Binary Prefix Divisible By 5

April 30, 2019

Introduction

Given an array A of 0s and 1s, consider N_i: the i-th subarray from A[0] to A[i] interpreted as a binary number (from most-significant-bit to least-significant-bit.)

Return a list of booleans answer, where answer[i] is true if and only if N_i is divisible by 5.

Example 1:

Input: [0,1,1]
Output: [true,false,false]
Explanation: 
The input numbers in binary are 0, 01, 011; which are 0, 1, and 3 in base-10.  Only the first number is divisible by 5, so answer[0] is true.

Example 2:

Input: [1,1,1]
Output: [false,false,false]

Example 3:

Input: [0,1,1,1,1,1]
Output: [true,false,false,false,true,false]

Example 4:

Input: [1,1,1,0,1]
Output: [false,false,false,false,false]

Note:

1 <= A.length <= 30000
A[i] is 0 or 1

Solution

Golang:

func prefixesDivBy5(A []int) []bool {

    ret := []bool{}
    v := 0
    
    for _, a := range A {
        v <<= 1
        v = (v + a) % 5
        ret = append(ret, v == 0)
    }
    
    return ret
}

Explanation

The only one catch in this problem is overflow. In order to prevent overflow of int, we need only to keep the reminder of division on 5.