void InsertSort(int r[])
{
 int n = sizeof(r) / sizeof(r[0]);
 for(int i = 1; i < n; ++i)
 {
  for(int j = i - 1; j >= 0; --j)
  {   
   if(r[j+1] < r[j])
   {
    int s = r[j+1];
    r[j+1] = r[j];
    r[j] = s;
   }
  }
 }
}

void BinInsertSort(int r[])
{
 int n = sizeof(r) / sizeof(r[0]);
 for(int i = 1; i < n; ++i)
 {
  int s = r[i];
  int low = 0;
  int high = i - 1;
  
  while(low <= high)
  {
   int mid = (low + high) / 2; //mid位置為要找的數(shù)
   if(s < r[mid])
    high = mid - 1;
   else
    low = mid + 1;
  }
  
  for(int j = i - 1; j >= high + 1; --j) //high+1即mid，執(zhí)行數(shù)的后移，直到mid的數(shù)后移
   r[j+1] = r[j];
  
  r[high+1] = s; //mid位置就存放本身
 }
}

void ShellSort(int r[])
{
 int n = sizeof(r) / sizeof(r[0]);
 int step = n / 2;
 
 while(step >= 1)
 {
  for(int i = step; i < n; ++i)
  {
   for(int j = i - step; j >= 0; j -= step)
   {    
    if(r[j+step] < r[j])
    {
     int s = r[j+step];
     r[j+step] = r[j];
     r[j] = s;
    }
   }
  }
  step /= 2;
 }
}

void SelectSort(int r[])
{
 int n = sizeof(r) / sizeof(r[0]);
 for(int i = 0; i < n - 1; ++i)
 {
  int samll = i;
  for(int j = i + 1; j < n; ++j)
  {
   if(r[small] > r[j])
    samll = j;
  }
  if(small != i)
  {
   int s = r[i];
   r[i] = r[small];
   r[small] = s;
  }
 }
}

void HeapAdjust(int r[]; int i; int j) //調(diào)整堆
{
 int child = 2 * i;
 int s = r[i]; //s臨時存放結(jié)點數(shù)據(jù)
 while(child <= j)
 {
  if(child < j && r[child+1] > r[child]) //比較2個子樹
   ++child;
  if(s >= r[child]) //結(jié)點與大子樹比較
   break;
  r[child/2] = r[child]; //如果大子樹比結(jié)點大，互換
  child = 2 * child; //繼續(xù)向子樹檢索
 }
 r[child/2] = s; //結(jié)點的數(shù)為最大的數(shù)
}

void HeapSort(int r[]) //建堆
{
 int n = sizeof(r) / sizeof(r[0]);
 for(int i = n / 2 - 1; i >= 0; --i) //只有n/2-1前的下標(biāo)才有子樹
 {
  HeapAdjust(r, i, n - 1); //構(gòu)造大頂堆，結(jié)點都比子樹大，最后根節(jié)點為最大的數(shù)
 }
 for(int i = n - 1; i > 0; --i)
 {
  //將當(dāng)前堆頂元素與當(dāng)前堆尾元素互換，即將最大的數(shù)移到末尾
  int s = r[0];
  r[0] = r[i];
  r[i] = s;
  HeapAdjust(r, 0, i -1); //將剩下的元素繼續(xù)調(diào)整，最后變成由小到大的順序
 }
}

void BubbleSort(int r[])
{
 int n = sizeof(r) / sizeof(r[0]);
 for(int i = 0; i < n - 1; ++i)
 {
  for(int j = 0; j < n - 1 - i; ++j)
  {
   if(r[j] > r[j+1])
   {
    int s = r[j];
    r[j] = r[j+1];
    r[j+1] = s;
   }
  }
 }
}

int Partition(int r[], int low, int high)
{
 int pivotkey = r[low];
 int i = low;
 int j = high;
 
