Niuke.com's sword refers to Offer - the number of 1s in binary

topic:

Input an integer and output the number of 1's in the binary representation of the number. Negative numbers are represented in complement.

Ideas:

Obviously, this question examines bit operations.

1. Shift the input number n to the right in turn, and use n&1 to determine whether the last digit is 1;

The problem with this method: if the integer is negative, it will get stuck in an infinite loop. Because when a negative number is shifted to the right, the left side is supplemented by 1, and the integer cannot be 0 during the process of right shifting, so it will fall into an infinite loop.

Two's complement shift:

Shift left, whether positive or negative, add 0 to the right;

Shift right, positive numbers are filled with 0 on the left, and negative numbers are filled with 1 on the left;

code show as below:

class Solution {
public:
     int  NumberOf1(int n) {
        int count=0;
        while(n){
            if(n&1)
                count++;
            n=n>>1;
        }
        return count;
     }
};

2. Shift 1 to the left by i bits in turn, and then perform the & & operation with the integer. If the result is not 0, the i-th bit is 1;

Question: How many times does an integer have to be looped

code show as below:

class Solution {
public:
     int  NumberOf1(int n) {
         int count = 0;
         int flag = 1;
         while( flag )
         {
             if( n & flag )
                 count++;
             flag = flag << 1;
         }
         return count;
     }
};

3. Use little tricks

Subtract 1 from an integer and then perform a bitwise AND operation with the original integer: n&(n-1) The result is equivalent to changing the rightmost 1 in the binary representation of the integer to 0. Through this little trick, we can count the number of 1s as long as we loop to determine whether n=n&(n-1) is 0.

How many 1s are there in the integer, how many times to loop.

code show as below:

class Solution {
public:
     int  NumberOf1(int n) {
         int count = 0;
         while( n )
         {
             count++;
             n = n & (n-1);
         }
         return count;
     }
};

4. Bit operation related topics

Using the above techniques, many binary problems can be solved:

• Use a statement to determine whether an integer is a power of 2.

if(n&(n-1)==0) return true;

• Given two integers m, n, how many bits in the binary representation of m need to be changed to get n?

int x=m^n; return NumberOf1(x);