From 59636d7b06428f6d750ccb290d2f66788eda82b4 Mon Sep 17 00:00:00 2001 From: JiYongKim Date: Thu, 31 Mar 2022 01:40:40 +0900 Subject: [PATCH 1/8] Create Graph.md --- 07/JiYongKim/Graph.md | 94 +++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 94 insertions(+) create mode 100644 07/JiYongKim/Graph.md diff --git a/07/JiYongKim/Graph.md b/07/JiYongKim/Graph.md new file mode 100644 index 00000000..8a3ce5f8 --- /dev/null +++ b/07/JiYongKim/Graph.md @@ -0,0 +1,94 @@ +## 그래프란? + +그래프란 ,수학자 오일러가 만든 “그래프 이론” 의 개념을 기초로 구성된 자료구조 + +## 그래프의 용어 + +![스크린샷 2022-03-30 오후 8.39.10.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/6807d0d0-481b-4783-9e3b-067efa08b8b5/스크린샷_2022-03-30_오후_8.39.10.png) + +- 파란색 동그라미 : 정점 ( Vertex ) +- 검정색 실선 : 간선 ( Edge ) + +## 그래프의 종류 + +- 방향 그래프 + + ![스크린샷 2022-03-30 오후 8.41.07.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/31b9f2e7-7688-4360-b421-08f7614b50b6/스크린샷_2022-03-30_오후_8.41.07.png) + + - 방향 그래프는 간선의 방향이 존재하는 그래프 + - ex) + - SNS 팔로우 + - 5명의 유저 팔로우 관계에서 A → B → D 관계로 팔로우 하고 있다 + + ⇒ A는 B를 통해 D를 건너 볼 수 있다. + + + 즉 방향 그래프는 간선이 추가되면 + + - 한쪽 정점에서 다른 정점으로 이동은 가능 (A → B) + - 하지만 반대로의 이동은 불가능 ( B → A) + +- 무방향 그래프 + + ![스크린샷 2022-03-30 오후 8.46.16.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/92962061-0b53-4e0f-a095-b433e2f3693b/스크린샷_2022-03-30_오후_8.46.16.png) + + - 무방향 그래프는 간선의 방향이 없어 서로간 왕복이 가능한 그래프 + + +## 그래프의 구현 방식 + +그래프의 구현 방식에는 2가지 방식으로 나뉜다. + +- 인접 리스트 기반 그래프 + - 인접 리스트 기반 그래프는 연결 리스트 배열을 만들고 다음과 같이 표현한다. + + ![스크린샷 2022-03-30 오후 8.49.41.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/075656d4-c5c5-42c5-b1e6-ad19706a592d/스크린샷_2022-03-30_오후_8.49.41.png) + +- 인접 행렬 기반 그래프 + - 인접 행렬 기반 그래프는 이차원 배열을 만들고 + - 연결된 곳은 1 + - 연결되지 않은 곳은 -1 + + ⇒ 같이 표현한다. + + + ![스크린샷 2022-03-30 오후 8.49.56.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/f0c78c2d-5e7b-4754-9d8e-cf79003c0dff/스크린샷_2022-03-30_오후_8.49.56.png) + + +즉 그래프를 가지고 위의 2가지 방식으로 표현이 가능하다. + +### 번외) + +[https://m.blog.naver.com/PostView.naver?isHttpsRedirect=true&blogId=demonic3540&logNo=221227400125](https://m.blog.naver.com/PostView.naver?isHttpsRedirect=true&blogId=demonic3540&logNo=221227400125) + +### ADT(Abstract Data Type) 란?? + +ADT의 정의 : **순수하게 기능이 무엇인지를 나열한 것을 가리켜 '추상 자료형' 혹은 ADT라고 한다.