给定二叉树的中序和后序遍历，打印前序遍历。
例子：
Input: Postorder traversal post[] = {4, 5, 2, 6, 3, 1}
Inorder traversal in[] = {4, 2, 5, 1, 3, 6}
Output: Preorder traversal 1, 2, 4, 5, 3, 6
Trversals in the above example represents following tree
1
/ \
2 3
/ \ \
4 5 6一种朴素的方法是首先从给定的后序和中序构造树，然后使用简单的递归方法打印构造树的前序遍历。
我们可以在不构造树的情况下打印预序遍历。这个想法是，root 总是前序遍历中的第一个项目，它必须是后序遍历中的最后一个项目。我们首先将右子树压入堆栈，然后将左子树压入堆栈，最后压入根。最后，我们打印堆栈的内容。为了在post[]和in[]中找到左右子树的边界，我们在in[]中搜索root，in[]中root之前的所有元素都是左子树的元素，root之后的所有元素都是右子树的元素。在 post[] 中，in[] 中 root 索引之后的所有元素都是右子树的元素。而index之前的元素（包括index处的元素，不包括第一个元素）是左子树的元素。
C++
// C++ program to print Postorder traversal from given
// Inorder and Preorder traversals.
#include
using namespace std;
int postIndex = 0;
// A utility function to search data in in[]
int search(int in[], int data,int n)
{
int i = 0;
for (i = 0; i < n; i++)
if (in[i] == data)
return i;
return i;
}
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int in[], int post[], int inStrt,
int inEnd, stack &s,int n)
{
if (inStrt > inEnd)
return;
// Find index of next item in postorder traversal in
// inorder.
int val = post[postIndex];
int inIndex = search(in, val, n);
postIndex--;
// traverse right tree
fillPre(in, post, inIndex + 1, inEnd, s, n);
// traverse left tree
fillPre(in, post, inStrt, inIndex - 1, s, n);
s.push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int in[], int post[],int n)
{
int len = n;
postIndex = len - 1;
stack s ;
fillPre(in, post, 0, len - 1, s, n);
while (s.size() > 0)
{
cout << s.top() << " ";
s.pop();
}
}
// Driver code
int main()
{
int in[] = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int post[] = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
int n=sizeof(in)/sizeof(int);
printPreMain(in, post,n);
}
// This code is contributed by Arnab Kundu Java
// Java program to print Postorder traversal from given
// Inorder and Preorder traversals.
import java.util.Stack;
public class PrintPre {
static int postIndex;
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int[] in, int[] post, int inStrt,
int inEnd, Stack s)
{
if (inStrt > inEnd)
return;
// Find index of next item in postorder traversal in
// inorder.
int val = post[postIndex];
int inIndex = search(in, val);
postIndex--;
// traverse right tree
fillPre(in, post, inIndex + 1, inEnd, s);
// traverse left tree
fillPre(in, post, inStrt, inIndex - 1, s);
s.push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int[] in, int[] post)
{
int len = in.length;
postIndex = len - 1;
Stack s = new Stack();
fillPre(in, post, 0, len - 1, s);
while (s.empty() == false)
System.out.print(s.pop() + " ");
}
// A utility function to search data in in[]
int search(int[] in, int data)
{
int i = 0;
for (i = 0; i < in.length; i++)
if (in[i] == data)
return i;
return i;
}
// Driver code
public static void main(String ars[])
{
int in[] = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int post[] = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
PrintPre tree = new PrintPre();
tree.printPreMain(in, post);
