Kth Maximum Level sum

Given a binary tree and a non negative integer k. Find and return the Kth maximum level sum in a binary tree. If the levels are less than k, return -1.

Examples:

Input: root = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], k = 2

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Output: 13.
Explanation: The sums of nodes at each level are:
Level 1: 1
Level 2: 2 + 3 = 5
Level 3: 4 + 5 + 6 + 7 = 22
Level 4: 8 + 9 = 17
Level 5: 10 + 11 = 21
The 2nd largest level sum is 21.

Input: root = [7, 9, 10, 12, 13, 14, 16, 25, 30], k = 2
Output: 13.
Explanation: The sums of nodes at each level are:
Level 1: 7.
Level 2: 9 + 10 = 19.
Level 3: 12 + 13 + 14 + 16 = 55.
Level 4: 30+ 40 = 70.
The 2nd largest level sum is 55.

:

This can be solved using queue data structure afterwards keep finding the sum of each level and store the sum of each level in a vector say ans. Sort the ans array and print the k^th maximum sum.

Below is the steps for above approach:

• Create an empty queue q and push root in q.
• Initialize vector ans.
• Run while loop until q is not empty.
  • Initialize s=q.size()
  • Define a data structure vector V of  size s
  • Run while loop until s-- .
    •  Initialize temp = q.front() and store temp->data in V.
    • pop front node from q.
    • Push temp children i.e. temp->left then temp->right to q.
  • Initialize sum=0.
  • Add the element of V and store them in vector ans.
• Sort the input array in the increasing order.
• Return -1 if K-1 is equal or greater than ans.size()  else return element at k-1 index.

55

Time Complexity: O(N log N), where N is the number of node in a binary tree.
Auxiliary Space: O(L), where L is the number of levels in a Binary tree.