Full search of the game "krypto".

krypto.py

lst = [11, 10, 22, 10, 25]
ans = 1
tolerance = 1e-4
size = len(lst)

def n_merge(N):
    ans = N
    for i in range(1, N):
        ans *= i**2
    return ans

def merge(size, n, ope):
    pos_num1 = n % size
    n = n // size
    pos_num2 = n % (size-1)
    n = n // (size-1)
    num1 = calc_lst[size-1][pos_num1]
    if pos_num1 < size-1:
        temp = calc_lst[size-1][:pos_num1] + calc_lst[size-1][pos_num1+1:]
    else:
        temp = calc_lst[size-1][:pos_num1]
    num2 = temp[pos_num2]
    if ope == 0:
        num = num1 + num2
    elif ope == 1:
        num = num1 - num2
    elif ope == 2:
        num = num1 * num2
    else:
        if num2 == 0:
            return None
        num = num1 / num2
    if pos_num2 < size - 2:
        calc_lst[size-2] = [num] + temp[:pos_num2] + temp[pos_num2+1:]
    else:
        calc_lst[size-2] = [num] + temp[:pos_num2]

    return n

def merge_show(size, ope, n):
    pos_num1 = n % size
    n = n // size
    pos_num2 = n % (size-1)
    n = n // (size-1)
    num1 = string_lst[size-1][pos_num1]
    if pos_num1 < size-1:
        temp = string_lst[size-1][:pos_num1] + string_lst[size-1][pos_num1+1:]
        pri_temp = pri_lst[size-1][:pos_num1] + pri_lst[size-1][pos_num1+1:]
    else:
        temp = string_lst[size-1][:pos_num1]
        pri_temp = pri_lst[size-1][:pos_num1]
    num2 = temp[pos_num2]
    if pri_lst[size-1][pos_num1] == 0:
        num1 = "(" + num1 + ")"
    if pri_temp[pos_num2] == 0:
        num2 = "(" + num2 + ")"
    if ope == 0:
        num = num1 + "+" + num2
        pri = 0
    elif ope == 1:
        num = num1 + "-" + num2
        pri = 0
    elif ope == 2:
        num = num1 + "*" + num2
        pri = 1
    else:
        num = num1 + "/" + num2
        pri = 1
    if pos_num2 < size - 2:
        string_lst[size-2] = [num] + temp[:pos_num2] + temp[pos_num2+1:]
        pri_lst[size-2] = [pri] + pri_temp[:pos_num2] + pri_temp[pos_num2+1:]
    else:
        string_lst[size-2] = [num] + temp[:pos_num2]
        pri_lst[size-2] = [num] + pri_temp[:pos_num2]
    return n



def show(size, ope_lst, N):
    for i in range(size-1):
        N = merge_show(size-i, ope_lst[i], N)
    return string_lst[0][0]

def solve(lst, ans):
    for N in range(n_merge(size)):
        for i in range(4**(size-1)):
            ope_lst = []
            ic = i
            for j in range(size-1):
                ope_lst.append(ic%4)
                ic = ic // 4
            Nc = N
            flag = True
            for j in range(size-1):
                Nc = merge(size-j, Nc, ope_lst[j])
                if Nc is None:
                    flag = False
                    break
            if flag and calc_lst[0][0] < ans + tolerance and calc_lst[0][0] > ans - tolerance:
                print(show(size, ope_lst, N)+"="+str(ans))
                return
    print("None.")
    return 

for i in range(30):
    calc_lst = [[0]*i for i in range(1, size)] + [lst]
    lst_to_str = [str(i) for i in lst]
    string_lst = [[""]*i for i in range(1, size)] + [lst_to_str]
    pri_lst = [[1]*i for i in range(1, size+1)]
    solve(lst, i)