剑指offer E6 根据前序和中序重构二叉树

/**
 * 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根结点。
 *
 * 前序遍历preorder：根、左、右
 * 中序遍历inorder：左、根、右
 * 后序遍历postorder：左、右、根
 */
public class E6 {
    public static void main(String[] args) {
        int preorder[] = {1,2,4,7,3,5,6,8};
        int inorder[] = {4,7,2,1,5,3,8,6};
        try {
            BinaryTreeNode root = constructTree(preorder, inorder);

            System.out.println("前序遍历：");
            preorderTraversalRecursively(root);
            System.out.println();
            preorderTraversalNonRecursively(root);
            System.out.println();

            System.out.println("中序遍历：");
            inorderTraversalRecursively(root);
            System.out.println();
            inorderTraversalNonRecursively(root);
            System.out.println();

            System.out.println("后序遍历：");
            postorderTraversalRecursively(root);
            System.out.println();
            postorderTraversalNonRecursively(root);
            System.out.println();
        } catch (Exception e) {
            e.printStackTrace();
        }

    }

    private static BinaryTreeNode constructTree(int[] preorder, int[] inorder) throws Exception {
        if (preorder == null || inorder == null
            || preorder.length == 0 || inorder.length!=preorder.length) {
            throw new Exception("Invalid input");
        }
        BinaryTreeNode root = constructRecursively(preorder, 0, preorder.length-1,
                inorder, 0, inorder.length-1);
        return root;
    }

    private static BinaryTreeNode constructRecursively(int[] preorder, int preStart,
             int preEnd, int[] inorder, int inStart, int inEnd) throws Exception {
        if (preStart>preEnd || inStart>inEnd || preEnd-preStart != inEnd-inStart) {
            return null;
        }
        BinaryTreeNode root = new BinaryTreeNode(preorder[preStart]);
        // 在中序遍历中找到该根节点，分成左右两个子树
        int inorderRootIndex = inStart;
        while (inorderRootIndex<=inEnd){
            if (inorder[inorderRootIndex] == root.getValue()) {
                break;
            }
            inorderRootIndex++;
        }
        if (inorderRootIndex>inEnd) {
            throw new Exception("Invalid input");
        }
        int leftLength = inorderRootIndex-inStart;
        root.setLeftNode(constructRecursively(preorder,preStart+1,preStart+leftLength,
                inorder,inStart,inorderRootIndex-1));
        root.setRightNode(constructRecursively(preorder, preStart+leftLength+1, preEnd,
                inorder,inorderRootIndex+1,inEnd));
        return root;
    }

    // 后序遍历(递归实现)
    private static void postorderTraversalRecursively(BinaryTreeNode root) {
        if (root == null) return;
        postorderTraversalRecursively(root.getLeftNode());
        postorderTraversalRecursively(root.getRightNode());
        System.out.print(root.getValue()+" ");
    }

    /**
     * 后序遍历(非递归实现)
     * 从根开始，将所有左子树入栈
     * peek栈顶节点，
     * 1）该节点有右子树，从右子树开始，将其所有左子树入栈
     * 2）该节点没有右子树，pop该节点并打印，若该节点是当前新栈顶的右子树，pop并打印,循环...
     */
    private static void postorderTraversalNonRecursively(BinaryTreeNode root) {
        if (root == null) return;
        Stack<BinaryTreeNode> stack = new Stack<>();
        BinaryTreeNode current = root;
        do {
            stack.push(current);
            current = current.getLeftNode();
        } while (current != null);

        while (!stack.isEmpty()) {
            if (stack.peek().getRightNode() != null) {
                current = stack.peek().getRightNode();
                do {
                    stack.push(current);
                    current = current.getLeftNode();
                } while (current != null);
            } else {
                do {
                    current = stack.pop();
                    System.out.print(current.getValue()+" ");
                }while (!stack.isEmpty() && current.equals(stack.peek().getRightNode()));
            }
        }
    }

    // 中序遍历
    private static void inorderTraversalRecursively(BinaryTreeNode root) {
        if (root == null) return;
        inorderTraversalRecursively(root.getLeftNode());
        System.out.print(root.getValue()+" ");
        inorderTraversalRecursively(root.getRightNode());
    }

    /**
     * 中序遍历(非递归实现)
     * 从根开始，将所有左子树入栈
     * 遍历栈顶节点，输出值，从右子树开始，将其所有左子树入栈
     */
    private static void inorderTraversalNonRecursively(BinaryTreeNode root) {
        if (root == null) return;
        Stack<BinaryTreeNode> stack = new Stack<>();
        BinaryTreeNode current = root;
        do {
            stack.push(current);
            current = current.getLeftNode();
        } while(current != null);

        while (!stack.isEmpty()) {
            BinaryTreeNode node = stack.pop();
            System.out.print(node.getValue()+" ");
            if (node.getRightNode() != null) {
                current = node.getRightNode();
                do {
                    stack.push(current);
                    current = current.getLeftNode();
                }while (current!=null);
            }
        }
    }

    // 前序遍历
    private static void preorderTraversalRecursively(BinaryTreeNode root) {
        if (root == null) return;
        System.out.print(root.getValue()+" ");
        preorderTraversalRecursively(root.getLeftNode());
        preorderTraversalRecursively(root.getRightNode());
    }

    /**
     * 前序遍历(非递归实现)
     * 栈辅助，将根节点入栈，pop栈顶元素直至栈为空
     * 对于每个栈顶元素，先将其右子树入栈，再将其左子树入栈
     */
    private static void preorderTraversalNonRecursively(BinaryTreeNode root) {
        if (root == null) return;
        Stack<BinaryTreeNode> stack = new Stack<>();
        stack.push(root);
        while (!stack.isEmpty()) {
            BinaryTreeNode node = stack.pop();
            System.out.print(node.getValue()+" ");
            if (node.getRightNode() != null) {
                stack.push(node.getRightNode());
            }
            if (node.getLeftNode()!= null) {
                stack.push(node.getLeftNode());
            }
        }
    }
}



class BinaryTreeNode {
    private int value;
    private BinaryTreeNode leftNode;
    private BinaryTreeNode rightNode;

    public BinaryTreeNode(int value) {
        this.value = value;
    }

    public int getValue() {
        return value;
    }

    public void setValue(int value) {
        this.value = value;
    }

    public BinaryTreeNode getLeftNode() {
        return leftNode;
    }

    public void setLeftNode(BinaryTreeNode leftNode) {
        this.leftNode = leftNode;
    }

    public BinaryTreeNode getRightNode() {
        return rightNode;
    }

    public void setRightNode(BinaryTreeNode rightNode) {
        this.rightNode = rightNode;
    }
}