给定一个非负数n和两个值l和r 。问题在于,以n的二进制表示形式对范围在l到r之间的设置位数进行计数,即,对从最右边的第l位到最右边的第r位的设置位进行计数。
约束: 1 <= l <= r <= n的二进制表示形式的位数。
例子:
Input : n = 42, l = 2, r = 5
Output : 2
(42)10 = (101010)2
There are '2' set bits in the range 2 to 5.
Input : n = 79, l = 1, r = 4
Output : 4
方法:以下是步骤:
- 计算num =(((1 << r)– 1)^((1 <<(l-1))– 1)。这将产生一个数字num,它具有r个位数,并且范围l至r的位数是唯一的设置位。
- 计算数字中的设置位数(n和num) 。请参阅这篇文章。
C++
// C++ implementation to count set bits in the
// given range
#include
using namespace std;
// Function to get no of set bits in the
// binary representation of 'n'
unsigned int countSetBits(int n)
{
unsigned int count = 0;
while (n) {
n &= (n - 1);
count++;
}
return count;
}
// function to count set bits in the given range
unsigned int countSetBitsInGivenRange(unsigned int n,
unsigned int l, unsigned int r)
{
// calculating a number 'num' having 'r' number
// of bits and bits in the range l to r are the
// only set bits
int num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);
// returns number of set bits in the range
// 'l' to 'r' in 'n'
return countSetBits(n & num);
}
// Driver program to test above
int main()
{
unsigned int n = 42;
unsigned int l = 2, r = 5;
cout << countSetBitsInGivenRange(n, l, r);
return 0;
}
Java
// Java implementation to count set bits in the
// given range
class GFG {
// Function to get no of set bits in the
// binary representation of 'n'
static int countSetBits(int n)
{
int count = 0;
while (n > 0) {
n &= (n - 1);
count++;
}
return count;
}
// function to count set bits in the given range
static int countSetBitsInGivenRange(int n, int l, int r)
{
// calculating a number 'num' having 'r' number
// of bits and bits in the range l to r are the
// only set bits
int num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);
// returns number of set bits in the range
// 'l' to 'r' in 'n'
return countSetBits(n & num);
}
// Driver code
public static void main(String[] args)
{
int n = 42;
int l = 2, r = 5;
System.out.print(countSetBitsInGivenRange(n, l, r));
}
}
// This code is contributed by Anant Agarwal.
Python3
# Python3 implementation to count
# set bits in the given range
# Function to get no of set bits in the
# binary representation of 'n'
def countSetBits(n):
count = 0
while (n):
n &= (n - 1)
count = count + 1
return count
# function to count set bits in
# the given range
def countSetBitsInGivenRange(n, l, r):
# calculating a number 'num' having
# 'r' number of bits and bits in the
# range l to r are the only set bits
num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1)
# returns number of set bits in the range
# 'l' to 'r' in 'n'
return countSetBits(n & num)
# Driver program to test above
n = 42
l = 2
r = 5
ans = countSetBitsInGivenRange(n, l, r)
print (ans)
# This code is contributed by Saloni Gupta.
C#
// C# implementation to count set bits in the
// given range
using System;
class GFG {
// Function to get no of set bits in the
// binary representation of 'n'
static int countSetBits(int n)
{
int count = 0;
while (n>0) {
n &= (n - 1);
count++;
}
return count;
}
// function to count set bits in the given range
static int countSetBitsInGivenRange(int n,
int l, int r)
{
// calculating a number 'num' having 'r' number
// of bits and bits in the range l to r are the
// only set bits
int num = ((1 << r) - 1) ^ ((1 << (l - 1)) - 1);
// returns number of set bits in the range
// 'l' to 'r' in 'n'
return countSetBits(n & num);
}
//Driver code
public static void Main()
{
int n = 42;
int l = 2, r = 5;
Console.WriteLine(countSetBitsInGivenRange(n, l, r));
}
}
// This code is contributed by Anant Agarwal.
PHP
Javascript
输出:
2