Given a value of n and a permutation which consist all the distinct values such that (1 <= ai <= n). Find out the maximum element wise remainder sum by choosing a permutation of your own following the condition that the permutation should have distinct values and (1 <= ai <= n).
Key to AC: n * (n - 1) / 2
The remainder of A divided by B is expressed as A mod B. If we express it as -
(1 mod 2) + (2 mod 3) +… + ((N1) mod N) + (N mod 1) = 1 + 2 + … + N1 =N * (N - 1) / 2
It is best to choose a permutation. This is explained below.
The selected permutation 1, 2, …, N just each 1 appeared one by times.
Suppose appears at the x ith position of the permutation . Then the objective function (the one we want to maximize ) is
When attention is paid to the sections at most each term is 0 , 1 , 2 , …, N - 1.
If xi = i − 1 and the remaining N is x 1 = N , then