}
} Python3
# Python3 program to prPostorder traversal from given
# Inorder and Preorder traversals.
# A utility function to search data in in[]
def search(inn, data,n):
i = 0
while i < n :
if (inn[i] == data):
return i
i += 1
return i
# Fills preorder traversal of tree with given
# inorder and postorder traversals in a stack
def fillPre(inn, post, inStrt, inEnd, n):
global s, postIndex
if (inStrt > inEnd):
return
# Find index of next item in postorder traversal in
# inorder.
val = post[postIndex]
inIndex = search(inn, val, n)
postIndex -= 1
# traverse right tree
fillPre(inn, post, inIndex + 1, inEnd, n)
# traverse left tree
fillPre(inn, post, inStrt, inIndex - 1, n)
s.append(val)
# This function basically initializes postIndex
# as last element index, then fills stack with
# reverse preorder traversal using printPre
def printPreMain(inn, post, n):
global s
lenn = n
postIndex = lenn - 1
fillPre(inn, post, 0, lenn - 1, n)
while ( len(s) > 0):
print(s[-1], end=" ")
del s[-1]
# Driver code
if __name__ == '__main__':
s,postIndex = [], 0
inn =[4, 10, 12, 15, 18, 22, 24, 25,31, 35, 44, 50, 66, 70, 90]
post =[4, 12, 10, 18, 24, 22, 15, 31,44, 35, 66, 90, 70, 50, 25]
n=len(inn)
printPreMain(inn, post,n)
# This code is contributed by divyeshrabadiya07C#
// C# program to print Postorder traversal from given
// Inorder and Preorder traversals.
using System;
using System.Collections.Generic;
public class PrintPre
{
static int postIndex;
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int[] a, int[] post, int inStrt,
int inEnd, Stack s)
{
if (inStrt > inEnd)
return;
// Find index of next item in postorder traversal in
// inorder.
int val = post[postIndex];
int inIndex = search(a, val);
postIndex--;
// traverse right tree
fillPre(a, post, inIndex + 1, inEnd, s);
// traverse left tree
fillPre(a, post, inStrt, inIndex - 1, s);
s.Push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int[] a, int[] post)
{
int len = a.Length;
postIndex = len - 1;
Stack s = new Stack();
fillPre(a, post, 0, len - 1, s);
while (s.Count!=0)
Console.Write(s.Pop() + " ");
}
// A utility function to search data in in[]
int search(int[] a, int data)
{
int i = 0;
for (i = 0; i < a.Length; i++)
if (a[i] == data)
return i;
return i;
}
// Driver code
public static void Main(String []args)
{
int []a = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int []post = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
PrintPre tree = new PrintPre();
tree.printPreMain(a, post);
}
}
// This code has been contributed by 29AjayKumar Javascript
Java
// Java program to print Postorder traversal from given
// Inorder and Preorder traversals.
import java.util.Stack;
import java.util.HashMap;
public class PrintPre {
static int postIndex;
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int[] in, int[] post, int inStrt, int inEnd,
Stack s, HashMap hm)
{
if (inStrt > inEnd)
return;
// Find index of next item in postorder traversal in
// inorder.
int val = post[postIndex];
int inIndex = hm.get(val);
postIndex--;
// traverse right tree
fillPre(in, post, inIndex + 1, inEnd, s, hm);
// traverse left tree
fillPre(in, post, inStrt, inIndex - 1, s, hm);
s.push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int[] in, int[] post)
{
int len = in.length;
postIndex = len - 1;
Stack s = new Stack();
// Insert values in a hash map and their indexes.
HashMap hm =
new HashMap();
for (int i = 0; i < in.length; i++)
hm.put(in[i], i);
// Fill preorder traversal in a stack
fillPre(in, post, 0, len - 1, s, hm);
// Print contents of stack
while (s.empty() == false)
System.out.print(s.pop() + " ");
}
// Driver code
public static void main(String ars[])
{
int in[] = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int post[] = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
PrintPre tree = new PrintPre();
tree.printPreMain(in, post);
}
} Python3
# Python3 program to print Postorder traversal from given
# Inorder and Preorder traversals.
postIndex = 0
# Fills preorder traversal of tree with given
# inorder and postorder traversals in a stack
def fillPre(In, post, inStrt, inEnd, s, hm):
global postIndex
if(inStrt > inEnd):
