From 726846a294607dda80fd3909511f814628d71cb6 Mon Sep 17 00:00:00 2001 From: beombu Date: Thu, 9 Jun 2022 17:39:28 +0900 Subject: [PATCH 1/2] add : select, bubble, insert, quick Sort --- 12/beom/Sorting.md | 141 +++++++++++++++++++++++++++++++++++++ 12/beom/assets/bubble.gif | Bin 0 -> 1186832 bytes 12/beom/assets/insert.gif | Bin 0 -> 1026440 bytes 12/beom/assets/quick.gif | Bin 0 -> 826250 bytes 12/beom/assets/select.png | Bin 0 -> 23403 bytes 12/beom/assets/select2.gif | Bin 0 -> 1360997 bytes 6 files changed, 141 insertions(+) create mode 100644 12/beom/Sorting.md create mode 100644 12/beom/assets/bubble.gif create mode 100644 12/beom/assets/insert.gif create mode 100644 12/beom/assets/quick.gif create mode 100644 12/beom/assets/select.png create mode 100644 12/beom/assets/select2.gif diff --git a/12/beom/Sorting.md b/12/beom/Sorting.md new file mode 100644 index 0000000..71a3e15 --- /dev/null +++ b/12/beom/Sorting.md @@ -0,0 +1,141 @@ +# 정렬 + +## 정렬 알고리즘이란 +정렬 알고리즘은 n개의 숫자가 입력으로 주어졌을 때, 이를 사용작다 지정한 기준에 맞게 정렬하여 출력하는 알고리즘이다. + +예를 들어 n개의 숫자가 저장되어있는 배열을, 오름차순의 조건으로 작성하여 입력하면 오름차순으로 정렬된 배열을 출력으로 구할수 있다. + +정렬 알고리즘은 정말 다양하고, 이에 따라 각각의 수행시간도 차이가 크다. + + +## 정렬 알고리즘 선택 기준 +1. 정렬할 데이터의 양 +2. 데이터와 메모리 +3. 이미 정렬된 정도 +4. 필요한 추가 메모리의 양 +5. 상대위치 보존여부 + +따라서 여러 정렬 알고리즘 중 알맞은 알고리즘을 사용해야 한다. + +## 버블 정렬(Bubble Sort) +> 인접한 두 개의 원소를 비교해서 자리를 교환하는 방식 + +### 동작과정 +1. 1회전에 첫 번째 원소와 두 번째 원소를, 두 번째 원소와 세번째 원소를... 이런식으로 (마지막-1)번째 원소와 마지막 원소를 비교하여 조건에 맞지 않는다면 서로를 교환한다. +2. `1번`이 수행되면 가장 큰 원소가 맨 뒤로 이동하므로 2회전에서는 맨 끝에 있는 원소는 제외하고, 2회전을 수행한다. 이렇게하면 (마지막-1)번째 원소가 정해진다. +3. 이 과정을 배열의 인덱스만큼 수행한다. + +![버블 정렬](assets/bubble.gif) + +### 시공간복잡도 +| 시간복잡도 | 공간복잡도 | +|---|---| +| O(n^2) | O(1) | + +### 장단점 +- 장점 + - 알고리즘이 단순하다. + - 정렬하고자하는 배열안에서 교환하는 방식으로 다른 메모리 공간이 필요로 하지 않는다.=> **제자리 정렬(in-place-sorting)** + - 안정 정렬(Stable Sort)이다. +- 단점 + - 시간복잡도가 크다. + - 정렬을 하기 위한 교환연산이 많이 일어난다. + +### 최적화 +```text +Initial: [1, 2, 3, 5, 4] + + Pass 1: [1, 2, 3, 4, 5] => Swap 있었음 + * + Pass 2: [1, 2, 3, 4, 5] => Swap 없었음 + * * +=> 이전 패스에서 swap이 한 번도 없었으니 종료 +``` + +조건문을 통해 스왑이 없는 경우 회전을 나가서 시간복잡도를 줄일 수 있다. + + +## 선택 정렬(Selection Sort) +> 선택 정렬은 현재 위치에 들어갈 값을 찾아 정렬하는 배열이다. + +### 동작 과정 +1. 정렬되지 않은 인덱스의 맨 앞에서부터, 이를 포함한 그 이후의 배열값 중 `최솟값`을 찾는다. +2. 최솟값을 찾으면, 그 값을 현재 인덱스의 값과 바꾼다. +3. 인덱스를 하나 뒤로 미루고, 위에 `1번`과 `2번`을 배열이 끝날 때까지 반복한다. + +![선택 정렬](assets/select.png) +![선택 정렬](assets/select2.gif) + +### 시공간복잡도 +| 시간복잡도 | 공간복잡도 | +|---|---| +| O(n^2) | O(1) | + +### 장단점 +- 장점 + - 알고리즘이 단순하다. + - 정렬을 위한 비교 횟수는 많지만, 인덱스가 증가할수록 점점 비교 횟수가 줄어들어 버블정렬에 비해 효율적이다. + - 정렬하고자하는 배열안에서 교환하는 방식으로 다른 메모리 공간이 필요로 하지 않는다.