 while(i < j)
 {
  while(i < j && r[j] > pivotkey) //從j往前找，找出第一個比pivotkey小的數(shù)
   --j;
  if(i < j)
  {
   r[i] = r[j];
   ++i;
  }
  
  while(i < j && r[i] < pivotkey) //從i往后找，找出第一個比pivotkey大的數(shù)
   ++i;
  if(i < j)
  {
   r[j] = r[i];
   --j;
  }
 }
 r[j] = pivotkey; //完成最終交換
 return j; //返回分界點，前面的數(shù)都比pivotkey小，后面的數(shù)都比pivokey大
}

void QuickSort(int r[], int low, int high) // 傳數(shù)組、0和長度-1
{
 if(low < high)
 {
  int pivot = Partition(r, low, high);
  QuickSort(r, low, pivot - 1); //遞歸，前半部分繼續(xù)進行快速排序
  QuickSort(r, pivot + 1; high); //遞歸，后半部分繼續(xù)進行快速排序
 }
}

void copyArray(int source[], int dest[], int len, int first)
{
  int i;
  int j = first;
  for(i = 0; i < len; ++i)
  {
    dest[j] = source[i];
    ++j;
  }
}

void merge(int a[], int left, int right)
{
  int begin1 = left;
  int mid = (left + right) / 2;
  int begin2 = mid + 1;
  int newArrayLen = right - left + 1;
  int *b = (int*)malloc(newArrayLen * sizeof(int));
  int k = 0;
  
  while(begin1 <= mid && begin2 <= right) //找出2組中比較后小的那個數(shù)按順序放進b空間
  {
    if(a[begin1] <= a[begin2])
      b[k++] = a[begin1++];
    else
      b[k++] = a[begin2++];
  }
  
  //把剩下的數(shù)放進b空間
  while(begin1 <= mid)
    b[k++] = a[begin1++];
  while(begin2 <= right)
    b[k++] = a[begin2++];
  
  copyArray(b, a, newArrayLen, left); //把b空間的數(shù)寫回原數(shù)組
  free(b);
}

void MergeSort(int r[], int left, int right) //傳數(shù)組、0和長度-1
{
  int i;
  //至少有兩個元素才進行排序
  if(left < right)
  {
    i = (left + right) / 2;
    MergeSort(r, left, i); //前半部分遞歸
    MergeSort(r, i + 1, right); //后半部分遞歸    
    merge(r, left, right); //10個數(shù)的比較順序為[0,1][0,2][3,4][0,4][5,6][5,7][8,9][5,9][0,9]
  }
}

void insert(list<int> &bucket, int val)
{
  auto iter = bucket.begin();
  while(iter != bucket.end() && val >= *iter)
    ++iter;
  //insert會在iter之前插入數(shù)據(jù)，這樣可以穩(wěn)定排序
  bucket.insert(iter, val);
}

void BuckdeSort(vector<int> &arr)
{
  int len = arr.size();
  if(len <= 1)
    return;
  int min = arr[0], max = min;
  for(int i = 1; i < len; ++i) //找出最小值和最大值
  {
    if(min > arr[i])
      min = arr[i];
    if(max < arr[i])
      max = arr[i];
  }
  
  int k = 10; //桶的大小
  
  //向上取整，例如[0,9]有10個數(shù)，就有(9-0)/k+1=1個桶
  int bucketsNum = (max - min) / k + 1; //桶的個數(shù)
  
  vector<list<int>> buckets(bucketsNum);
  for(int i = 0; i < len; ++i)
  {
    int value = arr[i];
    //(value-min)/k就是在哪個桶里面
    insert(buckets[(value-min)/k], value); //將數(shù)據(jù)放到各個桶里并排序
  }
  
  int index = 0;
  for(int i = 0; i < bucketsNum; ++i)
  {
    if(buckets[i].size())
    {
      for(auto &value : buckets[i])
        arr[index++] = value;
    }
  }
}