优先队列——二项队列（binominal queue）

#include "binominal_queue.h" 

#define MINIMAL 10000

int minimal(BinominalQueue bq)
{
    int capacity;
    int i;
    int minimal;
    int miniIndex;    

    minimal = MINIMAL;
    capacity = bq->capacity;
    for(i=0; i<capacity; i++)
    {
        if(bq->trees[i] && bq->trees[i]->value < minimal)
        {
            minimal = bq->trees[i]->value;
            miniIndex = i;
        }
    }

    return miniIndex;
}

// initialize the BinominalQueue with given capacity.
BinominalQueue init(int capacity)
{
    BinominalQueue queue;            
    BinominalTree* trees; 
    int i;

    queue = (BinominalQueue)malloc(sizeof(struct BinominalQueue));
    if(!queue)
    {
        Error("failed init, for out of space !");
        return queue;
    }    
    queue->capacity = capacity;
    
    trees = (BinominalTree*)malloc(capacity * sizeof(BinominalTree));
    if(!trees)
    {
        Error("failed init, for out of space !");
        return NULL;
    }    
    queue->trees = trees;

    for(i=0; i<capacity; i++)
    {
        queue->trees[i] = NULL;
    }
    
    return queue;
}  

// attention: the root must be the left child of the binominal tree.
int getHeight(BinominalTree root)
{
    int height;        
    if(root == NULL)
    {        
        return 0;        
    }

    height = 1;    
    while(root->nextSibling)
    {
        height++;
        root = root->nextSibling;
    }

    return height;
}


// merge BinominalQueue bq2 into bq1.
void outerMerge(BinominalQueue bq1, BinominalQueue bq2)
{
    int height;
    int i;

    for(i=0; i<bq2->capacity; i++)
    {
        height = -1;
        if(bq2->trees[i])
        {
            height = getHeight(bq2->trees[i]->leftChild);    
            // attention for the line above
            // height = height(bq2->trees[i]->leftChild); not height = height(bq2->trees[i]);
            merge(bq2->trees[i], height, bq1);
        }                    
    }        
}

// merge tree h1 and h2 = bq->trees[height], 
// who represents the new tree and old one respectively.
BinominalTree merge(BinominalTree h1, int height, BinominalQueue bq)
{            
    if(h1 == NULL)
    {
        return h1;
    }

    if(bq->trees[height] == NULL) // if the queue don‘t has the B0 tree.
    {        
        bq->trees[height] = h1;
        return bq->trees[height];
    }
    else // otherwise, compare the new tree‘s height with that of old one.
    {         
        if(h1->value > bq->trees[height]->value) // the new should be treated as the parent of the old.
        {        
            innerMerge(bq->trees[height], height, h1, bq);
        }
        else // the old should be treated as the parent of the new.
        {
            innerMerge(h1, height, bq->trees[height], bq);
        }
    }  

    return h1;
} 

BinominalTree lastChild(BinominalTree root)
{                
    while(root->nextSibling)
    {        
        root = root->nextSibling;
    }

    return root; 
}

// merge tree h1 and h2 = bq->trees[height], 
// who represents the new tree and old one respectively.
BinominalTree innerMerge(BinominalTree h1, int height, BinominalTree h2, BinominalQueue bq)
{
    if(h1->leftChild == NULL)
    {
        h1->leftChild = h2;
    }
    else
    {
        lastChild(h1->leftChild)->nextSibling = h2;
        // attention for the line above
        // lastChild(h1->leftChild)->nextSibling = h2 not lastChild(h1)->nextSibling = h2
    }
    height++;
    bq->trees[height-1] = NULL;
    merge(h1, height, bq);    
    
    return h1;
} 

// insert an element with value into the priority queue.
void insert(ElementType value, BinominalQueue bq)
{
    TreeNode node;

    node = (TreeNode)malloc(sizeof(struct TreeNode));
    if(!node)
    {
        Error("failed inserting, for out of space !");
        return ;
    }
    node->leftChild= NULL;
    node->nextSibling = NULL;    
    node->value = value;    
        
    merge(node, 0, bq);            
}

// analog print node values in the binominal tree, which involves preorder traversal. 
void printPreorderChildSibling(int depth, BinominalTree root)
{            
    int i;
    
    if(root) {        
        for(i = 0; i < depth; i++)
            printf("    ");
        printf("%d\n", root->value);            
        printPreorderChildSibling(depth + 1, root->leftChild);                                    
        printPreorderChildSibling(depth, root->nextSibling);
    } 
    else
    {
        for(i = 0; i < depth; i++)
            printf("    ");
        printf("NULL\n");
    }
}

// print Binominal Queue bq
void printBinominalQueue(BinominalQueue bq)
{
    int i;

    for(i=0; i<bq->capacity; i++)
    {
        printf("bq[%d] = \n", i);
        printPreorderChildSibling(1, bq->trees[i]);
    }    
}

void deleteMin(BinominalQueue bq)
{
    int i;    
    BinominalTree minitree;    
    BinominalTree sibling;

    i = minimal(bq);
    minitree = bq->trees[i]->leftChild; //minitree->value=51
    free(bq->trees[i]);
    bq->trees[i] = NULL;            

    while(minitree)
    {
        sibling = minitree->nextSibling;
        minitree->nextSibling = NULL;
        merge(minitree, getHeight(minitree->leftChild), bq);        
        minitree = sibling;
    }        
}

int main()
{
    BinominalQueue bq, bq1, bq2;    
    int data[] =  {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11};
    int data1[] = {65, 24, 12, 51, 16, 18};    
    int data2[] = {24, 65, 51, 23, 14, 26, 13};
    int i;
    int capacity;    

    // creating the binominal queue bq starts.
    capacity = 7;
    bq = init(capacity);        
    for(i=0; i<capacity; i++)
    {
        insert(data[i], bq);
    }
    printf("\n=== after the  binominal queue bq is created ===\n");    
    printBinominalQueue(bq);    
    // creating over.
     
    // creating the binominal queue bq1 starts.
    capacity = 6;
    bq1 = init(capacity);        
    for(i=0; i<capacity; i++)
    {
        insert(data1[i], bq1);
    }
    printf("\n=== after the binominal queue bq1 is created ===\n");    
    printBinominalQueue(bq1);    
    // creating over.

    // creating the binominal queue bq2 starts.
    capacity = 7;
    bq2 = init(capacity);        
    for(i=0; i<capacity; i++)
    {
        insert(data2[i], bq2);
    }
    printf("\n=== after the binominal queue bq2 is created ===\n");    
    printBinominalQueue(bq2);    
    // creating over.     

    // merge bq2 into the bq1 
    outerMerge(bq1, bq2);
     printf("\n=== after bq2 is merged into the bq1 ===\n");    
    printBinominalQueue(bq1);    
    // merge over. 
    
    // executing deleteMin opeartion towards binominal queue bq1    
    printf("\n=== after executing deleteMin opeartion towards binominal queue bq1 ===\n");    
    deleteMin(bq1);    
    printBinominalQueue(bq1);    
    // deleteMin over!
    return  0;
}