알고리즘 읽기 노트

Euclidean Algorithm

Euclid's algorithm finds gcd(a, b) by repeatedly replacing (a, b) with (b, a mod b) until the remainder becomes zero.

유형알고리즘카테고리Math깊이초급일반적인 복잡도O(log min(a,b))

짧은 면접 답변

이 멘탈 모델부터 시작하세요

Euclid's algorithm finds gcd(a, b) by repeatedly replacing (a, b) with (b, a mod b) until the remainder becomes zero.

간단한 설명

불필요한 전문용어 없이 동작 방식 이해하기

The key property is gcd(a, b) = gcd(b, a mod b).

It is much faster than checking every possible divisor.

실행

알고리즘을 연속된 의사결정으로 읽기

State the mathematical identity/property.

Choose numeric representation and constraints.

Translate the property into an iterative/recursive computation and analyze precision.

기억해 둘 작은 예제

Read a tiny input by hand and write down the state after every important operation. For Euclidean Algorithm, the goal is to make the invariant visible rather than to memorize code.

읽기 쉬운 JavaScript 구현JavaScript

function gcd(a, b) {
  a = Math.abs(a);
  b = Math.abs(b);
  while (b !== 0) {
    [a, b] = [b, a % b];
  }
  return a;
}

이 코드를 읽는 방법

문법을 외우지 마세요. 각 줄에서 바뀌는 상태를 따라가고 위에서 설명한 불변식과 연결하세요.

복잡도

O(log min(a,b))

Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.

언제 사용하는가

적합한 경우

Use the direct mathematical property when it removes unnecessary brute force.

흔한 실수

보통 어디에서 문제가 생기는가

Ignoring floating-point precision or integer range.
Using a formula outside its valid assumptions.

면접에서 설명하는 방법

전문적인 답변 구조

Explain the invariant/property behind the modulo step; do not present it as a magic loop.

문제→핵심 아이디어→불변식 / 상태→Big-O→트레이드오프

빠른 면접 체크

What problem does Euclidean Algorithm solve?

Euclid's algorithm finds gcd(a, b) by repeatedly replacing (a, b) with (b, a mod b) until the remainder becomes zero.

복잡도에 대해 무엇을 언급해야 하나요?

Its typical cost here is O(log min(a,b)), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

가장 흔한 실수는 무엇인가요?

Ignoring floating-point precision or integer range.

계속 읽기Number theoryNumerical precisionRecurrences

알고리즘 읽기 노트

Euclidean Algorithm

Euclid's algorithm finds gcd(a, b) by repeatedly replacing (a, b) with (b, a mod b) until the remainder becomes zero.

유형알고리즘카테고리Math깊이초급일반적인 복잡도O(log min(a,b))

짧은 면접 답변

이 멘탈 모델부터 시작하세요

Euclid's algorithm finds gcd(a, b) by repeatedly replacing (a, b) with (b, a mod b) until the remainder becomes zero.

간단한 설명

불필요한 전문용어 없이 동작 방식 이해하기

The key property is gcd(a, b) = gcd(b, a mod b).

It is much faster than checking every possible divisor.

실행

알고리즘을 연속된 의사결정으로 읽기

State the mathematical identity/property.

Choose numeric representation and constraints.

Translate the property into an iterative/recursive computation and analyze precision.

기억해 둘 작은 예제

Read a tiny input by hand and write down the state after every important operation. For Euclidean Algorithm, the goal is to make the invariant visible rather than to memorize code.

읽기 쉬운 JavaScript 구현JavaScript

function gcd(a, b) {
  a = Math.abs(a);
  b = Math.abs(b);
  while (b !== 0) {
    [a, b] = [b, a % b];
  }
  return a;
}

이 코드를 읽는 방법

문법을 외우지 마세요. 각 줄에서 바뀌는 상태를 따라가고 위에서 설명한 불변식과 연결하세요.

복잡도

O(log min(a,b))

언제 사용하는가

적합한 경우

Use the direct mathematical property when it removes unnecessary brute force.

흔한 실수

보통 어디에서 문제가 생기는가

Ignoring floating-point precision or integer range.
Using a formula outside its valid assumptions.

면접에서 설명하는 방법

전문적인 답변 구조

Explain the invariant/property behind the modulo step; do not present it as a magic loop.

문제→핵심 아이디어→불변식 / 상태→Big-O→트레이드오프

빠른 면접 체크

What problem does Euclidean Algorithm solve?

Euclid's algorithm finds gcd(a, b) by repeatedly replacing (a, b) with (b, a mod b) until the remainder becomes zero.

복잡도에 대해 무엇을 언급해야 하나요?

Its typical cost here is O(log min(a,b)), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.

가장 흔한 실수는 무엇인가요?

Ignoring floating-point precision or integer range.

계속 읽기Number theoryNumerical precisionRecurrences