代表数字7的8位像这样:

00000111

设置了三个比特。

确定32位整数中设置位数的算法是什么?


当前回答

我给出了两个算法来回答这个问题,

package countSetBitsInAnInteger;

import java.util.Scanner;

public class UsingLoop {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        try {
            System.out.println("Enter a integer number to check for set bits in it");
            int n = in.nextInt();
            System.out.println("Using while loop, we get the number of set bits as: " + usingLoop(n));
            System.out.println("Using Brain Kernighan's Algorithm, we get the number of set bits as: " + usingBrainKernighan(n));
            System.out.println("Using ");
        }
        finally {
            in.close();
        }
    }

    private static int usingBrainKernighan(int n) {
        int count = 0;
        while(n > 0) {
            n& = (n-1);
            count++;
        }
        return count;
    }

    /*
        Analysis:
            Time complexity = O(lgn)
            Space complexity = O(1)
    */

    private static int usingLoop(int n) {
        int count = 0;
        for(int i=0; i<32; i++) {
            if((n&(1 << i)) != 0)
                count++;
        }
        return count;
    }

    /*
        Analysis:
            Time Complexity = O(32) // Maybe the complexity is O(lgn)
            Space Complexity = O(1)
    */
}

其他回答

下面是示例代码,可能很有用。

private static final int[] bitCountArr = new int[]{0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8};
private static final int firstByteFF = 255;
public static final int getCountOfSetBits(int value){
    int count = 0;
    for(int i=0;i<4;i++){
        if(value == 0) break;
        count += bitCountArr[value & firstByteFF];
        value >>>= 8;
    }
    return count;
}

一个快速的c#解决方案,使用预先计算的字节位计数表,并根据输入大小进行分支。

public static class BitCount
{
    public static uint GetSetBitsCount(uint n)
    {
        var counts = BYTE_BIT_COUNTS;
        return n <= 0xff ? counts[n]
             : n <= 0xffff ? counts[n & 0xff] + counts[n >> 8]
             : n <= 0xffffff ? counts[n & 0xff] + counts[(n >> 8) & 0xff] + counts[(n >> 16) & 0xff]
             : counts[n & 0xff] + counts[(n >> 8) & 0xff] + counts[(n >> 16) & 0xff] + counts[(n >> 24) & 0xff];
    }

    public static readonly uint[] BYTE_BIT_COUNTS =
    {
        0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4,
        1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
        1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
        2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
        1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
        2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
        2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
        3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
        1, 2, 2, 3, 2, 3, 3, 4, 2, 3, 3, 4, 3, 4, 4, 5,
        2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
        2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
        3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
        2, 3, 3, 4, 3, 4, 4, 5, 3, 4, 4, 5, 4, 5, 5, 6,
        3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
        3, 4, 4, 5, 4, 5, 5, 6, 4, 5, 5, 6, 5, 6, 6, 7,
        4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 6, 7, 7, 8
    };
}

对于JavaScript,你可以使用一个查找表来计算一个32位值的设置位的数量(这段代码可以很容易地翻译成C语言)。此外,添加了8位和16位版本,以供通过网络搜索查找的人使用。

const COUNT_BITS_TABLE = makeLookupTable() function makeLookupTable() { const table = new Uint8Array(256) for (let i = 0; i < 256; i++) { table[i] = (i & 1) + table[(i / 2) | 0]; } return table } function countOneBits32(n) { return COUNT_BITS_TABLE[n & 0xff] + COUNT_BITS_TABLE[(n >> 8) & 0xff] + COUNT_BITS_TABLE[(n >> 16) & 0xff] + COUNT_BITS_TABLE[(n >> 24) & 0xff]; } function countOneBits16(n) { return COUNT_BITS_TABLE[n & 0xff] + COUNT_BITS_TABLE[(n >> 8) & 0xff] } function countOneBits8(n) { return COUNT_BITS_TABLE[n & 0xff] } console.log('countOneBits32', countOneBits32(0b10101010000000001010101000000000)) console.log('countOneBits32', countOneBits32(0b10101011110000001010101000000000)) console.log('countOneBits16', countOneBits16(0b1010101000000000)) console.log('countOneBits8', countOneBits8(0b10000010))

我个人使用这个:

  public static int myBitCount(long L){
      int count = 0;
      while (L != 0) {
         count++;
         L ^= L & -L; 
      }
      return count;
  }

如果您恰好使用Java,则内置方法Integer。bitCount会这样做。