from math import log, floor # for use in Kill3 """ Killing Circle Problem Ascertain the surviving spot and the killing order recursively. Inputs: n = num people in circle, people in circle would be represented starting at 0 k = position of person killed in sequence (eg: k=3 ~> 1 & 2 skipped, 3rd is killed, 4 & 5 skipped, 6th killed etc.) """ def kill1(n, k): p, i, seq = list(range(n)), 0, [] while p: i = (i + k - 1) % len(p) seq.append(p.pop(i)) return 'Killing order: %s.\nSurvivor: %i\n' % (', '.join(str(i) for i in seq[:-1]), seq[-1]) # a slightly faster method to ascertain the surviver without keeping track of killing order. def kill2(n, k): r = 0 for i in range(1, n + 1): r = (r + k) % i return r # fastest mathod to arrive at answer mathematically (instead of algorithmically) # assumes k==2 def kill3(n): r = int(2 * (n - 2 ** (floor(log(n, 2))))) return r
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