** + +### ADT의 사용 사례 + +C언어    + +- 구조체를 통해 사용자 정의 자료형이 정의된다. 지갑의 예를 들어보자. + + ![https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMzcg/MDAxNTIwODUzNzI1NTA1.0cB6D2CC6cz4LJEVL4v6p3pPK80L4DNndbCN7KUQINwg.dh8cvREwEIIXAd65WjiZ0FIhmAJluWodIQ4HwPAfNEgg.PNG.demonic3540/image.png?type=w800](https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMzcg/MDAxNTIwODUzNzI1NTA1.0cB6D2CC6cz4LJEVL4v6p3pPK80L4DNndbCN7KUQINwg.dh8cvREwEIIXAd65WjiZ0FIhmAJluWodIQ4HwPAfNEgg.PNG.demonic3540/image.png?type=w800) + + +- 위의 구조체 정의를 통해 Wallet 자료형을 정의하고 속성으로 500원 동전, 1000원 지폐가 몇 개 담겨 있느냐를 표현하였다.(그러나 Wallet자료형에는 돈을 빼는 것, 돈을 넣는 것 이라는 기능이 있을 수 있다.) + + ![https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMjU4/MDAxNTIwODUzODQ2MDQy.hpFuhI-mGb_SXqqxAVVEDLHY0T1bw5q_3fo0NTnRH3og.dT_ktwEIxxLDXowFMcG9vv7X5NwRV8IP8WmszwmsTYUg.PNG.demonic3540/image.png?type=w800](https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMjU4/MDAxNTIwODUzODQ2MDQy.hpFuhI-mGb_SXqqxAVVEDLHY0T1bw5q_3fo0NTnRH3og.dT_ktwEIxxLDXowFMcG9vv7X5NwRV8IP8WmszwmsTYUg.PNG.demonic3540/image.png?type=w800) + + ⇒ 이 기능들을 담고 있는 함수가 구조체 아래의 두 함수이다. + + +**결론)** + +자료구조(연결리스트, 스택, 큐 등)의 ADT는 + +- data를 담을 저장소를 만드는 것과 +- data를 다루는 함수들을 정의하는 것을 + + ⇒ 포함하는 개념인 것이다. + + +**즉, 특정 자료형과 그 자료형을 바탕으로 하는 기능들(함수들)의 집합을 ADT라고 하는 것!** \ No newline at end of file From f59fa39d67ef23b1b2c07ff51328d2f4ba0ac246 Mon Sep 17 00:00:00 2001 From: JiYong Kim <81874493+JiYongKim-A@users.noreply.github.com> Date: Thu, 31 Mar 2022 01:44:57 +0900 Subject: [PATCH 2/8] Update Graph.md --- 07/JiYongKim/Graph.md | 32 +++++++++++++++++--------------- 1 file changed, 17 insertions(+), 15 deletions(-) diff --git a/07/JiYongKim/Graph.md b/07/JiYongKim/Graph.md index 8a3ce5f8..60a41b55 100644 --- a/07/JiYongKim/Graph.md +++ b/07/JiYongKim/Graph.md @@ -4,7 +4,7 @@ ## 그래프의 용어 -![스크린샷 2022-03-30 오후 8.39.10.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/6807d0d0-481b-4783-9e3b-067efa08b8b5/스크린샷_2022-03-30_오후_8.39.10.png) +스크린샷 2022-03-31 오전 1 41 52 - 파란색 동그라미 : 정점 ( Vertex ) - 검정색 실선 : 간선 ( Edge ) @@ -13,8 +13,8 @@ - 방향 그래프 - ![스크린샷 2022-03-30 오후 8.41.07.