二叉搜索树的简单操作（BST）

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只写一个先序遍历,中序和后序就顺序不同

结构体,基本数据类型和两个指向左右节点的指针

typedef struct TNode * Position;
typedef Position BinTree;
struct TNode {
  int data;
  BinTree left;
  BinTree right;
};

插入

BinTree insert(BinTree BST, int x) {
  if (!BST) {
    BST = (BinTree)malloc(sizeof(struct TNode));  //为空则申请空间
    BST->data = x;
    BST->left = BST->right = NULL;    //将子节点置为空
  } else {
    if (x < BST->data) {
      BST->left = insert(BST->left, x);    //左递归
    } else if (x > BST->data){
      BST->right = insert(BST->right, x);
    }
    return BST;
  }
}

最大值

//比BST->data大的都在右子树，递归遍历
Position findMax(BinTree BST) {
  if (!BST) {
    return NULL;
  } else if (!BST->right) { //右子树为空
    return BST;
  } else {      
    return findMax(BST->right);
  }
}

最小值

//比BST->data小的都在左子树,递归遍历
Position findMin(BinTree BST) {
  if (!BST) {
    return NULL;
  } else if (!BST->left) {  //左子树为空
    return BST;
  } else {    
    return findMin(BST->left);
  }
}

删除

BinTree deleteValue(BinTree BST, int x) {
  Position pos;
  if (!BST) {
    printf("未找到指定元素\n");
  } else {
    if (x < BST->data) {
      BST->left = deleteValue(BST->left, x);
    } else if (x > BST->data) {
      BST->right = deleteValue(BST->right, x);
    } else {
      if (BST->left && BST->right) {  //存在两个子节点时
        pos = findMin(BST->right);  //找到右子树的最小值
        BST->data = pos->data;
        BST->right = deleteValue(BST->right, BST->data);
      } else {      //存在一个子节点或者无子节点的时候
        pos = BST;
        if (!BST->left) {
          BST = BST->right;
        } else {
          BST = BST->left;
        }
        free(pos);
      }
    }
  }
  return BST;
}

查找特定元素

Position find(BinTree BST, int x) {
  if (!BST) {
    return NULL;
  }

  if (BST->data < x) {      //小于在左，大于在右
    return find(BST->right, x);
  } else if (BST->data > x) {
    return find(BST->left, x);
  } else {
    return BST;
  }
}

具体实现如下

#include<stdio.h>
#include<stdlib.h>

typedef struct TNode * Position;
typedef Position BinTree;
struct TNode {
  int data;
  BinTree left;
  BinTree right;
};

void preOrder(BinTree BST) {
  if (!BST) {
    return ;
  } else {
    printf("%d ", BST->data);   
    preOrder(BST->left);
    preOrder(BST->right);
  }
}

BinTree insert(BinTree BST, int x) {
  if (!BST) {
    BST = (BinTree)malloc(sizeof(struct TNode));  //为空则申请空间
    BST->data = x;
    BST->left = BST->right = NULL;    //将子节点置为空
  } else {
    if (x < BST->data) {
      BST->left = insert(BST->left, x);
    } else if (x > BST->data){
      BST->right = insert(BST->right, x);
    }
    return BST;
  }
}

Position findMin(BinTree BST) {
  if (!BST) {
    return NULL;
  } else if (!BST->left) {
    return BST;
  } else {
    return findMin(BST->left);
  }
}

Position findMax(BinTree BST) {
  if (!BST) {
    return NULL;
  } else if (!BST->right) {
    return BST;
  } else {
    return findMax(BST->right);
  }
}

Position find(BinTree BST, int x) {
  if (!BST) {
    return NULL;
  }

  if (BST->data < x) {      //小于在左，大于在右
    return find(BST->right, x);
  } else if (BST->data > x) {
    return find(BST->left, x);
  } else {
    return BST;
  }
}

BinTree deleteValue(BinTree BST, int x) {
  Position pos;
  if (!BST) {
    printf("未找到指定元素\n");
  } else {
    if (x < BST->data) {
      BST->left = deleteValue(BST->left, x);
    } else if (x > BST->data) {
      BST->right = deleteValue(BST->right, x);
    } else {
      if (BST->left && BST->right) {  //存在两个子节点时
        pos = findMin(BST->right);  //找到右子树的最小值
        BST->data = pos->data;
        BST->right = deleteValue(BST->right, BST->data);
      } else {      //存在一个子节点或者无子节点的时候
        pos = BST;
        if (!BST->left) {
          BST = BST->right;
        } else {
          BST = BST->left;
        }
        free(pos);
      }
    }
  }
  return BST;
}

int main(void)
{
  BinTree BST, MinP, MaxP, Tmp;
  int x;
  int N, i, flag;
  BST = NULL;

  printf("输入初始元素个数:\n");
  scanf("%d", &N);
  printf("输入各个元素:\n");
  for (int i = 0; i < N; i++) {
    scanf("%d", &x);
    BST = insert(BST, x);
  }

  printf("1.插入元素   2.删除元素   3.查找最小值\n");
  printf("4.查找最大值   5.查找指定元素   6.先序输出   7.退出\n");
  while (scanf("%d", &flag) != EOF && flag != 7) {
    switch (flag) {
      case 1: printf("输入插入元素:\n");scanf("%d", &x);BST = insert(BST, x);break;
      case 2: printf("输入删除元素:\n");scanf("%d", &x);BST = deleteValue(BST, x);break;
      case 3: MinP = findMin(BST); printf("最小值为:%d\n\n", MinP->data);break;
      case 4: MaxP = findMax(BST); printf("最大值为:%d\n\n", MaxP->data);break;
      case 5: printf("输入查找元素:\n");scanf("%d", &x);Tmp = find(BST, x); //用一个容器，不然在一个元素未找到时会被置为NULL，先序遍历无法输出
       if (!Tmp) {printf("未找到该元素\n\n");} else {printf("找到%d\n\n", Tmp->data);} break;
      case 6: printf("先序遍历如下:\n"); preOrder(BST);printf("\n\n");break;
      default: printf("请输入合法操作!\n\n");break;
    }
    printf("1.插入元素   2.删除元素   3.查找最小值\n");
    printf("4.查找最大值   5.查找指定元素   6.先序输出   7.退出\n");
  }
  return 0;
}

测试如下