Verify Preorder Sequence in Binary Search Tree in C++

Suppose we have a sequence of numbers; we have to check whether it is the correct preorder traversal sequence of a binary search tree. We can assume that each number in the sequence is unique. Consider the following binary search tree −

So, if the input is like [5,2,1,3,6], then the output will be true

To solve this, we will follow these steps −

• itr := -1

• low := -infinity

• for initialize i := 0, when i < size of preorder, update (increase i by 1), do −

  • x := preorder[i]

  • if x < low, then −

    • return false

  • while (itr >= 0 and preorder[itr] < x), do −

    • low := preorder[itr]

    • (decrease itr by 1)

  • (increase itr by 1)

  • preorder[itr] := x

• return true

Example 

Let us see the following implementation to get a better understanding −

#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
   bool verifyPreorder(vector<int<& preorder) {
      int itr = -1;
      int low = INT_MIN;
      for (int i = 0; i < preorder.size(); i++) {
         int x = preorder[i];
         if (x < low)
            return false;
         while (itr >= 0 && preorder[itr] < x) {
            low = preorder[itr];
            itr--;
         }
         itr++;
         preorder[itr] = x;
      }
      return true;
   }
};
main(){
   Solution ob;
   vector<int< v = {5,2,1,3,6};
   cout << (ob.verifyPreorder(v));
}

Input

{5,2,1,3,6}

Output

1