输入某二叉树的前序遍历和中序遍历的结果,请重建出该二叉树。假设输入的前序遍历和中序遍历的结果中都不含重复的数字。例如输入前序遍历序列{1,2,4,7,3,5,6,8}和中序遍历序列{4,7,2,1,5,3,8,6},则重建二叉树并返回。
思路:找到前序数组每一个元素在中序数组中的下标,该下标的值是子树中的根节点的值,其左右子树可以按照中序的下标的前后划分。如此循环迭代直至数组中的每个元素都粘到树上面。下面是我的实现(为了验证重建的正确性,我将重建的树又按照前序遍历和中序遍历数出来,可供校验)
package com.example.test;
public class TreeRebuild {
public class TreeNode {
int val;
TreeNode left;
TreeNode right;
TreeNode(int x) {
val = x;
}
}
public static void main(String[] args) {
int []pre={1,2,4,7,3,5,6,8};
int[] in = {4,7,2,1,5,3,8,6};
TreeRebuild treeRebuild =new TreeRebuild();
TreeNode tree=treeRebuild.reConstructBinaryTree(pre, in);
System.out.println("树的前序遍历:");
treeRebuild.printByPre(tree);
System.out.println("\n树的中序遍历:");
treeRebuild.printByOrder(tree);
}
public TreeNode reConstructBinaryTree(int[] pre, int[] in) {
TreeNode tree=reConstructBinaryTree(pre, 0, pre.length, in, 0, in.length);
return tree;
}
public TreeNode reConstructBinaryTree(int[] pre, int pstart,int pend,int[] in, int istart,int iend){
if(pend-pstart<=0||iend-istart<=0)
return null;
TreeNode treeNode=new TreeNode(pre[pstart]);
for(int i=0;i<iend;i++){
if(in[i]==pre[pstart]){
treeNode.left=reConstructBinaryTree(pre, pstart+1,pstart+1+i-istart, in, istart, i);
treeNode.right=reConstructBinaryTree(pre, pstart+1+i-istart, pend, in, i+1, iend);
}
}
return treeNode;
}
public void printByPre(TreeNode treeNode){
if(treeNode==null)
return;
System.out.print(treeNode.val+" ");
printByPre(treeNode.left);
printByPre(treeNode.right);
}
public void printByOrder(TreeNode treeNode){
if(treeNode==null)
return;
printByOrder(treeNode.left);
System.out.print(treeNode.val+" ");
printByOrder(treeNode.right);
}
}