Prior queue

Introduction:usually,we tend to insert a new value into a container and get a min or max value from the container,if the input frequency and the output frequency are about the same ,then we may construct a contanier with average less operation time.we can use the heap structure,it's a compelete binary tree.

so firstly we may see the usual operation:

constructed function:

public IntMinPQ(){elements=new Integer[1];elements[0]=Integer.MAX_VALUE;}
public IntMinPQ(int max){maxSize=max+1;elements=new Integer[maxSize];elements[0]=Integer.MAX_VALUE;}
public IntMinPQ(Integer[]a){
    int len=a.length;
    maxSize=len+1;
    elements=new Integer[maxSize];
    elements[0]=Integer.MAX_VALUE;
    for(int i=0;i<len;++i){
        insert(a[i]);
    }
}

then the often used functions:

public void insert(Integer v){
    if(size<maxSize){
        elements[++size]=v;
    }
    swimUpdate(size);
}
public Integer min(){return elements[1];}
public Integer delMin(){
    Integer temp=elements[1];
    percolateDown();
    return temp;
}

public boolean isEmpty(){return size==0;}
public int size(){return size;}

In the above functions there are some assistant fucntions:

In order to get a value from the container with O(log(N)) time , we need a insert fucntion to keep the insert time:

private void swim(int k){
    while(k>1){
        if(less(k,k/2)){
            swap(k,k/2);
        }else{
            break;
        }
        k/=2;
    }
}

also we need a function to keep the get time with O(log(N)) time:

private void percolateDown(){
    int index=1;
    while(2*index<size){
        if(less(2*index,2*index+1)){
            elements[index]=elements[2*index];
            index=2*index;
        }else{
            elements[index]=elements[2*index+1];
            index=2*index+1;
        }
    }
    elements[index]=elements[size];
    elements[size]=null;
    --size;
}
the problem is how to handle with the last element,the function given above is called

percolateDown(),just as its name implies:the element with less value is jump down step by step.

besides that ,some inner variables are also needed: 

private Integer[] elements=null;
private int size=0;
private int maxSize=0;

The end.