Consulta de rango para el recuento de bits establecidos

Dada una array de enteros positivos y q consulta que contiene dos enteros, L & R. La tarea es encontrar el número de bits establecidos para un rango dado.
Requisito previo: Bitwise Hacks

Ejemplos: 

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

La solución simple a este problema es ejecutar un bucle de L a R y contar el número de bits establecidos en un rango. Esta solución toma O(nlog(s)) (donde s es el tamaño de bits) para cada consulta.

La solución eficiente se basa en el hecho de que si almacenamos el recuento de todos los bits de números establecidos en una array «BitCounts», entonces respondemos cada consulta en tiempo O (1). Entonces, comience a recorrer los elementos de la array y cuente los bits establecidos para cada elemento y almacene en la array. Ahora, encuentre la suma acumulada de esta array. Esta array ayudará a responder consultas. 

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

A continuación se muestra la implementación de la idea anterior. 

// C++ program to Range query for
// Count number of set bits
#include <bits/stdc++.h>
using namespace std;
 
// 2-D array that will stored the count
// of bits set in element of array
int BitCount[10000] = { 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[][2], int q)
{
    for (int i = 0; i < q; i++)
        cout << (BitCount[Q[i][1]] -
                 BitCount[Q[i][0] - 1]) << endl;
}
 
// Driver Code
int main()
{
    int Arr[] = { 1, 5, 6, 10, 9, 4, 67 };
    int n = sizeof(Arr) / sizeof(Arr[0]);
 
    fillSetBitsMatrix(Arr, n);
 
    int q = 2;
    int Q[2][2] = { { 1, 5 }, { 2, 6 } };
 
    Query(Q, q);
 
    return 0;
}

// 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 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# 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[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++)
            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.

<script>
 
// Javascript 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
var BitCount = Array.from({length: 10000}, (_, i) => 0);
 
// Function store the set bit
// count in BitCount Array
function fillSetBitsMatrix(arr, n)
{
 
    // traverse over all bits
    for(i = 0; i < 32; i++)
    {
         
        // mark elements with i'th bit set
        for(j = 0; j < n; j++)
        {
             
            // Check whether the current
            // bit is set or not if it's
            // set then mark it.
            var temp = arr[j] >> i;
            if (temp % 2 != 0)
                BitCount[j] += 1;
        }
    }
 
    // store cumulative sum of bits
    for(i = 1; i < n; i++)
        BitCount[i] += BitCount[i - 1];
}
 
// Function to process queries
function Query(Q, q)
{
    for(i = 0; i < q; i++)
        document.write((BitCount[Q[i][1]] -
                        BitCount[Q[i][0] - 1]) + "<br>");
}
 
// Driver Code
var Arr = [ 1, 5, 6, 10, 9, 4, 67 ];
var n = Arr.length;
 
fillSetBitsMatrix(Arr, n);
 
var q = 2;
var Q = [ [ 1, 5 ], [ 2, 6 ] ];
 
Query(Q, q);
 
// This code is contributed by Rajput-Ji
 
</script>

9
10

Complejidad de tiempo: O(1) para cada consulta.