AcWing 数位DP相关问题 1082. 数字游戏

import sys
from functools import lru_cache
sys.stdin = open('data.txt', 'r')


# 小于等于n的符合条件的数字个数
def get_num(n):

    if n == 0:
        return 1

    arr = []
    val = n
    while val:
        arr.append(val % 10)
        val //= 10

    # 前i位做选择，更高的一位选择数值是higher_val且更高的所有位都选择了最大值的标志是all_higher_max的约束下，合法的数值的个数
    @lru_cache(typed=False, maxsize=128000000)
    def dp(i, higher_val, all_higer_max):
        if i == 0:
            low_bound, up_bound = higher_val, arr[i] if all_higer_max else 9
            return max(0, up_bound - low_bound + 1)
        else:
            low_bound, up_bound = higher_val, arr[i] if all_higer_max else 9
            if low_bound > up_bound:
                return 0

            ans = 0
            for cur_val in range(low_bound, up_bound+1):
                ans += dp(i-1, cur_val, all_higer_max and cur_val == arr[i])
            return ans

    return dp(len(arr)-1, 0, True)

while True:
    try:
        a, b = map(int, input().split())
    except:
        break

    print( get_num(b) - get_num(a-1) )