二叉排序树的删除操作

算法思想

二叉排序树，删除操作主要针对三种情况。

1 叶子节点-直接删除就可以了

2 没有左孩子的节点-直接嫁接右子树就可以了(没有右孩子的节点-直接嫁接左子树就可以了)

3 如果左右子树都存在，则寻找删除节点的直接前驱（即左子树里面的最右的节点）

编程时需要注意，函数时针对指针的操作，因此为了修改指针，要使用二级指针传参才可以

例如：

void delete(BinaryTree **b){



　　....



}



int main(){



　　BinaryTree *b = (BinaryTree *)malloc(sizeof(BinaryTree));



　　delete(&b);



}

函数代码：

bool deleteTree(BTree **b,int key){

    if(!*b)

        return false;

    else{

        if((*b)->data == key){

            return deleteNode(&(*b));

        }

        else if((*b)->data > key)

            return deleteTree(&(*b)->lchild,key);

        else

            return deleteTree(&(*b)->rchild,key);

    }

}

bool deleteNode(BTree **b){

    BTree *p,*s;

    if((*b)->lchild == NULL ){

        p = (*b);

        (*b) = (*b)->rchild;

        free(p);

    }else if((*b)->rchild == NULL){

        p = (*b);

        (*b) = (*b)->lchild;

        free(p);

    }else{

        p = (*b);

        s = (*b)->lchild;

        while(s->rchild != NULL){

            p = s;

            s = s->rchild;

        }

        (*b)->data = s->data;

        if(p != (*b))

            p->rchild = s->lchild;

        else

            p->lchild = s->lchild;

        free(s);

        return true;

    }

}

全部代码：

  1 #include <stdio.h>

  2 #include <stdlib.h>

  3 typedef struct bTree{

  4     int data;

  5     struct bTree *lchild,*rchild;

  6 }BTree;

  7 

  8 void initialTree(BTree *b);

  9 bool insertTree(BTree *b,int key);

 10 int searchTree(BTree *b,int key,BTree *f,BTree *&p);

 11 void InOrderTree(BTree *b);

 12 bool deleteTree(BTree **b,int key);

 13 bool deleteNode(BTree **b);

 14 

 15 int main(){

 16     BTree *b = (BTree *)malloc(sizeof(BTree));

 17     b->data = 5;

 18     b->lchild = b->rchild = NULL;

 19     initialTree(b);

 20     InOrderTree(b);

 21     deleteTree(&b,4);

 22     InOrderTree(b);

 23     getchar();

 24     return 0;

 25 }

 26 bool deleteTree(BTree **b,int key){

 27     if(!*b)

 28         return false;

 29     else{

 30         if((*b)->data == key){

 31             return deleteNode(&(*b));

 32         }

 33         else if((*b)->data > key)

 34             return deleteTree(&(*b)->lchild,key);

 35         else

 36             return deleteTree(&(*b)->rchild,key);

 37     }

 38 }

 39 bool deleteNode(BTree **b){

 40     BTree *p,*s;

 41     if((*b)->lchild == NULL ){

 42         p = (*b);

 43         (*b) = (*b)->rchild;

 44         free(p);

 45     }else if((*b)->rchild == NULL){

 46         p = (*b);

 47         (*b) = (*b)->lchild;

 48         free(p);

 49     }else{

 50         p = (*b);

 51         s = (*b)->lchild;

 52         while(s->rchild != NULL){

 53             p = s;

 54             s = s->rchild;

 55         }

 56         (*b)->data = s->data;

 57         if(p != (*b))

 58             p->rchild = s->lchild;

 59         else

 60             p->lchild = s->lchild;

 61         free(s);

 62         return true;

 63     }

 64 }

 65 void InOrderTree(BTree *b){

 66     if( !b )

 67         return;

 68     InOrderTree(b->lchild);

 69     printf("%d ",b->data);

 70     InOrderTree(b->rchild);

 71 }

 72 

 73 void initialTree(BTree *b){

 74     insertTree(b,5);

 75     insertTree(b,3);

 76     insertTree(b,4);

 77     insertTree(b,6);

 78     insertTree(b,2);

 79     insertTree(b,1);

 80     insertTree(b,8);

 81 }

 82 int searchTree(BTree *b,int key,BTree *f,BTree *&p){

 83     if(!b){

 84         p = f;

 85         printf("++%d\n",p->data);

 86         return 0;

 87     }

 88     else if( key == b->data){

 89         p = b;

 90         printf("--%d \n",p->data);

 91         printf("找到元素key:%d\n",key);

 92         return 1;

 93     }

 94     else if(key > b->data)

 95         return searchTree(b->rchild,key,b,p);

 96     else

 97         return searchTree(b->lchild,key,b,p);

 98 }

 99 bool insertTree(BTree *b,int key){

100     BTree *p,*s;

101     if(!searchTree(b,key,NULL,p)){

102         printf("%d 没有出现在树中，可以插入在%d之后\n",key,p->data);

103         s = (BTree *)malloc(sizeof(BTree));

104         s->data = key;

105         s->lchild = s->rchild = NULL;

106         if(!b){

107             b = s;

108         }

109         else if(key < p->data){

110             p->lchild = s;

111         }else{ 

112             p->rchild = s;

113         }

114         return true;

115     }else

116         return false;

117 }

View Code

运行示例：