2713. Find the Divisibility Array of a String

Medium
Array
Math
String

Description

You are given a 0-indexed string word of length n consisting of digits, and a positive integer m.

The divisibility array div of word is an integer array of length n such that:

  • div[i] = 1 if the numeric value of word[0,...,i] is divisible by m, or
  • div[i] = 0 otherwise.

Return the divisibility array of word.

 

Example 1:

Input: word = "998244353", m = 3
Output: [1,1,0,0,0,1,1,0,0]
Explanation: There are only 4 prefixes that are divisible by 3: "9", "99", "998244", and "9982443".

Example 2:

Input: word = "1010", m = 10
Output: [0,1,0,1]
Explanation: There are only 2 prefixes that are divisible by 10: "10", and "1010".

 

Constraints:

  • 1 <= n <= 105
  • word.length == n
  • word consists of digits from 0 to 9
  • 1 <= m <= 109

Hints

Hint 1
We can check if the numeric value of the prefix of the given string is divisible by m by computing the remainder of the numeric value of the prefix when divided by m.
Hint 2
The remainder of the numeric value of a prefix ending at index i can be computed from the remainder of the prefix ending at index i-1.

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