Counting Bits

原创于 2016-06-14 14:30:42 发布 · 251 阅读

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本文提供了一种使用C++和Python实现的高效算法来计算一个整数范围内所有数的二进制表示中1的个数。通过使用位操作和缓存技术减少重复计算，显著提高了算法效率。

c++

class Solution {
public:
    vector<int> countBits(int num) {
        if (num < 0) return vector<int>();
        vector<int> res;
        for (int i = 0; i <=num; ++i) {
            res.push_back(popcount(i));
        }
        return res;
    }
private:
    unordered_map<int, int> cache;
    int popcnt(int u)
    {
        int ret = 0;
        while (u){
            if (cache.find(u) == cache.end()) {
                ret++;
                u = (u & (u - 1));
            }else{
                ret += cache[u];
                break;
            }
        }
        cache[u] = ret;
        return ret;
    }
    unsigned popcount(unsigned u)
    {
        u = (u & 0x55555555) + ((u >> 1) & 0x55555555);
        u = (u & 0x33333333) + ((u >> 2) & 0x33333333);
        u = (u & 0x0F0F0F0F) + ((u >> 4) & 0x0F0F0F0F);
        u = (u & 0x00FF00FF) + ((u >> 8) & 0x00FF00FF);
        u = (u & 0x0000FFFF) + ((u >> 16) & 0x0000FFFF);
        return u;
    }
};

python

class Solution(object):
    def countBits(self, num):
        """
        :type num: int
        :rtype: List[int]
        """
        res = [bin(x).count('1') for x in xrange(num+1)]
        return res