二叉树的创建和遍历

一、二叉树的创建

typedef struct node {int nValue;struct node *lchild;struct node *rchild;}BTNode;

1.递归创建

void RecCreateBiTree(BTNode **pRoot){int nNum;if(pRoot == NULL)return;cin>>nNum;if(nNum == 0)return;//添加节点*pRoot = new BTNode;(*pRoot)->nValue = nNum;(*pRoot)->lchild = NULL;(*pRoot)->rchild = NULL;//处理当前节点的左右RecCreateBiTree(&((*pRoot)->lchild));RecCreateBiTree(&((*pRoot)->rchild));}

2.数组创建

BTNode *ArrToBiTree(int arr[],int nLen){BTNode *pTree = NULL;int i;if(arr == NULL || nLen <=0)return NULL;//根据数组长度创建结构体数组pTree = new BTNode[nLen];//数组元素拷贝  结构数组赋初值for(i = 0;i<nLen;i++){pTree[i].nValue = arr[i];pTree[i].lchild = NULL;pTree[i].rchild = NULL;}//根据左右关系关联for(i = 0;i < nLen/2; i++){if(2*i+1 < nLen)pTree[i].lchild = pTree+2*i+1;if(2*i +2 < nLen)pTree[i].rchild = pTree+2*i+2;}return pTree;}

二、二叉树的遍历

（一）递归遍历

1.前序遍历

void PreOrderTraversal(BTNode *pRoot){if(pRoot == NULL)return;//根cout<<pRoot->nValue<<" ";//左PreOrderTraversal(pRoot->lchild);//右PreOrderTraversal(pRoot->rchild);}

2.中序遍历

void InOrderTraversal(BTNode *pRoot){if(pRoot == NULL)return;//左InOrderTraversal(pRoot->lchild);//根cout<<pRoot->nValue<<" ";//右InOrderTraversal(pRoot->rchild);}

3.后序遍历

void PostOrderTraversal(BTNode *pRoot){if(pRoot == NULL)return;//左PostOrderTraversal(pRoot->lchild);//右PostOrderTraversal(pRoot->rchild);//根cout<<pRoot->nValue<<" ";}

（二）非递归遍历

1.前序遍历

void PreOrderWithoutRec(BTNode* pRoot)  {      if (pRoot == NULL)return;      BTNode* p = pRoot;      stack<BTNode*> s;      while (!s.empty() || p)      {          //边遍历边打印，并存入栈中          while (p)          {      cout << p->nValue<< " ";              s.push(p);              p = p->lchild;          }          //当p为空时，说明根和左子树都遍历完了，该进入右子树了          if (!s.empty())          {              p = s.top();              s.pop();              p = p->rchild;          }      }  }

2.中序遍历

void InOrderWithoutRec(BTNode* pRoot)  {      if (pRoot == NULL)return;      BTNode* p = pRoot;      stack<BTNode*> s;      while (!s.empty() || p)      {          //一直遍历到左子树最下边，边遍历边保存根节点到栈中          while (p)          {              s.push(p);              p = p->lchild;          }          //当p为空时，说明已经到达左子树最下边,这时需要出栈了          if (!s.empty())          {              p = s.top();              s.pop();      cout << p->nValue<< " ";              //进入右子树，开始新的一轮左子树遍历             p = p->rchild;          }      }  }

3.后序遍历

void PostOrderWithoutRec(BTNode *pRoot){if (pRoot == NULL)return;BTNode *p = pRoot;stack<BTNode*> s;BTNode *pre = NULL;//pre表示最近一次访问的结点while(!s.empty() || p){//沿着左孩子方向走到最左下 。while(p){s.push(p);p = p->lchild;}//get the top element of the stackp = s.top();//如果p没有右孩子或者其右孩子刚刚被访问过if(p->rchild == NULL || p->rchild == pre){//visit this element and then pop itcout << p->nValue << " ";s.pop();pre = p;p = NULL;}elsep = p->rchild;}}