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/31b9f2e7-7688-4360-b421-08f7614b50b6/스크린샷_2022-03-30_오후_8.41.07.png) - + 스크린샷 2022-03-31 오전 1 42 01 + - 방향 그래프는 간선의 방향이 존재하는 그래프 - ex) - SNS 팔로우 @@ -30,8 +30,8 @@ - 무방향 그래프 - ![스크린샷 2022-03-30 오후 8.46.16.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/92962061-0b53-4e0f-a095-b433e2f3693b/스크린샷_2022-03-30_오후_8.46.16.png) - + 스크린샷 2022-03-31 오전 1 42 06 + - 무방향 그래프는 간선의 방향이 없어 서로간 왕복이 가능한 그래프 @@ -42,8 +42,8 @@ - 인접 리스트 기반 그래프 - 인접 리스트 기반 그래프는 연결 리스트 배열을 만들고 다음과 같이 표현한다. - ![스크린샷 2022-03-30 오후 8.49.41.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/075656d4-c5c5-42c5-b1e6-ad19706a592d/스크린샷_2022-03-30_오후_8.49.41.png) - + 스크린샷 2022-03-31 오전 1 42 12 + - 인접 행렬 기반 그래프 - 인접 행렬 기반 그래프는 이차원 배열을 만들고 - 연결된 곳은 1 @@ -52,8 +52,8 @@ ⇒ 같이 표현한다. - ![스크린샷 2022-03-30 오후 8.49.56.png](https://s3-us-west-2.amazonaws.com/secure.notion-static.com/f0c78c2d-5e7b-4754-9d8e-cf79003c0dff/스크린샷_2022-03-30_오후_8.49.56.png) - + 스크린샷 2022-03-31 오전 1 42 18 + 즉 그래프를 가지고 위의 2가지 방식으로 표현이 가능하다. @@ -67,17 +67,19 @@ ADT의 정의 : **순수하게 기능이 무엇인지를 나열한 것을 가리 ### ADT의 사용 사례 -C언어    +C언어 - 구조체를 통해 사용자 정의 자료형이 정의된다. 지갑의 예를 들어보자. - ![https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMzcg/MDAxNTIwODUzNzI1NTA1.0cB6D2CC6cz4LJEVL4v6p3pPK80L4DNndbCN7KUQINwg.dh8cvREwEIIXAd65WjiZ0FIhmAJluWodIQ4HwPAfNEgg.PNG.demonic3540/image.png?type=w800](https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMzcg/MDAxNTIwODUzNzI1NTA1.0cB6D2CC6cz4LJEVL4v6p3pPK80L4DNndbCN7KUQINwg.dh8cvREwEIIXAd65WjiZ0FIhmAJluWodIQ4HwPAfNEgg.PNG.demonic3540/image.png?type=w800) - + + 스크린샷 2022-03-31 오전 1 42 24 + - 위의 구조체 정의를 통해 Wallet 자료형을 정의하고 속성으로 500원 동전, 1000원 지폐가 몇 개 담겨 있느냐를 표현하였다.(그러나 Wallet자료형에는 돈을 빼는 것, 돈을 넣는 것 이라는 기능이 있을 수 있다.) - ![https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMjU4/MDAxNTIwODUzODQ2MDQy.hpFuhI-mGb_SXqqxAVVEDLHY0T1bw5q_3fo0NTnRH3og.dT_ktwEIxxLDXowFMcG9vv7X5NwRV8IP8WmszwmsTYUg.PNG.demonic3540/image.png?type=w800](https://mblogthumb-phinf.pstatic.net/MjAxODAzMTJfMjU4/MDAxNTIwODUzODQ2MDQy.hpFuhI-mGb_SXqqxAVVEDLHY0T1bw5q_3fo0NTnRH3og.dT_ktwEIxxLDXowFMcG9vv7X5NwRV8IP8WmszwmsTYUg.PNG.demonic3540/image.png?type=w800) - + + 스크린샷 2022-03-31 오전 1 42 32 + ⇒ 이 기능들을 담고 있는 함수가 구조체 아래의 두 함수이다. @@ -91,4 +93,4 @@ C언어    ⇒ 포함하는 개념인 것이다. -**즉, 특정 자료형과 그 자료형을 바탕으로 하는 기능들(함수들)의 집합을 ADT라고 하는 것!