Given a binary tree of N nodes with odd value. The task is to check whether all the nodes of the tree can be represented as the sum of the two prime numbers or not.
All the nodes in the tree can be represented as the sum of two prime numbers as:
9 = 2 + 7
15 = 2 +13
7 = 2 + 5
19 = 2 + 17
25 = 2 + 23
13 = 11 + 2
5 = 2 + 3
The node with value 27 cannot be represented as the sum of two prime numbers.
- The idea is to use Goldbach’s Weak Conjecture which states that every odd number greater than 5 can be expressed as the sum of three primes.
- To represent odd number(say N) as a sum of two prime numbers, fix one prime number as 2 and if (N – 2) is also prime, then N can be represented as a sum of two prime numbers.
- Check the above condition for all the nodes in a tree. If any node doesn’t follow the above condition then print “No” else print “Yes”.
Time complexity : O (N * log(log N))
Auxiliary Space : O (N)
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