Python实现快速计算24点游戏的示例代码

from scipy.special import comb

comb(9, 4, repetition=True)

from operator import add, mul, sub, truediv

ops = [add, mul, sub, truediv]


def judgePoint24(nums) -> bool:
    if not nums:
        return False
    n = len(nums)
    if n == 1:
        return round(nums[0], 3) == 24
    for i, j in permutations(range(n), 2):
        # 选2个数字
        x, y = nums[i], nums[j]
        newNums = []
        # 选择加减乘除 4 种运算操作之一，用得到的结果取代选出的 2 个数字
        for k, z in enumerate(nums):
            if k != i and k != j:
                newNums.append(z)
        for k in range(4):
            if k < 2 and i > j:
                # 加法和乘法满足交换律,跳过第二种顺序
                continue
            if k == 3 and round(y, 3) == 0:
                # 除法运算除数不能为0
                continue
            newNums.append(ops[k](x, y))
            if judgePoint24(newNums):
                return True
            newNums.pop()
    return False

from scipy.special import comb

​​​​​​​total = int(comb(9, 4, repetition=True))
cnt = sum(judgePoint24(nums)
          for nums in combinations_with_replacement(range(1, 10), 4))
print(f'{cnt}/{total}={cnt/total:.2%}')

from operator import add, mul, sub, truediv
from itertools import permutations, combinations_with_replacement
from collections import defaultdict


def judgePoint24(nums) -> bool:
    ops = [add, mul, sub, truediv]
    op_char = "+*-/"
    record = []

    def solve(nums) -> bool:
        if not nums:
            return False
        n = len(nums)
        if n == 1:
            return round(nums[0], 3) == 24
        for i, j in permutations(range(n), 2):
            # 选2个数字
            x, y = nums[i], nums[j]
            newNums = []
            # 选择加减乘除 4 种运算操作之一，用得到的结果取代选出的 2 个数字
            # 先添加未选择的数字
            newNums = [z for k, z in enumerate(nums) if k not in (i, j)]
            for k in range(4):
                if k < 2 and i > j:
                    # 加法和乘法满足交换律,跳过第二种顺序
                    continue
                if k == 3 and (round(y, 3) == 0):
                    # 除法运算除数不能为0
                    continue
                v = ops[k](x, y)
                newNums.append(v)
                record.append(([round(x, 3), round(y, 3)],
                              op_char[k], round(v, 3)))
                if solve(newNums):
                    return True
                newNums.pop()
                record.pop()
        return False
    flag = solve(nums)
    if not flag:
        return False, ""
    cache = defaultdict(list)
    for ns, op, v in record:
        for i in range(2):
            if cache[ns[i]]:
                ns[i] = "("+cache[ns[i]].pop()+")"
        a, b = ns
        cache[v].append(f"{a}{op}{b}")
    return flag, cache[24][0]+"=24"

total = cnt = 0
for nums in combinations_with_replacement(range(1, 10), 4):
    total += 1
    r, expression = judgePoint24(nums)
    if r:
        print(expression, end="\t")
        cnt += 1
        if cnt % 8 == 0:
            print()
print()
print(f'{cnt}/{total}={cnt/total:.2%}')