** \ No newline at end of file +**즉, 특정 자료형과 그 자료형을 바탕으로 하는 기능들(함수들)의 집합을 ADT라고 하는 것!** From 557fbd3729df2f435f88c7e41131137c435ede75 Mon Sep 17 00:00:00 2001 From: JiYongKim Date: Thu, 31 Mar 2022 01:46:00 +0900 Subject: [PATCH 3/8] Update Graph.md --- 07/JiYongKim/Graph.md | 1 - 1 file changed, 1 deletion(-) diff --git a/07/JiYongKim/Graph.md b/07/JiYongKim/Graph.md index 60a41b55..ff910a48 100644 --- a/07/JiYongKim/Graph.md +++ b/07/JiYongKim/Graph.md @@ -59,7 +59,6 @@ ### 번외) -[https://m.blog.naver.com/PostView.naver?isHttpsRedirect=true&blogId=demonic3540&logNo=221227400125](https://m.blog.naver.com/PostView.naver?isHttpsRedirect=true&blogId=demonic3540&logNo=221227400125) ### ADT(Abstract Data Type) 란?? From 9ffd0fb4db41705eab0df844d39e93dbba93ea3f Mon Sep 17 00:00:00 2001 From: JiYongKim Date: Sat, 16 Apr 2022 16:54:24 +0900 Subject: [PATCH 4/8] Create DFS_BFS.md --- 07/JiYongKim/DFS_BFS.md | 425 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 425 insertions(+) create mode 100644 07/JiYongKim/DFS_BFS.md diff --git a/07/JiYongKim/DFS_BFS.md b/07/JiYongKim/DFS_BFS.md new file mode 100644 index 00000000..dba800d7 --- /dev/null +++ b/07/JiYongKim/DFS_BFS.md @@ -0,0 +1,425 @@ +**※ 그래프 탐색** + +- 하나의 정점으로부터 시작하여 차례대로 모든 정점들을 한 번씩 방문하는 것 + +Ex) 특정 도시에서 다른 도시로 갈 수 있는지 없는지, 전자 회로에서 특정 단자와 단자가 서로 연결되어 있는지 + +
+ +**※ 깊이 우선 탐색 (DFS, Depth-First Search)의 개념** + +- 루트 노드(혹은 다른 임의의 노드)에서 시작해서 다음 분기(branch)로 넘어가기 전에 해당 분기를 완벽하게 탐색하는 방법 + +1. 미로를 탐색할 때 한 방향으로 갈 수 있을 때까지 계속 가다가 더 이상 갈 수 없게 되면 다시 가장 가까운 갈림길로 돌아와서 이곳으로부터 다른 방향으로 다시 탐색을 진행하는 방법과 유사함 + +2. 즉 넓게(wide) 탐색하기 전에 깊게(deep) 탐색함 + +**3. 모든 노드를 방문하고자 하는 경우에 이 방법을 선택함** + +4. 깊이 우선 탐색(DFS)이 너비 우선 탐색(BFS)보다 좀 더 간단함 + +5. 검색 속도 자체는 너비 우선 탐색(BFS)에 비해서 느림 + +
+ +**※ 깊이 우선 탐색(DFS)의 특징** + +- 자기 자신을 호출하는 순환 알고리즘의 형태를 지님 +- 이 알고리즘을 구현할 때 가장 큰 차이점은 그래프 탐색의 경우 어떤 노드를 방문했었는지 여부를 반드시 검사해야한다는 것 (이를 검사하지 않을 경우 무한루프에 빠질 위험이 있음) + +
+ +**※ 깊이 우선 탐색(DFS)의 과정** + +[https://t1.daumcdn.net/cfile/tistory/9983A7335BD0156910](https://t1.daumcdn.net/cfile/tistory/9983A7335BD0156910) + +
