount ` ` `  `    ``# traverse over all bits ` `    ``for` `i ``in` `range``(``32``): ` ` `  `        ``# mark elements with i'th bit set ` `        ``for` `j ``in` `range``(n): ` ` `  `            ``# Check whether the current bit is ` `            ``# set or not if it's set then mark it. ` `            ``temp ``=` `arr[j] >> i ` `            ``if` `temp ``%` `2` `!``=` `0``: ` `                ``BitCount[j] ``+``=` `1` ` `  `    ``# store cumulative sum of bits ` `    ``for` `i ``in` `range``(``1``, n): ` `        ``BitCount[i] ``+``=` `BitCount[i ``-` `1``] ` ` `  `# Function to process queries ` `def` `Query(Q: ``list``, q: ``int``): ` `    ``for` `i ``in` `range``(q): ` `        ``print``(BitCount[Q[i][``1``]] ``-` `BitCount[Q[i][``0``] ``-` `1``]) ` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` ` `  `    ``Arr ``=` `[``1``, ``5``, ``6``, ``10``, ``9``, ``4``, ``67``] ` `    ``n ``=` `len``(Arr) ` ` `  `    ``fillSetBitsmatrix(Arr, n) ` ` `  `    ``q ``=` `2` `    ``Q ``=` `[(``1``, ``5``), (``2``, ``6``)] ` `    ``Query(Q, q) ` ` `  `# This code is contributed by ` `# sanjeev2552 `

## C#

 `// C# program to Range query for ` `// Count number of set bits ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// 2-D array that will stored the count ` `    ``// of bits set in element of array ` `    ``static` `int` `[]BitCount = ``new` `int``; ` `     `  `    ``// Function store the set bit ` `    ``// count in BitCount Array ` `    ``static` `void` `fillSetBitsMatrix(``int` `[]arr, ``int` `n) ` `    ``{ ` `     `  `        ``// traverse over all bits ` `        ``for` `(``int` `i = 0; i < 32; i++) { ` `     `  `            ``// mark elements with i'th bit set ` `            ``for` `(``int` `j = 0; j < n; j++) { ` `     `  `                ``// Check whether the current  ` `                ``// bit is set or not if it's  ` `                ``// set then mark it. ` `                ``long` `temp = arr[j] >> i; ` `                ``if` `(temp % 2 != 0) ` `                    ``BitCount[j] += 1; ` `            ``} ` `        ``} ` `     `  `        ``// store cumulative sum of bits ` `        ``for` `(``int` `i = 1; i < n; i++) ` `            ``BitCount[i] += BitCount[i - 1]; ` `    ``} ` `     `  `    ``// Function to process queries ` `    ``static` `void` `Query(``int` `[,]Q, ``int` `q) ` `    ``{ ` `        ``for` `(``int` `i = 0; i < q; i++) ` `            ``Console.WriteLine( (BitCount[Q[i,1]] ` `                        ``- BitCount[Q[i,0] - 1])); ` `    ``} ` `     `  `    ``// Driver Code ` `    ``public` `static` `void` `Main () ` `    ``{ ` `        ``int` `[]Arr = { 1, 5, 6, 10, 9, 4, 67 }; ` `        ``int` `n = Arr.Length; ` `     `  `        ``fillSetBitsMatrix(Arr, n); ` `     `  `        ``int` `q = 2; ` `        ``int` `[,]Q = { { 1, 5 }, { 2, 6 } }; ` `     `  `        ``Query(Q, q); ` `    ``} ` `} ` ` `  `// This code is contributed by anuj_67. `

Output:

```9
10
```

Time Complexity : O(1) for each query.

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