To_10_r_100_5---查找最小的K个元素

题目：

输入n个整数，输出其中最小的K个。

思路：

1. 复杂度O(nlogn)    ：快排之类，然后输出最小的K个。

2. 复杂度O(kn)         ：遍历找k次最大值

3. 堆排序O(n+klogn)：建堆O(n)，取出k个最小值O(klogn)。

C++代码：

3. 堆排序

// Heap class
template <class E> class heap{
private:
 E* Heap;    // Pointer to the heap array
 int maxsize;   // Maximum size of the heap
 int n;     // Number of elements now in the heap

 bool Prior(E x, E y){
  return x < y;
 }

 void swap(E* source, int x, int y){
  E temp = source[x];
  source[x] = source[y];
  source[y] = temp;
 }

 void Assert(bool test, string error){
  if (!test){
   cout << error << endl;
   exit(1);
  }
 }

 // Helper function to put element in its correct place
 void siftdown(int pos){
  while (!isLeaf(pos)){ // Stop if pos is a leaf
   int j = leftchild(pos);
   int rc = rightchild(pos);
   if ((rc < n) && Prior(Heap[rc], Heap[j]))
    j = rc;   // Set j to greater child's value
   if (Prior(Heap[pos], Heap[j]))  
    return;   //Done
   swap(Heap, pos, j);
   pos = j;   //Move down
  }
 }

public:
 heap(E* h, int num, int max) // Constructor
 {
  Heap = h;
  n = num;
  maxsize = max;
  buildHeap();
 }
 int size() const{
  return n;
 }
 bool isLeaf(int pos) const{
  return (pos >= n / 2) && (pos < n);
 }
 int leftchild(int pos) const{
  return pos * 2 + 1;
 }
 int rightchild(int pos) const{
  return pos * 2 + 2;
 }
 int parent(int pos) const{
  return (pos - 1) / 2;
 }
 void buildHeap(){     //从暂时的堆的最底层父节点开始往上层调整
  for (int i = n / 2 - 1; i >= 0; i--)
   siftdown(i);
 }

 // Insert "it" into the heap
 void insert(const E& it){
  Assert(n < maxsize, "Heap is full");
  int cur = n++;
  Heap[curr] = it;    // Start at end of heap
  // Now sift up until curr's parnt>curr
  while ((curr != 0) && (Prior(Heap[curr], Heap[parent(curr)]))){ //只跟踪插入元素进行追踪调整
   swap(Heap, curr, parent(curr));
   curr = parent(curr);
  }
 }

 // Remove first value
 E removefirst(){
  Assert(n > 0, "Heap is empty");
  swap(Heap, 0, --n);
  if (n != 0)
   siftdown(0);     // Siftdown new root val
  return Heap[n];      // Return deleted value 
 }

 // Remove and return element at specified position
 E remove(int pos){
  Assert((pos >= 0) && (pos < n), "Bad position");
  if (pos == (n - 1))
   n--; // Last element, no work to do
  else{
   swap(Heap, pos, --n);  //Swap with last value
   while ((pos != 0) && (Prior(Heap[pos], Heap[parent(pos)]))){  // Push up large key
    swap(Heap, pos, parent(pos));
    pos = parent(pos);
   }
   if (n != 0)
    siftdown(pos);              // Push down small key
  }
  return Heap[n];
 }
 void
};

int main(){
 int source[7] = { 7, 4, 6, 1, 2, 3, 5 };
 heap<int> test(source, 7, 100);
 cout << test.removefirst() << endl;
 cout << test.removefirst() << endl;
 cout << test.removefirst() << endl;
 cout << test.removefirst() << endl;
 return 0;
}