NIM(3), python
false_table = dict()true_table = dict()def possible_next_moves(m,n): for i in range(0,m): yield(i,n) for i in range(0,n): if m<i: yield(m,i) else: yield(i,m) for i in range(0,m): yield(i,n-m+i) def can_reach(m,n,m1,n1): if m==m1 and n==n1: return False if m==m1 or n==n1 or m-m1 == n-n1: return True else: return False; def quick_check(m,n,name): for k,v in false_table.items(): if can_reach(m,n,v[1][0],v[1][1]): true_table[name] = (True,v[1]) return (True,v[1]) return Nonedef nim(m,n): if m>n: m,n = n,m name = str(m) + '+' +str(n) if name in false_table: return false_table[name] if name in true_table: return true_table[name] #Used for Optimization, but optional check = quick_check(m,n,name) if check: return check for possible in possible_next_moves(m,n): r=nim(possible[0],possible[1]) if r[0] == False: true_table[name] = (True,possible) return (True, possible)# elif can_reach(m, n, r[1][0], r[1][1]):# true_table[name] = (True,r[1])# return (True,r[1]) false_table[name] = (False,(m,n)) return (False,(m,n))def assert_false(m,n): size = 0 for possible in possible_next_moves(m,n): size = size +1 r = nim (possible[0],possible[1]) if r[0] != True: print('error!',m,n,'should be false but it has false sub move', possible) return print('all',size,'possible moves are checked!')if __name__ == '__main__': assert_false(6,8)