+ +**※ 깊이 우선 탐색(DFS)의 시간 복잡도** + +- DFS는 그래프(정점의 수 : N, 간선의 수: E)의 모든 간선을 조회함 +- 인접 리스트로 표현된 그래프 : O(N+E) +- 인접 행렬로 표현된 그래프 : O(N^2) + +
+ +* * * +
+ +**※ 너비 우선 탐색 (BFS, Breadth-First Search)** + +- 루트 노드(혹은 다른 임의의 노드)에서 시작해서 인접한 노드를 먼저 탐색하는 방법 + +1. 시작 정점으로부터 가까운 정점을 먼저 방문하고 멀리 떨어져 있는 정점을 나중에 방문하는 순회 방법 + +2. 즉 깊게(deep) 탐색하기 전에 넓게(wide) 탐색하는 것 + +3. **두 노드 사이의 최단 경로 혹은 임의의 경로를 찾고 싶을 때 이 방법을 선택함** + +ex) 지구 상에 존재하는 모든 친구 관계를 그래프로 표현한 후 Ash 와 Vanessa 사이에 존재하는 경로를 찾는 경우 + +- 깊이 우선 탐색의 경우 - 모든 친구 관계를 다 살펴봐야할지도 모름 +- 너비 우선 탐색의 경우 - Ash와 가까운 관계부터 탐색 + +
+ +**※ 너비 우선 탐색(BFS)의 특징** + +- BFS 는 재귀적으로 동작하지 않는다. +- 이 알고리즘을 구현할 때 가장 큰 차이점은 그래프 탐색의 경우 어떤 노드를 방문했었는지 여부를 반드시 검사해야한다는 것이다 이를 검사하지 않을 경우 무한 루프에 빠질 위험이 있다. +- BFS 는 방문한 노드들을 차례로 저장한 후 꺼낼 수 있는 자료 구조인 큐(Queue)를 사용함 +- 즉 선입선출(FIFO) 원칙으로 탐색 + +
+ +**※ 너비 우선 탐색(BFS)이 과정** + +- 깊이가 1인 모든 노드를 방문하고 나서 그 다음에는 깊이가 2인 모든 노드를, 그 다음에는 깊이가 3인 모든 노드를 방문하는 식으로 계속 방문하다가 더 이상 방문할 곳이 없으면 탐색을 마친다. + +[https://t1.daumcdn.net/cfile/tistory/99960F405BD01A8D18](https://t1.daumcdn.net/cfile/tistory/99960F405BD01A8D18) + +
+ +**※ DFS 와 BFS 의 차이** + +[https://t1.daumcdn.net/cfile/tistory/997C3C3E5BD01AF41D](https://t1.daumcdn.net/cfile/tistory/997C3C3E5BD01AF41D) + +
+ +* * * +
+ +## 구현 + +DFS 구현 +
+ DFS + ## DFS + +· DFS(**Depth-First Search**)는 **깊이 우선 탐색**이라고 부르며, 그래프에서 깊은 부분을 우선적으로 탐색하는 알고리즘 + +### 알고리즘 동작 방식 + +· **스택 자료구조**를 이용한다. + +1. 탐색 시작 노드를 스택에 삽입하고, 방문 처리한다. + +2. 스택의 최상단 노드에 방문하지 않은 인접 노드가 있으면 그 인접 노드를 스택에 넣고 방문 처리하고, + +방문하지 않은 인접 노드가 없으면 스택에서 최상단 노드를 꺼낸다. + +3. 위의 1번과 2번 과정을 더 이상 수행할 수 없을 때까지 반복한다. + +- ‘**방문 처리':** 스택에 한 번 삽입되어 처리된 노드가 다시 삽입되지 않게 체크하는 것을 의미한다. 이를 통해 각 노드를 한 번씩만 처리할 수 있다. + +▶ 예시 - 그래프의 노드 1을 시작 노드로 설정하여 DFS를 이용해 탐색 + +![https://blog.kakaocdn.net/dn/pULIc/btqUtpM4pXE/UgjZXl2srkmwDklAwISWV1/img.png](https://blog.kakaocdn.net/dn/pULIc/btqUtpM4pXE/UgjZXl2srkmwDklAwISWV1/img.png) + +인접한 노드 중에서 방문하지 않은 노드가 여러 개 있으면 번호가 낮은 순서부터 처리한다. + +방문 처리된 노드는 회색으로, 현재 처리하는 스택의 최상단 노드는 하늘색으로 표현한다. + +**step1.**  시작 노드 ‘1’을 스택에 삽입하고 방문 처리 + +![https://blog.kakaocdn.net/dn/cw7uiF/btqUBvyaPjV/DPUBNI6l00rD5oQpRHpif1/img.png](https://blog.kakaocdn.net/dn/cw7uiF/btqUBvyaPjV/DPUBNI6l00rD5oQpRHpif1/img.png) + +**step2.