桶排序

桶排序期望的运行时间是Θ(n)
局限：输入数组要在[0,1)之间（下面有更通用的版本3⃣️）
1⃣️内置排序没有用插入排序而是c++自带的sort，要用插入排序可保证算法稳定性。

void bucket_sort(float *array,int length){vector<vector<float>> bucket(length);for (int i = 0; i < length; ++i) {bucket[(int)(length*array[i])].push_back(array[i]);}for (int i = 0; i < length; ++i) {sort(bucket[i].begin(),bucket[i].end());}int index = 0;for (int i = 0; i < length; ++i) {while (bucket[i].size()>0){array[index] = bucket[i][bucket[i].size()-1];bucket[i].pop_back();index++;}}
}

2⃣️对半径为1的圆周内不包含边界的点，对离圆心的距离进行排序

void bucket_sort(vector<Vector2>& array)
{vector<vector<Vector2>> buckets(array.size());for (int i = 0; i < array.size(); ++i) {buckets[(int)(array[i].module()*array.size())].push_back(array[i]);}for (int i = 0; i < array.size(); ++i) {sort(buckets[i].begin(),buckets[i].end(), compare);}int index = 0;for (int i = 0; i < array.size(); ++i) {while (buckets[i].size()>0){array[index] = buckets[i][buckets[i].size()-1];buckets[i].pop_back();index++;}}
}

辅助Vector2类

class Vector2 {
public:float x;float y;
public:Vector2(float x = 0.0,float y = 0.0);float module() const;
};
static bool compare(const Vector2 &item1,const Vector2 &item2)
{return item1.module() <= item2.module();
}

#include "Vector2.h"
Vector2::Vector2(float x,float y):x(x),y(y){}
float Vector2::module() const{return sqrt(x*x+y*y);
}

3⃣️对变长整数的排序
算法导论第三版8-3a题，变长数据项的排序

void bucket_sort_variable_length(int *array,int length)
{vector<vector<int>> positive_bucket(length);vector<vector<int>> negative_bucket(length);for (int i = 0; i < length; ++i) {int len = get_int_length(array[i]);if(array[i]<0){negative_bucket[len-1].push_back(array[i]);}else{positive_bucket[len-1].push_back(array[i]);}}for (int i = 0; i < length -1; ++i) {if(negative_bucket[i].size()>0){radix_sort(negative_bucket[i],i+1);}if(positive_bucket[i].size()>0){radix_sort(positive_bucket[i],i+1);}}int index = 0;for (int i = length -1; i >= 0; --i) {if(negative_bucket[i].size()>0){copy(negative_bucket[i].begin(),negative_bucket[i].end(),array+index);index += negative_bucket[i].size();}}for (int i = 0; i < length -1; ++i) {if(positive_bucket[i].size()>0){copy(positive_bucket[i].begin(),positive_bucket[i].end(),array+index);index += positive_bucket[i].size();}}
}

辅助函数 get_int_length

int get_int_length(int value)
{int length = 0;while (value != 0){value /=10;length++;}return  length == 0 ? 1 : length;
}

辅助排序地址
1⃣️基数排序
2⃣️计数排序

4⃣️对变长字符串数组的的排序
算法导论第三版8-3b题，变长数据项的排序

void bucket_sort(vector<string>& array){vector<vector<string>> bucket(26);for (int i = 0; i < array.size(); ++i) {bucket[tolower(array[i][0])-'a'].push_back(array[i]);}sort(bucket.begin(),bucket.end());int index = 0;for (int i = 0; i < 26; ++i) {while (bucket[i].size()>0){array[index] = bucket[i][0];bucket[i].erase(bucket[i].begin());index++;}}
}