下一个比N大的数字，N的二进制表示形式仅相差一位

给定数字N。任务是找到最小的数字，该数字大于N，并且在N的二进制表示形式中只有一位不同。

注意：此处N可能非常大10 ^ 9

例子：

Input : N = 11
Output : The next number is 15
The binary representation of 11 is 1011
So the smallest number greater than 11 
with one bit different is 1111 which is 15.

Input : N = 17
Output : The next number is 19

简单方法：我们将从N + 1开始运行循环，直到找到一个与N完全不同的数字。如果有大量数字，则此过程可能需要很长时间才能处理

高效方法：在高效方法中，我们必须以二进制形式表示数字。现在，仅当我们保持数字N的所有置位不变并将最低的可能的比特(从0切换为1)时，才可能有大于N的数字且只有1位的不同。

让我们以1001为例，它是9的二进制形式
如果将1001的设置位切换为1000或0001，则发现数字为8和1，小于N。而如果将0设置为1，则发现数字为11(1011)或13(1101)，因此，如果将可能的最低位从0切换为1，则我们得到的最小可能数大于N，只有1位不同，在这种情况下为11(1011)。

注意：保证输入数字N的所有位都未设置。 N的二进制表示形式中至少有一个未设置的位。

下面是上述方法的实现：

C++

// CPP program to find next greater number than N 
// with exactly one bit different in binary
// representation of N
  
#include 
using namespace std;
  
// Function to find next greater number than N 
// with exactly one bit different in binary
// representation of N
long long nextGreater(long long N)
{
    long long power_of_2 = 1, shift_count = 0;
  
    // It is guaranteed that there 
    // is a bit zero in the number
    while (true) {
        // If the shifted bit is zero then break
        if (((N >> shift_count) & 1) % 2 == 0)
            break;
  
        // increase the bit shift
        shift_count++;
  
        // increase the power of 2
        power_of_2 = power_of_2 * 2;
    }
  
    // set the lowest bit of the number
    return (N + power_of_2);
}
  
// Driver code
int main()
{
    long long N = 11;
  
    // display the next number
    cout << "The next number is = " << nextGreater(N);
  
    return 0;
}

Java

// Java program to find next greater number than N 
// with exactly one bit different in binary 
// representation of N 
  
class GFG{
// Function to find next greater number than N 
// with exactly one bit different in binary 
// representation of N 
static int nextGreater(int N) 
{ 
    int power_of_2 = 1, shift_count = 0; 
  
    // It is guaranteed that there 
    // is a bit zero in the number 
    while (true) { 
        // If the shifted bit is zero then break 
        if (((N >> shift_count) & 1) % 2 == 0) 
            break; 
  
        // increase the bit shift 
        shift_count++; 
  
        // increase the power of 2 
        power_of_2 = power_of_2 * 2; 
    } 
  
    // set the lowest bit of the number 
    return (N + power_of_2); 
} 
  
// Driver code 
public static void main(String[]a) 
{ 
    int N = 11; 
  
    // display the next number 
    System.out.println("The next number is = " + nextGreater(N)); 
  
}
}

Python3

# Python3 program to find next greater 
# number than N with exactly one
# bit different in binary
# representation of N
  
# Function to find next greater 
# number than N with exactly 
# one bit different in binary
# representation of N
def nextGreater(N):
  
    power_of_2 = 1; 
    shift_count = 0;
  
    # It is guaranteed that there 
    # is a bit zero in the number
    while (True):
          
        # If the shifted bit is
        # zero then break
        if (((N >> shift_count) & 1) % 2 == 0):
            break;
  
        # increase the bit shift
        shift_count += 1;
  
        # increase the power of 2
        power_of_2 = power_of_2 * 2;
  
    # set the lowest bit 
    # of the number
    return (N + power_of_2);
  
# Driver code
N = 11;
  
# display the next number
print("The next number is =", 
             nextGreater(N));
  
# This code is contributed by mits

C#

// C# program to find next 
// greater number than N with  
// exactly one bit different in
// binary representation of N 
using System;
  
class GFG
{
// Function to find next greater 
// number than N with exactly 
// one bit different in binary 
// representation of N 
static int nextGreater(int N) 
{ 
    int power_of_2 = 1, 
        shift_count = 0; 
  
    // It is guaranteed that there 
    // is a bit zero in the number 
    while (true)
    { 
        // If the shifted bit is 
        // zero then break 
        if (((N >> shift_count) & 1) % 2 == 0) 
            break; 
  
        // increase the bit shift 
        shift_count++; 
  
        // increase the power of 2 
        power_of_2 = power_of_2 * 2; 
    } 
  
    // set the lowest bit 
    // of the number 
    return (N + power_of_2); 
} 
  
// Driver code 
public static void Main() 
{ 
    int N = 11; 
  
    // display the next number 
    Console.WriteLine("The next number is = " + 
                               nextGreater(N)); 
}
} 
  
// This code is contributed 
// by anuj_67

PHP

> $shift_count) & 1) % 2 == 0)
            break;
  
        // increase the bit shift
        $shift_count++;
  
        // increase the power of 2
        $power_of_2 = $power_of_2 * 2;
    }
  
    // set the lowest bit of the number
    return ($N + $power_of_2);
}
  
// Driver code
$N = 11;
  
// display the next number
echo "The next number is = " , 
              nextGreater($N);
  
// This code is contributed 
// by anuj_67
?>

输出：

The next number is = 15

时间复杂度： O(log(N))