=> **제자리 정렬(in-place-sorting)** +- 단점 + - 시간복잡도가 크다. + - **불안정 정렬(Unstable Sort)**이다. + + + +## 삽입 정렬(Insertion Sort) +> 삽입 정렬은 현재 위치에서, 그 이하의 배열들을 비교하여 자신이 들어갈 위치를 찾아 그 위치에 삽입하는 알고리즘이다. + +### 동작 과정 +1. 삽입 정렬은 두 번째 인덱스부터 시작한다. 현재 인덱스는 별도의 변수에 저장해주고, 비교 인덱스를 현재 인덱스-1로 잡는다. +2. 별도로 저장해 둔 삽입을 위한 변수와, 비교 인덱스의 배열의 값을 비교한다. +3. 삽입 변수의 값이 더 작으면 현재 인덱스로 비교 인덱스의 값을 저장해주고, 비교 인덱스를 -1하여 비교를 반복한다. +4. 만약 삽입 변수가 더 크면, 비교 인덱스+1에 삽입 변수를 저장한다. + +![삽입 정렬](assets/insert.gif) + +### 시공간복잡도 +| 시간복잡도 | 공간복잡도 | +|---|---| +| O(n^2) | O(1) | + +### 장단점 +- 장점 + - 대부분의 원소가 이미 정렬되어 있는 경우, 최선의 시간복잡도가 O(n)으로 효율적이다. + - 제자리 정렬이다.(다른 메모리 공간 사용 x) + - 안정 정렬이다. +- 단점 + - 평균과 최악의 시간복잡도가 O(n^2)으로 비효율적 + - 비열이 길어질 수록 비효율적이다. + + + +## 퀵 정렬(Quick Sort) +> **분할 정복 방법**을 통해 주어진 배열을 정렬한다. +- 분할 정렬 방법 : 문제를 2개의 작은 문제로 분리하고 각각을 해결한 다음, 결과를 모아서 원래의 문제를 해결하는 전략. + +### 동작과정 +1. pivot point로 잡을 배열의 값 하나를 정한다. 보통 맨 앞이나 맨 뒤, 혹은 전체 배열 값 중 중간값이나 랜덤 값으로 정한다. +2. 분할을 진행하기에 앞서, 비교를 진행하기 위해 가장 왼쪽 배열의 인덱스를 저장하는 left변수, 가장 오른쪽 배열의 인덱스를 저장한 right변수를 생성한다. +3. right부터 비교를 진행한다. 비교는 right가 left보다 클 때만 반복하며, 비교한 배열값이 pivot point보다 크면 right를 하나 감소시키고 비교를 반복한다. +pivot point보다 작은 배열 값을 찾으면, 반복을 중지한다. +4. 그 다음 left부터 비교를 진행한다. 비교는 right가 left보다 클 때만 반복하며, 비교한 배열값이 pivot point보다 작으면 left를 하나 증가시키고 비교를 반복한다. +pivot point보다 큰 배열 값을 찾으면, 반복을 중지한다. +5. left인덱스의 값과 rigft인덱스의 값을 바꿔준다. +6. 3,4,5 과정을 left < right가 만족할 때까지 반복한다. +7. 위 과정이 끝나면 left의 값과 pivot point를 바꿔준다. +8. 맨 왼쪽부터 left-1까지, left+1부터 맨 오른쪽까지는 나눠 퀵 정렬을 반복한다. + +![퀵 정렬](assets/quick.gif) + +### 시공간복잡도 +| 시간복잡도 | 공간복잡도 | +|---|---| +| O(n log n) | O(1) | + +### 장단점 +- 장점 + - 불필요한 데이터의 이동을 줄이고 먼 거리의 데이터를 교환할 뿐만 아니라, 한 번 결정된 피벗들이 추후 연산에서 제외되는 득성 때문에 시간복잡도가 O(n log n)으로 빠르다. + - 제자리 정렬이다.(다른 메모리 공간 사용 x) +- 단점 + - 정렬된 배열에 대해서는 퀵정렬의 불균형 분할에 의해 시간복잡도가 증가한다. + - 불안정 정렬이다. \ No newline at end of file diff --git a/12/beom/assets/bubble.gif b/12/beom/assets/bubble.gif new file mode 100644 index 0000000000000000000000000000000000000000..a7679ddf18d2b13e83b3bda320adb6fd14d1d407 GIT binary patch literal 1186832 zcmeF(RZyE<^eFrgk`Ub8-6`(wUaVMw0>!OCi?&IypvB$Y3lw+PQk>$&3$#$6Ek)YA zC;#ueI9KQPT%C2bXU{XUXV%OkYwz`Yv~)D3WgPafvH*VofUe3{5VL1t(zn>?*ph{kemqUX;Onfn;$h#fQz~g3ekeIl%j^qt=c6{*|pa z<7He70P!raQkX3bGxhc5^^fb@k%QCk7Z>zwf@44Kd@^ltGeGHceNmIO)Wp7 z<*k(-Fujma3CqJ$*pG{gf}U}%629m{uwc0uSuzn$K5)HM{Nmz5O2=3*kbi8d?7kA~ zcO|rabtfPORlNLh`s6IZ+?Bd{8qWR^6mQm 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