Getting the lowest possible sum from numbers' difference

Question

I have to find the lowest possible sum from numbers\' difference.

Let\'s say I have 4 numbers. 1515, 1520, 1500 and 1535. The lowest sum of difference is 30, becaus

Answer 1

Taking the edit into account:

Start by sorting the list. Then use a dynamic programming solution, with state i, n representing the minimum sum of n differences when considering only the first i numbers in the sequence. Initial states: dp[*][0] = 0, everything else = infinity. Use two loops: outer loop looping through i from 1 to N, inner loop looping through n from 0 to R (3 in your example case in your edit - this uses 3 pairs of numbers which means 6 individual numbers). Your recurrence relation is dp[i][n] = min(dp[i-1][n], dp[i-2][n-1] + seq[i] - seq[i-1]).

You have to be aware of handling boundary cases which I've ignored, but the general idea should work and will run in O(N log N + NR) and use O(NR) space.