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Given three integers A, B and N the task is to find N Arithmetic means between A and B. We basically need to insert N terms in an Arithmetic progression. where A and B are first and last terms. Examples:
Input : A = 20 B = 32 N = 5 Output : 22 24 26 28 30 The Arithmetic progression series as 20 22 24 26 28 30 32 Input : A = 5 B = 35 N = 5 Output : 10 15 20 25 30
Approach : Let A1, A2, A3, A4......An be N Arithmetic Means between two given numbers A and B . Then A, A1, A2 ..... An, B will be in Arithmetic Progression . Now B = (N+2)th term of the Arithmetic progression . So : Finding the (N+2)th term of the Arithmetic progression Series where d is the Common Difference B = A + (N + 2 - 1)d B - A = (N + 1)d So the Common Difference d is given by. d = (B - A) / (N + 1) So now we have the value of A and the value of the common difference(d), now we can find all the N Arithmetic Means between A and B.
22 24 26 28 30
Time Complexity : O(N) ,where N is the number of terms
Space Complexity : O(1), since no extra space has been taken.