**  스택의 최상단 노드 ‘1’에 방문하지 않은 인접 노드 ‘2’, ‘3’, ‘8’ 중에서 가장 작은 노드 ‘2’를 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/bojcxK/btqUwyWu37u/PYaKHm2sypxE3dABjTqmwk/img.png](https://blog.kakaocdn.net/dn/bojcxK/btqUwyWu37u/PYaKHm2sypxE3dABjTqmwk/img.png) + +**step3.**  스택의 최상단 노드 ‘2’에 방문하지 않은 인접 노드 ‘7’을 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/dPzdSW/btqUBwcMlMp/EehLKRqinj2ptuzuanlVS1/img.png](https://blog.kakaocdn.net/dn/dPzdSW/btqUBwcMlMp/EehLKRqinj2ptuzuanlVS1/img.png) + +**step4.**  스택의 최상단 노드 ‘7’에 방문하지 않은 인접 노드 ‘6’과 ‘8’ 중에서 가장 작은 노드인 ‘6’을 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/0lMDn/btqUtW4WhZq/5uNYdki0k7glf81FfjtvS0/img.png](https://blog.kakaocdn.net/dn/0lMDn/btqUtW4WhZq/5uNYdki0k7glf81FfjtvS0/img.png) + +**step5.**  스택의 최상단 노드 ‘6’에 방문하지 않은 인접 노드가 없으므로, 스택에서 ‘6’번 노드를 꺼냄 + +![https://blog.kakaocdn.net/dn/bvw8xL/btqUBxbHl4Z/fKExHBlbPR04vmw8iEeRr1/img.png](https://blog.kakaocdn.net/dn/bvw8xL/btqUBxbHl4Z/fKExHBlbPR04vmw8iEeRr1/img.png) + +**step6.**  스택의 최상단 노드 ‘7’에 방문하지 않은 인접 노드 ‘8’이 있으므로, ‘8’번 노드를 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/0oWCS/btqUvDqdjPi/ng4E6N48Gf5sXklvI3TV91/img.png](https://blog.kakaocdn.net/dn/0oWCS/btqUvDqdjPi/ng4E6N48Gf5sXklvI3TV91/img.png) + +**step7.**  스택 최상단 노드 ‘8’에 방문하지 않은 인접 노드가 없으므로, 스택에서 ‘8’번 노드를 꺼냄 + +![https://blog.kakaocdn.net/dn/bqV1XL/btqUwy91PmZ/XamQfxAyu19BYxcXeFEkS0/img.png](https://blog.kakaocdn.net/dn/bqV1XL/btqUwy91PmZ/XamQfxAyu19BYxcXeFEkS0/img.png) + +**step8.**  스택의 최상단 노드 ‘7’에 방문하지 않은 인접 노드가 없으므로, 스택에서 ‘7’번 노드를 꺼냄 + +![https://blog.kakaocdn.net/dn/eh4lVY/btqUwx4m9Wm/pvIFHKZkJxSnCpo5TSFfe0/img.png](https://blog.kakaocdn.net/dn/eh4lVY/btqUwx4m9Wm/pvIFHKZkJxSnCpo5TSFfe0/img.png) + +**step9.**  스택의 최상단 노드 ‘2’에 방문하지 않은 인접 노드가 없으므로, 스택에서 ‘2’번 노드를 꺼냄 + +![https://blog.kakaocdn.net/dn/M3YNn/btqUsdlLvE3/ShKXEQLTJ7HCPmWxFsN6Bk/img.png](https://blog.kakaocdn.net/dn/M3YNn/btqUsdlLvE3/ShKXEQLTJ7HCPmWxFsN6Bk/img.png) + +**step10.**  스택의 최상단 노드 ‘1’에 방문하지 않은 인접 노드 ‘3’을 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/XEiJC/btqUuNs5XEk/dzSSo1pvPYrqxKSkhZdfW1/img.png](https://blog.kakaocdn.net/dn/XEiJC/btqUuNs5XEk/dzSSo1pvPYrqxKSkhZdfW1/img.png) + +**step11.