import random
import math


def d1(a, b): return abs(a - b) + (1 + b - a)*((a == 10 and b == 1) or (a == 1 and b == 10))


def d2(a, b):
    if (a == 1 and b == 2) or (a == 9 and b == 10): return 1
    else:
        return (a != b)*(a**3 + b**3 - a**2*b - b**2*a + 4*a**2 - 4*b**2 + 4*a + 4*b) if b <= a else d2(b, a)


def E(perm, d): return sum(d(perm[i], perm[i+1]) for i in range(9))


def nowe_s(S):
    i = random.randint(1, 9)
    j = random.randint(0, i - 1)
    S[i], S[j] = S[j], S[i]
    return S


def accept(T, S, S1, d):
    rand = random.random()
    return E(S1, d) - E(S, d) < 0 or rand < math.e**((E(S, d) - E(S1, d))/T)


def nowe_t(t, T):
    return T/(1+math.log(t+1))


def annealing(M, L, T0, d):
    S = list(range(1, 11))
    random.shuffle(S) # losowy start
    t, accsol, T = 0, 0, T0
    while accsol < L:
        for x in range(0, M):
            S1 = nowe_s(S)
            if accept(T, S, S1, d):
                S = S1
                accsol += 1
            T = nowe_t(t, T)
            t += 1
    return S


pom = annealing(10, 3, 100, d1)
while E(pom , d1) > 15:
    pom = annealing(10, 3, 100, d1)
print(pom, E(pom, d1))
pom = annealing(10, 3, 100, d2)
print(pom, E(pom, d2))