DSA-PROBLEMS/Burning_Tree.cpp at main · Harsh1118/DSA-PROBLEMS · GitHub

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/*
Given a binary tree and a target node, determine the minimum time required to burn the entire tree if the target node is set on fire.
In one second, the fire spreads from a node to its left child, right child, and parent.
Note: The tree contains unique values.

Examples :

Input: root[] = [1, 2, 3, 4, 5, 6, 7], target = 2

Output: 3
Explanation: Initially 2 is set to fire at 0 sec
At 1 sec: Nodes 4, 5, 1 catches fire.
At 2 sec: Node 3 catches fire.
At 3 sec: Nodes 6, 7 catches fire.
It takes 3s to burn the complete tree.
Input: root[] = [1, 2, 3, 4, 5, N, 7, 8, N, 10], target = 10

Output: 5
Explanation: Initially 2 is set to fire at 0 sec
At 1 sec: Node 5 catches fire.
At 2 sec: Node 2 catches fire.
At 3 sec: Nodes 1 and 4 catches fire.
At 4 sec: Node 3 and 8 catches fire.
At 5 sec: Node 7 catches fire.
It takes 5s to burn the complete tree.
Constraints:
1 ≤ number of nodes ≤ 105
1 ≤ node->data ≤ 105

Expected Complexities
Time Complexity: O(n)
Auxiliary Space: O(h)
*/
#include<iostream>
using namespace std;

class Node
{
    public:
    int data;
    Node *left , *right;

    Node(int val)
    {
        data = val;
        left = right = NULL;
    }
};

class Solution {
  public:

  int Burn(Node *root ,int &target ,int &timer)
  {
      if(!root)
      {
          return 0;
      }
      if(root->data == target)
      {
          return -1;
      }
      int left = Burn(root->left,target,timer);
      int right = Burn(root->right,target,timer);

      if(left<0)
      {
          timer = max(timer,abs(left)+right);
          return left-1;
      }

      if(right<0)
      {
          timer = max(timer,abs(right)+left);
          return right-1;
      }

      return 1+max(left,right);
  }

  void find(Node *root , int &target , Node * &BurnNode)
  {
      if(!root)
      {
          return;
      }

      if(root->data==target)
      {
          BurnNode = root;
          return;
      }

      find(root->left,target,BurnNode);
      find(root->right,target,BurnNode);
  }

  int Height(Node *root)
  {
      if(!root)
      {
          return 0;
      }

      return 1+max(Height(root->left),Height(root->right));
  }

    int minTime(Node* root, int target) {
        // code here
        int timer = 0;
        Burn(root,target,timer);

        Node *BurnNode = NULL;
        find(root,target,BurnNode);

        int high = Height(BurnNode)-1;

        return max(timer , high);
    }
};