**  스택의 최상단 노드 ‘3’에 방문하지 않은 인접 노드 ‘4’, ‘5’ 중 가장 작은 노드 ‘4’를 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/RqWko/btqUtp7g8O3/lGJCGYfbggrW8x0svbn0EK/img.png](https://blog.kakaocdn.net/dn/RqWko/btqUtp7g8O3/lGJCGYfbggrW8x0svbn0EK/img.png) + +**step12.**  스택의 최상단 노드 ‘4’에 방문하지 않은 인접 노드 ‘5’가 있으므로, ‘5’번 노드를 스택에 넣고 방문 처리 + +![https://blog.kakaocdn.net/dn/NnZu2/btqUtq6d9Yg/wkH8QmzwqHY6UgvW7BkZn0/img.png](https://blog.kakaocdn.net/dn/NnZu2/btqUtq6d9Yg/wkH8QmzwqHY6UgvW7BkZn0/img.png) + +**step13.**  남아 있는 노드에 방문하지 않은 인접 노드가 없다. 따라서 모든 노드를 차례대로 꺼내면 다음과 같다. + +![https://blog.kakaocdn.net/dn/lHKq0/btqUGUYu3Fg/K6BND5VgNBzjQqm7aea9i1/img.png](https://blog.kakaocdn.net/dn/lHKq0/btqUGUYu3Fg/K6BND5VgNBzjQqm7aea9i1/img.png) + +위 단계에서 노드의 탐색 순서(스택에 들어간 순서)는 다음과 같다. + +1 -> 2 -> 7 -> 6 -> 8 -> 3 -> 4 -> 5 + +**·** 깊이 우선 탐색 알고리즘인 DFS는 **스택 자료구조**에 기초하므로, 실제 구현은 **재귀 함수**를 이용했을 때 간결하게 구현할 수 있다. + +**· 소요시간:** 데이터의 개수가 N개인 경우, O(N) + +▶ 예시 - 재귀 함수를 통해 dfs 구현 + +```java +public class DFSExamRecursion { +//각 노드가 방문된 정보를 1차원 배열 자료형으로 표현public static boolean [] visited = {false, false, false ,false ,false ,false ,false ,false, false}; +// 각 노드가 연결된 정보를 2차원 배열 자료형으로 표현public static int[][] graph = {{}, + {2, 3, 8}, + {1, 7}, + {1, 4, 5}, + {3, 5}, + {3, 4}, + {7}, + {2, 6, 8}, + {1, 7}}; + + public static void main(String[] args){ + int start = 1;// 시작 노드 + dfs(start); + } + +/* + * dfs 알고리즘을 수행하는 함수 + * @param v 탐색할 노드 + */public static void dfs(int v){ +// 현재 노드 방문 처리 + visited[v] = true; +// 방문 노드 출력 + System.out.print(v + ""); + +// 인접 노드 탐색for (int i : graph[v]){ +// 방문하지 않은 인접 노드 중 가장 작은 노드를 스택에 넣기if (visited[i]==false){ + dfs(i); + } + } + } +} +``` + +![https://blog.kakaocdn.net/dn/bqijpM/btqUvD4O2A0/2mgaoD9ZLsOI98HTArY8zk/img.png](https://blog.kakaocdn.net/dn/bqijpM/btqUvD4O2A0/2mgaoD9ZLsOI98HTArY8zk/img.png) + +DFSExam 결과 + +예시 - Stack 클래스를 통한 DFS 구현 + +```sql +public class DFS_Stack { + public static void main(String[] args){ + + //각 노드가 연결된 정보를 2차원 배열 자료형으로 표현 + int [][]graph = {{}, + {2, 3, 8}, + {1, 7}, + {1, 4, 5}, + {3, 5}, + {3, 4}, + {7}, + {2, 6, 8}, + {1, 7}}; + + //각 노드가 방문된 정보를 1차원 배열 자료형으로 표현 + boolean [] visited = {false, false, false ,false ,false ,false ,false ,false, false}; + + //정의된 