快速排序和归并排序

归并排序

采用分治的思想，将两个有序的排序合并为一个有序的排序。

void merge(vector<int> vec,int low, int mid, int high)
{
    vector<int>tmp(vec.begin(),vec.end());
    
    for(int i = low, j = mid+1, k=i;low <=mid && j<=high; k++)
    {
        if(tmp[i] < tmp[j]) vec[k]=tmp[i++];    
        else vec[k]=tmp[j++];
    }
    
    while(i <= mid) vec[k++]=tmp[i++];
    while(j <= high) vec[k++]=tmp[j++];
}

//递归算法
void MergeSort(vector<int> vec, int low, int high)
{
    if(low<high)
    {
        mid = (low+high)>>1;
        MergeSort(vec,low,mid);
        MergeSort(vec,mid+1,high);
        Merge(vec,low,mid,high);
    }
}

//非递归算法
void MergeSort(vector<int> vec)
{
    int low, high, mid;
    
    for(int size=1; size <vec.size(); size *=2)
    {
        while(low + size < vec.size())
        {
            mid = low + size - 1;
            high = mid + size;
            if(high >= vec.size()) high = vec.size()-1;
            merge(vec, low, mid, high);
            low = high + 1;
        }
    }
    
}

快速排序

快速排序是找到一个元素作为基准，比该元素大的放到右侧，比该元素小的放置到左侧。

int  Position(vector<int> vec, int low ,int high)
{
    int tmp = vec[low];

    while(low < high && vec[high]>tmp)high--;
    vec[low] = vec[high];
    while(low < high && vec[low]<tmp)low++;
    vec[high] = vec[high];

    vec[low] = tmp;
    
    return low;
}

//递归的快速排序
void QuickSort(vector<int> vec, int low, int high)
{
    if(low < high)
    {
          int mid = Position(vec, low, high);
          QuickSort(vec, low, mid-1);
          QuickSort(vec, mid+1,high); 
    }    
}

//非递归的快速排序
void QuickSort(vector<int> vec, int low,int high)
{
    stack<int> s;

    if(low < high)
    {
        int mid = Position(vec, low, high);
        if(mid -1 <high){
            s.push(low);s.push(mid-1);
        }
        if(mid+1 < high)
        {
            s.push(mid+1);s.push(high);
        }
        
        while(!s.empty()){
            int qh = s.top();s.pop();
            int pl = s.top();s.pop();
            int pm = Position(vec, ql, qh);
            if(pm-1 > pl)
            {
                s.push(pl);s.push(pm-1);
            }
            if(pm+1 < ph)
            {
                s.push(pm+1);s.push(ph);
            }
        }
    }
}