#3270

Easy

auto_awesomeMath-driven solution strategy

LeetCode Problem Workspace

Find the Key of the Numbers

Determine the four-digit key from three given numbers using a precise math-driven approach for exact digit alignment.

Problem Statement

You are given three positive integers num1, num2, and num3, each at most four digits. Your task is to compute a four-digit key by analyzing corresponding digits across all numbers.

The key is created by comparing each digit position: if all digits in the same position are equal, that digit is retained; otherwise, it is replaced with zero. Return the key as an integer without leading zeros.

Examples

Example 1

Input: num1 = 1, num2 = 10, num3 = 1000

Output: 0

On padding, num1 becomes "0001" , num2 becomes "0010" , and num3 remains "1000" . Hence, the key is "0000" , i.e. 0.

Example 2

Input: num1 = 987, num2 = 879, num3 = 798

Output: 777

Example details omitted.

Example 3

Input: num1 = 1, num2 = 2, num3 = 3

Output: 1

Example details omitted.

Constraints

1 <= num1, num2, num3 <= 9999

Solution Approach

Normalize Numbers to Four Digits

Convert each number to a string and pad with leading zeros to ensure four-digit length. This guarantees correct alignment for digit-by-digit comparison.

Compare Digits Across Numbers

Iterate through each of the four positions. If num1, num2, and num3 share the same digit at a position, keep it; otherwise, assign zero. Build the key string from these results.

Convert Key String to Integer

Once the key string is formed, convert it to an integer to remove any leading zeros. Return this integer as the final key output.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(1) since there are exactly four digits to process. Space complexity is O(1) as only fixed-length strings and the resulting integer are stored.

What Interviewers Usually Probe

Are you correctly handling numbers with fewer than four digits by padding zeros?
Can you explain how digit comparison at each position ensures correctness?
How would your solution scale if numbers had more than four digits?

Common Pitfalls or Variants

Common pitfalls

Forgetting to pad numbers leads to misaligned digit comparisons.
Returning a string instead of an integer may produce leading zeros incorrectly.
Assuming input numbers always have identical digit lengths without normalization.

Follow-up variants

Compute the key for n numbers instead of three, still using digit-by-digit comparison.
Return the key as a string preserving all leading zeros instead of converting to integer.
Use a modulus and division approach to extract digits instead of string conversion for comparison.

FAQ

What exactly is the key in Find the Key of the Numbers?

The key is a four-digit number formed by comparing each corresponding digit of the three numbers. If digits match, retain them; otherwise, use zero.

Do I need to handle leading zeros in the output?

No, convert the resulting key string to an integer to remove any leading zeros before returning.

Can this method be extended to more than three numbers?

Yes, the same digit-by-digit comparison approach works for n numbers, taking zero whenever any digit differs.

Is string conversion necessary for this problem?

String conversion simplifies digit alignment and comparison, but numeric operations using division and modulus are also valid.

Why is this considered a math-driven solution pattern?

Because the solution relies on precise digit-level arithmetic and comparison rather than iterative search or brute force, following a defined mathematical pattern.

terminal

Solution

Solution 1: Simulation

We can directly simulate this process by defining a variable $\textit{ans}$ to store the answer and a variable $\textit{k}$ to represent the current digit place, where $\textit{k} = 1$ represents the units place, $\textit{k} = 10$ represents the tens place, and so on.

1

2

3

4

5

6

7

8

class Solution:
    def generateKey(self, num1: int, num2: int, num3: int) -> int:
        ans, k = 0, 1
        for _ in range(4):
            x = min(num1 // k % 10, num2 // k % 10, num3 // k % 10)
            ans += x * k
            k *= 10
        return ans

Continue Practicing

#3272 find the count of good integers #3274 check if two chessboard squares have the same color #3264 final array state after k multiplication operations i