LeetCode #1018 — EASY

Binary Prefix Divisible By 5

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

You are given a binary array nums (0-indexed).

We define x_i as the number whose binary representation is the subarray nums[0..i] (from most-significant-bit to least-significant-bit).

For example, if nums = [1,0,1], then x₀ = 1, x₁ = 2, and x₂ = 5.

Return an array of booleans answer where answer[i] is true if x_i is divisible by 5.

Example 1:

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

Constraints:

1 <= nums.length <= 10⁵
nums[i] is either 0 or 1.

Step 01

Brute Force Baseline

Problem summary: You are given a binary array nums (0-indexed). We define xi as the number whose binary representation is the subarray nums[0..i] (from most-significant-bit to least-significant-bit). For example, if nums = [1,0,1], then x0 = 1, x1 = 2, and x2 = 5. Return an array of booleans answer where answer[i] is true if xi is divisible by 5.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Bit Manipulation

Example 1

[0,1,1]

Example 2

[1,1,1]

Core Insight

What unlocks the optimal approach

If X is the first i digits of the array as a binary number, then 2X + A[i] is the first i+1 digits.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1018: Binary Prefix Divisible By 5
class Solution {
    public List<Boolean> prefixesDivBy5(int[] nums) {
        List<Boolean> ans = new ArrayList<>();
        int x = 0;
        for (int v : nums) {
            x = (x << 1 | v) % 5;
            ans.add(x == 0);
        }
        return ans;
    }
}

// Accepted solution for LeetCode #1018: Binary Prefix Divisible By 5
func prefixesDivBy5(nums []int) (ans []bool) {
	x := 0
	for _, v := range nums {
		x = (x<<1 | v) % 5
		ans = append(ans, x == 0)
	}
	return
}

# Accepted solution for LeetCode #1018: Binary Prefix Divisible By 5
class Solution:
    def prefixesDivBy5(self, nums: List[int]) -> List[bool]:
        ans = []
        x = 0
        for v in nums:
            x = (x << 1 | v) % 5
            ans.append(x == 0)
        return ans

// Accepted solution for LeetCode #1018: Binary Prefix Divisible By 5
struct Solution;

impl Solution {
    fn prefixes_div_by5(a: Vec<i32>) -> Vec<bool> {
        let mut x = 0;
        let n = a.len();
        let mut res: Vec<bool> = vec![false; n];
        for i in 0..n {
            x = (x * 2 + a[i]) % 5;
            res[i] = x == 0;
        }
        res
    }
}

#[test]
fn test() {
    let a = vec![0, 1, 1];
    let res = vec![true, false, false];
    assert_eq!(Solution::prefixes_div_by5(a), res);
    let a = vec![1, 1, 1];
    let res = vec![false, false, false];
    assert_eq!(Solution::prefixes_div_by5(a), res);
    let a = vec![0, 1, 1, 1, 1, 1];
    let res = vec![true, false, false, false, true, false];
    assert_eq!(Solution::prefixes_div_by5(a), res);
    let a = vec![1, 1, 1, 0, 1];
    let res = vec![false, false, false, false, false];
    assert_eq!(Solution::prefixes_div_by5(a), res);
}

// Accepted solution for LeetCode #1018: Binary Prefix Divisible By 5
function prefixesDivBy5(nums: number[]): boolean[] {
    const ans: boolean[] = [];
    let x = 0;
    for (const v of nums) {
        x = ((x << 1) | v) % 5;
        ans.push(x === 0);
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(1)

Approach Breakdown

SORT + SCAN

O(n log n) time

O(n) space

Sort the array in O(n log n), then scan for the missing or unique element by comparing adjacent pairs. Sorting requires O(n) auxiliary space (or O(1) with in-place sort but O(n log n) time remains). The sort step dominates.

BIT MANIPULATION

O(n) time

O(1) space

Bitwise operations (AND, OR, XOR, shifts) are O(1) per operation on fixed-width integers. A single pass through the input with bit operations gives O(n) time. The key insight: XOR of a number with itself is 0, which eliminates duplicates without extra space.

Shortcut: Bit operations are O(1). XOR cancels duplicates. Single pass → O(n) time, O(1) space.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.