Given an array arr[] containing N integers and an array queries[] containing Q queries in the form of {L, R}, the task is to count the total number of set bits from L to R in array arr for each query.
Example:
Input: arr[]={1, 2, 3, 4, 5, 6}, queries[]={{0, 2}, {1, 1}, {3, 5}}
Output:
4
2
5
Explanation:
Query 1 (0, 2): Elements {1, 2, 3} have set bits {1, 1, 2} respectively. So sum=1+1+2=4
Query 1 (1, 1): Element {2} have set bit {1}. So sum=1
Query 1 (3, 5): Elements {4, 5, 6} have set bits {1, 2, 2} respectively. So sum=1+2+2=5
Input: arr[]={2, 4, 3, 5, 6}, queries[]={{0, 1}, {2, 4}}
Output:
2
6
Approach: To solve this question, follow the below steps:
- Create a vector, say onBits, in which each ith element will represent the number of set bits from arr[0] to arr[i].
- Run a loop from i=0 to i<N, and on each iteration, find the number of set bits in arr[i], say bits and make onBits[i]=onBits[i-1] + bits.
- Now traverse the array queries and for each query {L, R}, the number of set bits from L to R is onBits[R]-onBits[L-1].
- Print the answer according to the above observation.
Below is the implementation of the above approach:
C++
#include <bits/stdc++.h>
using namespace std;
int setBitsinLtoR(int L, int R,
vector<int>& onBits)
{
if (L == 0) {
return onBits[R];
}
return onBits[R] - onBits[L - 1];
}
void totalSetBits(vector<int>& arr,
vector<pair<int, int> >& queries)
{
int N = arr.size();
vector<int> onBits(N, 0);
onBits[0] = __builtin_popcount(arr[0]);
for (int i = 1; i < N; ++i) {
onBits[i]
= onBits[i - 1]
+ __builtin_popcount(arr[i]);
}
for (auto x : queries) {
int L = x.first;
int R = x.second;
cout << setBitsinLtoR(L, R, onBits)
<< endl;
}
}
int main()
{
vector<int> arr = { 1, 2, 3, 4, 5, 6 };
vector<pair<int, int> > queries
= { { 0, 2 }, { 1, 1 }, { 3, 5 } };
totalSetBits(arr, queries);
}
|
Java
import java.util.*;
class GFG{
static class pair
{
int first, second;
public pair(int first, int second)
{
this.first = first;
this.second = second;
}
}
static int setBitsinLtoR(int L, int R,int []onBits)
{
if (L == 0) {
return onBits[R];
}
return onBits[R] - onBits[L - 1];
}
static void totalSetBits(int[] arr,
pair[] queries)
{
int N = arr.length;
int []onBits = new int[N];
onBits[0] = Integer.bitCount(arr[0]);
for (int i = 1; i < N; ++i) {
onBits[i]
= onBits[i - 1]
+ Integer.bitCount(arr[i]);
}
for (pair x : queries) {
int L = x.first;
int R = x.second;
System.out.print(setBitsinLtoR(L, R, onBits)
+"\n");
}
}
public static void main(String[] args)
{
int []arr = { 1, 2, 3, 4, 5, 6 };
pair []queries
= { new pair( 0, 2 ), new pair( 1, 1 ), new pair( 3, 5 ) };
totalSetBits(arr, queries);
}
}
|
Python3
def __builtin_popcount(n):
count = 0
while (n):
count += n & 1
n >>= 1
return count
def setBitsinLtoR(L, R, onBits):
if (L == 0):
return onBits[R];
return onBits[R] - onBits[L - 1];
def totalSetBits(arr, queries):
N = len(arr);
onBits = [0] * N
onBits[0] = __builtin_popcount(arr[0]);
for i in range(1, N):
onBits[i] = onBits[i - 1] + __builtin_popcount(arr[i]);
for x in queries:
L = x[0];
R = x[1];
print(setBitsinLtoR(L, R, onBits))
arr = [ 1, 2, 3, 4, 5, 6 ];
queries = [ [ 0, 2 ], [ 1, 1 ], [ 3, 5 ] ];
totalSetBits(arr, queries);
|
C#
using System;
class GFG{
class pair
{
public int first, second;
public pair(int first, int second)
{
this.first = first;
this.second = second;
}
}
static int setBitsinLtoR(int L, int R, int []onBits)
{
if (L == 0)
{
return onBits[R];
}
return onBits[R] - onBits[L - 1];
}
static void totalSetBits(int[] arr,
pair[] queries)
{
int N = arr.Length;
int []onBits = new int[N];
onBits[0] = bitCount(arr[0]);
for(int i = 1; i < N; ++i)
{
onBits[i] = onBits[i - 1] +
bitCount(arr[i]);
}
foreach (pair x in queries)
{
int L = x.first;
int R = x.second;
Console.Write(setBitsinLtoR(L, R, onBits) +
"\n");
}
}
static int bitCount(int x)
{
int setBits = 0;
while (x != 0)
{
x = x & (x - 1);
setBits++;
}
return setBits;
}
public static void Main(String[] args)
{
int []arr = { 1, 2, 3, 4, 5, 6 };
pair []queries = { new pair(0, 2),
new pair(1, 1),
new pair(3, 5) };
totalSetBits(arr, queries);
}
}
|
Javascript
<script>
function __builtin_popcount(x)
{
return((x).toString(2).split('').
filter(x => x == '1').length);
}
function setBitsinLtoR(L, R, onBits)
{
if (L == 0)
{
return onBits[R];
}
return onBits[R] - onBits[L - 1];
}
function totalSetBits(arr, queries)
{
let N = arr.length;
let onBits = new Array(N).fill(0);
onBits[0] = __builtin_popcount(arr[0]);
for(let i = 1; i < N; ++i)
{
onBits[i] = onBits[i - 1] +
__builtin_popcount(arr[i]);
}
for(let x of queries)
{
let L = x[0];
let R = x[1];
document.write(
setBitsinLtoR(L, R, onBits) + '<br>')
}
}
let arr = [ 1, 2, 3, 4, 5, 6 ];
let queries = [ [ 0, 2 ], [ 1, 1 ], [ 3, 5 ] ];
totalSetBits(arr, queries);
</script>
|
Time Complexity: O(Q*N*logK), where N is the size of array arr, Q is the number of queries and K is the number of bits
Auxiliary Space: O(N)