Leetcode 3756. Concatenate Non-Zero Digits and Multiply by Sum II

• Leetcode 3756. Concatenate Non-Zero Digits and Multiply by Sum II
  • 1. 解题思路
  • 2. 代码实现

• 题目链接：3756. Concatenate Non-Zero Digits and Multiply by Sum II

1. 解题思路

这一题是Leetcode周赛477的第三题，是一道medium的题目，也是题目3754. Concatenate Non-Zero Digits and Multiply by Sum I的进阶版。

这一题的话，我们只需要求出每一个位置上对应的后续有效数字对于$10^9+7$的模，这样，我们要求出对以一个区间的数字，只需要将对其左右区间范围的两个数相减，然后除以$10^m$即可，其中$m$为右边界对应的$10$的阶数。

2. 代码实现

给出python代码实现如下：

MOD = 10**9+7

class Solution:
    def sumAndMultiply(self, s: str, queries: List[List[int]]) -> List[int]:
        n = len(s)
        remains = [0 for _ in range(n+1)]
        powers = [1 for _ in range(n+1)]
        tot = [0 for _ in range(n+1)]
        flag = 1
        for i in range(n-1, -1, -1):
            digit = int(s[i])
            tot[i] = tot[i+1] + digit
            if digit == 0:
                remains[i] = remains[i+1]
                powers[i] = powers[i+1]
            else:
                remains[i] = (remains[i+1] + digit * flag) % MOD
                flag = (flag * 10) % MOD
                powers[i] = (powers[i+1] * pow(10, -1, MOD)) % MOD

        def query(i, j):
            return (remains[i] - remains[j+1]) * powers[j+1] * (tot[i] - tot[j+1]) % MOD

        return [query(i,j) for i, j in queries]

提交代码评测得到：耗时767ms，占用内存52.30MB。