return
# Find index of next item in postorder traversal in
# inorder.
val = post[postIndex]
inIndex = hm[val]
postIndex -= 1
# traverse right tree
fillPre(In, post, inIndex + 1, inEnd, s, hm)
# traverse left tree
fillPre(In, post, inStrt, inIndex - 1, s, hm)
s.append(val)
# This function basically initializes postIndex
# as last element index, then fills stack with
# reverse preorder traversal using printPre
def printPreMain(In, post):
global postIndex
Len = len(In)
postIndex = Len - 1
s = []
# Insert values in a hash map and their indexes.
hm = {}
for i in range(len(In)):
hm[In[i]] = i
# Fill preorder traversal in a stack
fillPre(In, post, 0, Len - 1, s, hm)
# Print contents of stack
while(len(s) > 0):
print(s.pop(), end = " ")
# Driver code
In = [4, 10, 12, 15, 18, 22, 24, 25,31, 35, 44, 50, 66, 70, 90 ]
post = [4, 12, 10, 18, 24, 22, 15, 31,44, 35, 66, 90, 70, 50, 25 ]
printPreMain(In, post)
# This code is contributed by avanitrachhadiya2155C#
// C# program to print Postorder traversal from
// given Inorder and Preorder traversals.
using System;
using System.Collections.Generic;
class PrintPre
{
static int postIndex;
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int[] iN, int[] post, int inStrt,
int inEnd, Stack s,
Dictionary hm)
{
if (inStrt > inEnd)
return;
// Find index of next item in
// postorder traversal in inorder.
int val = post[postIndex];
int inIndex = hm[val];
postIndex--;
// traverse right tree
fillPre(iN, post, inIndex + 1,
inEnd, s, hm);
// traverse left tree
fillPre(iN, post, inStrt,
inIndex - 1, s, hm);
s.Push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int[] iN, int[] post)
{
int len = iN.Length;
postIndex = len - 1;
Stack s = new Stack();
// Insert values in a hash map
// and their indexes.
Dictionary hm =
new Dictionary();
for (int i = 0; i < iN.Length; i++)
hm.Add(iN[i], i);
// Fill preorder traversal in a stack
fillPre(iN, post, 0, len - 1, s, hm);
// Print contents of stack
while (s.Count != 0)
Console.Write(s.Pop() + " ");
}
// Driver code
public static void Main(String []ars)
{
int []iN = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int []post = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
PrintPre tree = new PrintPre();
tree.printPreMain(iN, post);
}
}
// This code is contributed by Rajput-Ji Javascript
输出：
25 15 10 4 12 22 18 24 50 35 31 44 70 66 90时间复杂度：上述函数访问数组中的每个节点。对于每次访问，它调用需要 O(n) 时间的搜索。因此，该函数的整体时间复杂度为 O(n 2 )
O(n) 解决方案
我们可以进一步优化上述解决方案，首先对中序遍历的所有项目进行散列，这样我们就不必线性搜索项目。有了哈希表，我们就可以在 O(1) 时间内搜索一个项目。
Java
// Java program to print Postorder traversal from given
// Inorder and Preorder traversals.
import java.util.Stack;
import java.util.HashMap;
public class PrintPre {
static int postIndex;
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int[] in, int[] post, int inStrt, int inEnd,
Stack s, HashMap hm)
{
if (inStrt > inEnd)
return;
// Find index of next item in postorder traversal in
// inorder.
int val = post[postIndex];
int inIndex = hm.get(val);
postIndex--;
// traverse right tree
fillPre(in, post, inIndex + 1, inEnd, s, hm);
// traverse left tree
fillPre(in, post, inStrt, inIndex - 1, s, hm);
s.push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int[] in, int[] post)
{
int len = in.length;
postIndex = len - 1;
Stack s = new Stack();
// Insert values in a hash map and their indexes.
