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5. Find two Missing Numbers in a Sequence of Consecutive Numbers

Objective : Write an algorithm to find two Missing Numbers in a Sequence of Consecutive Numbers

Input:  Array, arrA[] with two missing numbers and Range

Output : Two missing numbers

Approach:

  • Approach is very simple, Add all the given numbers say S
  • Calculate sum of N numbers by formula n(n+1)/2 , say N
  • Find sum of two missing numbers a+b = N-S
  • Now take the product of all given numbers say P
  • Now take the product of N numbers , say Np;
  • Find the product of two missing numbers ab = Np-P
  • Now we have a+b and ab , we can easily calculate a and b

Example :

Given array : {10,2,3,5,7,8,9,1}; Range : 10

N (Sum of 1 to 10 ) = 55

S (Sum of given elements ) = 45

a+b = 10------------------------------------(1)

Np(Product of 1 to 10) = 3628800

P(Product of given elements) = 151200

So a*b = 24---------------------------------(2)

Now we have two equations and two variables, if we solve we will get values 6 and 4.
Missing numbers are :6 and 4

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