Preorder from Inorder and Postorder traversals

Given Inorder and Postorder traversals of a binary tree, print Preorder traversal. 

Example:

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

Traversals in the above example represents following tree 
         1
      /    \       
     2       3
   /   \      \  
  4     5      6

A naive method is to first construct the tree from given postorder and inorder, then use a simple recursive method to print preorder traversal of the constructed tree.

We can print preorder traversal without constructing the tree. 
The idea is, root is always the first item in preorder traversal and it must be the last item in postorder traversal. We first push right subtree to a stack, then left subtree, and finally, we push root. Finally, we print contents of stack. To find boundaries of left and right subtrees in post[] and in[], we search root in in[], all elements before root in in[] are elements of left subtree, and all elements after root are elements of right subtree. In post[], all elements after index of root in in[] are elements of right subtree. And elements before index (including the element at index and excluding the first element) are elements of left subtree. 

Implementation:

C++

// C++ program to print Postorder traversal from given
// Inorder and Preorder traversals.
#include<bits/stdc++.h>
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<int> &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<int> 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<Integer> 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<Integer> s = new Stack<Integer>();
        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 print Postorder 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 divyeshrabadiya07

C#

// 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<int> 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<int> s = new Stack<int>();
        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

<script>

// JavaScript program to print
// Postorder traversal from given
// Inorder and Preorder traversals.

let  postIndex;

// A utility function to search data in in[]
function search(In,data)
{
    let i = 0;
        for (i = 0; i < In.length; i++)
            if (In[i] == data)
                return i;
        return i;
}

// Fills preorder traversal of tree with given
    // inorder and postorder traversals in a stack
function fillPre(In,post,inStrt,inEnd,s)
{
    if (inStrt > inEnd)
            return;

        // Find index of next item
        // in postorder traversal in
        // inorder.
        let val = post[postIndex];
        let 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
function printPreMain(In,post)
{
    let len = In.length;
        postIndex = len - 1;
        let s = [];
        fillPre(In, post, 0, len - 1, s);
        while (s.length!=0)
            document.write(s.pop() + " ");
}


// Driver code
let In=[4, 10, 12, 15, 18, 22, 24, 25,
                     31, 35, 44, 50, 66, 70, 90 ];

let post=[4, 12, 10, 18, 24, 22, 15, 31,
                       44, 35, 66, 90, 70, 50, 25 ];

printPreMain(In, post);


// This code is contributed by unknown2108

</script>

Output

25 15 10 4 12 22 18 24 50 35 31 44 70 66 90 

Time Complexity: The above function visits every node in array. For every visit, it calls search which takes O(n) time. Therefore, overall time complexity of the function is O(n²)

O(n) Solution: We can further optimize above solution to first hash all items of inorder traversal so that we do not have to linearly search items. With hash table available to us, we can search an item in O(1) time.

Implementation:

C++

// C++ program to print Postorder traversal from
// given Inorder and Preorder traversals.
#include <bits/stdc++.h>
using namespace std;

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<int> &s,
             map<int, int> 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 N)
{
    int len = N;
    postIndex = len - 1;
    stack<int> s;

    // Insert values in a hash map
    // and their indexes.
    map<int, int> hm;
    for (int i = 0; i < N; i++)
        hm[iN[i]] = i;

    // Fill preorder traversal in a stack
    fillPre(iN, post, 0, len - 1, s, hm);

    // Print contents of stack
    while (s.size() != 0)
    {
        cout << s.top() << " ";
        s.pop();
    }
}

int main()
{
    int iN[] = { 4, 10, 12, 15, 18, 22, 24, 25,
                31, 35, 44, 50, 66, 70, 90 };
    int N = sizeof(iN) / sizeof(iN[0]);
    int post[] = { 4, 12, 10, 18, 24, 22, 15, 31,
                  44, 35, 66, 90, 70, 50, 25 };
    printPreMain(iN, post, N);

    return 0;
}

// This code is contributed by decode2207.

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<Integer> s, HashMap<Integer, Integer> 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<Integer> s = new Stack<Integer>();

        // Insert values in a hash map and their indexes.
        HashMap<Integer, Integer> hm =
                     new HashMap<Integer, Integer>();
        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 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<int> s,
                 Dictionary<int, int> 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<int> s = new Stack<int>();

        // Insert values in a hash map
        // and their indexes.
        Dictionary<int, int> hm =
                        new Dictionary<int, int>();
        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

<script>
// Javascript program to print Postorder traversal from given
// Inorder and Preorder traversals.

    let postIndex;

    // Fills preorder traversal of tree with given
    // inorder and postorder traversals in a stack
    function fillPre(In,post,inStrt,inEnd,s,hm)
    {
        if (inStrt > inEnd)
            return;

        // Find index of next item in postorder traversal in
        // inorder.
        let val = post[postIndex];
        let 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
    function printPreMain(In,post)
    {
        let len = In.length;
        postIndex = len - 1;
        let s = [];

        // Insert values in a hash map and their indexes.
        let hm = new Map();
        for (let i = 0; i < In.length; i++)
            hm.set(In[i], i);

        // Fill preorder traversal in a stack
        fillPre(In, post, 0, len - 1, s, hm);

        // Print contents of stack
        while (s.length != 0)
            document.write(s.pop() + " ");
    }

    // Driver code
    let In=[4, 10, 12, 15, 18, 22, 24, 25,
                     31, 35, 44, 50, 66, 70, 90];

    let post=[4, 12, 10, 18, 24, 22, 15, 31,
                       44, 35, 66, 90, 70, 50, 25];

    printPreMain(In, post);


// This code is contributed by patel2127
</script>

Output

25 15 10 4 12 22 18 24 50 35 31 44 70 66 90 

Time Complexity: O(n).
Auxiliary Space: O(N), where N is the number of elements in the inorder and postorder traversal array. We are using a stack and a hashmap of size N.