LeetCode #728 — EASY

Self Dividing Numbers

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

The Problem

Problem Statement

A self-dividing number is a number that is divisible by every digit it contains.

For example, 128 is a self-dividing number because 128 % 1 == 0, 128 % 2 == 0, and 128 % 8 == 0.

A self-dividing number is not allowed to contain the digit zero.

Given two integers left and right, return a list of all the self-dividing numbers in the range [left, right] (both inclusive).

Example 1:

Input: left = 1, right = 22
Output: [1,2,3,4,5,6,7,8,9,11,12,15,22]

Example 2:

Input: left = 47, right = 85
Output: [48,55,66,77]

Constraints:

1 <= left <= right <= 10⁴

Step 01

Brute Force Baseline

Problem summary: A self-dividing number is a number that is divisible by every digit it contains. For example, 128 is a self-dividing number because 128 % 1 == 0, 128 % 2 == 0, and 128 % 8 == 0. A self-dividing number is not allowed to contain the digit zero. Given two integers left and right, return a list of all the self-dividing numbers in the range [left, right] (both inclusive).

Baseline thinking

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

Pattern signal: Math

Example 1

1
22

Example 2

47
85

Core Insight

What unlocks the optimal approach

For each number in the range, check whether it is self dividing by converting that number to a character array (or string in Python), then checking that each digit is nonzero and divides the original number.

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 #728: Self Dividing Numbers
class Solution {
    public List<Integer> selfDividingNumbers(int left, int right) {
        List<Integer> ans = new ArrayList<>();
        for (int x = left; x <= right; ++x) {
            if (check(x)) {
                ans.add(x);
            }
        }
        return ans;
    }

    private boolean check(int x) {
        for (int y = x; y > 0; y /= 10) {
            if (y % 10 == 0 || x % (y % 10) != 0) {
                return false;
            }
        }
        return true;
    }
}

// Accepted solution for LeetCode #728: Self Dividing Numbers
func selfDividingNumbers(left int, right int) (ans []int) {
	check := func(x int) bool {
		for y := x; y > 0; y /= 10 {
			if y%10 == 0 || x%(y%10) != 0 {
				return false
			}
		}
		return true
	}
	for x := left; x <= right; x++ {
		if check(x) {
			ans = append(ans, x)
		}
	}
	return
}

# Accepted solution for LeetCode #728: Self Dividing Numbers
class Solution:
    def selfDividingNumbers(self, left: int, right: int) -> List[int]:
        def check(x: int) -> bool:
            y = x
            while y:
                if y % 10 == 0 or x % (y % 10):
                    return False
                y //= 10
            return True

        return [x for x in range(left, right + 1) if check(x)]

// Accepted solution for LeetCode #728: Self Dividing Numbers
impl Solution {
    pub fn self_dividing_numbers(left: i32, right: i32) -> Vec<i32> {
        fn check(x: i32) -> bool {
            let mut y = x;
            while y > 0 {
                if y % 10 == 0 || x % (y % 10) != 0 {
                    return false;
                }
                y /= 10;
            }
            true
        }

        (left..=right).filter(|&x| check(x)).collect()
    }
}

// Accepted solution for LeetCode #728: Self Dividing Numbers
function selfDividingNumbers(left: number, right: number): number[] {
    const check = (x: number): boolean => {
        for (let y = x; y; y = Math.floor(y / 10)) {
            if (y % 10 === 0 || x % (y % 10) !== 0) {
                return false;
            }
        }
        return true;
    };
    return Array.from({ length: right - left + 1 }, (_, i) => i + left).filter(check);
}

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(log n)

Space

O(1)

Approach Breakdown

ITERATIVE

O(n) time

O(1) space

Simulate the process step by step — multiply n times, check each number up to n, or iterate through all possibilities. Each step is O(1), but doing it n times gives O(n). No extra space needed since we just track running state.

MATH INSIGHT

O(log n) time

O(1) space

Math problems often have a closed-form or O(log n) solution hidden behind an O(n) simulation. Modular arithmetic, fast exponentiation (repeated squaring), GCD (Euclidean algorithm), and number theory properties can dramatically reduce complexity.

Shortcut: Look for mathematical properties that eliminate iteration. Repeated squaring → O(log n). Modular arithmetic avoids overflow.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Overflow in intermediate arithmetic

Wrong move: Temporary multiplications exceed integer bounds.

Usually fails on: Large inputs wrap around unexpectedly.

Fix: Use wider types, modular arithmetic, or rearranged operations.