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Check if given number can be represented as sum of two great numbers

  • Difficulty Level : Easy
  • Last Updated : 03 Nov, 2017

We are given a number N. We need to check if the given number N can be represented as sum of two Great numbers. If yes then print those two great numbers else print no. Great numbers are those which are represented in the form : ((b)*(b+1)*(2*b+1))/6 where b is a natural number.


Input  : N = 35
Output : 5 and 30

Input  : 105
Output : 14 and 91

Input : 99
Output : No the given number is not 
a sum of two great numbers

As we know ((b)*(b+1)*(2*b+1))/6 where b is a natural number represents the sum of square of first b natural numbers. For example if b = 3 then 1+4+9 = 14. So to check if the input number n can be represented as sum of two great numbers then we will first compute all the great numbers less than n in an array. Then we will use two pointer approach to find the pair than can sum up to the given number n.

To compute the array of all the great numbers we will iterate over i=0 to i 14 and 91

Time Complexity: O(N)
Auxiliary Space : O(N)

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