HashMap hm =
new HashMap();
for (int i = 0; i < in.length; i++)
hm.put(in[i], i);
// Fill preorder traversal in a stack
fillPre(in, post, 0, len - 1, s, hm);
// Print contents of stack
while (s.empty() == false)
System.out.print(s.pop() + " ");
}
// Driver code
public static void main(String ars[])
{
int in[] = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int post[] = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
PrintPre tree = new PrintPre();
tree.printPreMain(in, post);
}
}
蟒蛇3
# Python3 program to print Postorder traversal from given
# Inorder and Preorder traversals.
postIndex = 0
# Fills preorder traversal of tree with given
# inorder and postorder traversals in a stack
def fillPre(In, post, inStrt, inEnd, s, hm):
global postIndex
if(inStrt > inEnd):
return
# Find index of next item in postorder traversal in
# inorder.
val = post[postIndex]
inIndex = hm[val]
postIndex -= 1
# traverse right tree
fillPre(In, post, inIndex + 1, inEnd, s, hm)
# traverse left tree
fillPre(In, post, inStrt, inIndex - 1, s, hm)
s.append(val)
# This function basically initializes postIndex
# as last element index, then fills stack with
# reverse preorder traversal using printPre
def printPreMain(In, post):
global postIndex
Len = len(In)
postIndex = Len - 1
s = []
# Insert values in a hash map and their indexes.
hm = {}
for i in range(len(In)):
hm[In[i]] = i
# Fill preorder traversal in a stack
fillPre(In, post, 0, Len - 1, s, hm)
# Print contents of stack
while(len(s) > 0):
print(s.pop(), end = " ")
# Driver code
In = [4, 10, 12, 15, 18, 22, 24, 25,31, 35, 44, 50, 66, 70, 90 ]
post = [4, 12, 10, 18, 24, 22, 15, 31,44, 35, 66, 90, 70, 50, 25 ]
printPreMain(In, post)
# This code is contributed by avanitrachhadiya2155
C＃
// C# program to print Postorder traversal from
// given Inorder and Preorder traversals.
using System;
using System.Collections.Generic;
class PrintPre
{
static int postIndex;
// Fills preorder traversal of tree with given
// inorder and postorder traversals in a stack
void fillPre(int[] iN, int[] post, int inStrt,
int inEnd, Stack s,
Dictionary hm)
{
if (inStrt > inEnd)
return;
// Find index of next item in
// postorder traversal in inorder.
int val = post[postIndex];
int inIndex = hm[val];
postIndex--;
// traverse right tree
fillPre(iN, post, inIndex + 1,
inEnd, s, hm);
// traverse left tree
fillPre(iN, post, inStrt,
inIndex - 1, s, hm);
s.Push(val);
}
// This function basically initializes postIndex
// as last element index, then fills stack with
// reverse preorder traversal using printPre
void printPreMain(int[] iN, int[] post)
{
int len = iN.Length;
postIndex = len - 1;
Stack s = new Stack();
// Insert values in a hash map
// and their indexes.
Dictionary hm =
new Dictionary();
for (int i = 0; i < iN.Length; i++)
hm.Add(iN[i], i);
// Fill preorder traversal in a stack
fillPre(iN, post, 0, len - 1, s, hm);
// Print contents of stack
while (s.Count != 0)
Console.Write(s.Pop() + " ");
}
// Driver code
public static void Main(String []ars)
{
int []iN = { 4, 10, 12, 15, 18, 22, 24, 25,
31, 35, 44, 50, 66, 70, 90 };
int []post = { 4, 12, 10, 18, 24, 22, 15, 31,
44, 35, 66, 90, 70, 50, 25 };
PrintPre tree = new PrintPre();
tree.printPreMain(iN, post);
}
}
// This code is contributed by Rajput-Ji
Javascript
输出：
25 15 10 4 12 22 18 24 50 35 31 44 70 66 90时间复杂度： O(n)
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