DFS 함수 호출 + DFS_Stack dfsExam = new DFS_Stack(); + dfsExam.dfs(graph, 1, visited); + } + +/* + * dfs 메서드 + * graph 노드 연결 정보를 저장 + * v 방문을 시작하는 최상단 노드의 위치 + * visited 노드 방문 정보를 저장 + */ + void dfs(int [][]graph,int start, boolean [] visited){ + //시작 노드를 방문 처리 + visited[start] = true; + System.out.print(start + " ");//방문 노드 출력 + + Deque stack = new LinkedList<>(); + stack.push(start); //시작 노드를 스택에 입력 + + while(!stack.isEmpty()){ + int now = stack.peek(); + + boolean hasNearNode = false; // 방문하지 않은 인접 노드가 있는지 확인 + //인접한 노드를 방문하지 않았을 경우 스택에 넣고 방문처리 + for(int i: graph[now]){ + if (!visited[i]) { + hasNearNode = true; + stack.push(i); + visited[i] = true; + System.out.print(i + " ");//방문 노드 출력 + break; + } + } + //반문하지 않은 인접 노드가 없는 경우 해당 노드 꺼내기 + if(hasNearNode==false) + stack.pop(); + } + } + } +``` +
+ +BFS 구현 +
+ BFS + **·** BFS(Breadth First Search)의 약자로 ‘**너비 우선 탐색**’ 알고리즘을 의미한다. + +- 즉, **가까운 노드부터 탐색**하는 알고리즘이다. + +- 최대한 멀리 있는 노드를 우선으로 탐색하는 DFS와는 반대다. + +### 알고리즘의 동작 방식 + +**·** 선입선출 방식인 **큐** 자료구조를 이용하는 것이 정석이다. + +**- 인접한 노드를 반복적으로 큐에 넣도록 알고리즘을 작성**하면 자연스럽게 먼저 들어온 것이 먼저 나가며, 가까운 노드부터 탐색하게 된다. + +1. 탐색 시작 노드를 큐에 삽입하고 방문 처리한다. + +2. 큐에서 노드를 꺼내 해당 노드의 인접 노드 중에서 방문하지 않은 노드를 모두 큐에 삽입하고 방문 처리한다. + +3. 위의 1번과 2번 과정을 더 이상 수행할 수 없을 때까지 반복한다. + +**▶ 예시 - 그래프의 노드 1을 시작 노드로 설정하여 BFS를 이용해 탐색** + +**·**  인접한 노드가 여러 개 있을 때, 숫자가 작은 노드부터 먼저 큐에 삽입한다고 가정한다. + +큐에 원소가 들어올 때, 위에서 들어오고 아래쪽에서 꺼낸다. + +![https://blog.kakaocdn.net/dn/prwHL/btqUBwjyDuN/i3WmRIe9JdvZxSIFatU7Bk/img.png](https://blog.kakaocdn.net/dn/prwHL/btqUBwjyDuN/i3WmRIe9JdvZxSIFatU7Bk/img.png) + +**step 1.**  시작 노드 ‘1’을 큐에 삽입하고 방문 처리 한다. + +방문 처리된 노드는 회색으로, 큐에서 꺼내 현재 처리하는 노드는 하늘색으로 표시하다. + +![https://blog.kakaocdn.net/dn/bQpd86/btqUtqd6lv2/tclv2r7rxo890PFpaHK891/img.png](https://blog.kakaocdn.net/dn/bQpd86/btqUtqd6lv2/tclv2r7rxo890PFpaHK891/img.png) + +**step 2.**  큐에서 노드 ‘1’을 꺼내고 방문하지 않은 인접 노드 ‘2’, ‘3’, ‘8’을 모두 큐에 삽입하고 방문 처리한다. + +![https://blog.kakaocdn.net/dn/kGtWY/btqUzu0DQRY/o69as4nCkSKk9oreosker0/img.png](https://blog.kakaocdn.net/dn/kGtWY/btqUzu0DQRY/o69as4nCkSKk9oreosker0/img.png) + +**step 3.**  큐에서 노드 ‘2’를 꺼내고 방문하지 않은 인접 노드 ‘7’을 큐에 삽입하고 방문 처리 한다. + +![https://blog.kakaocdn.net/dn/ce4PpK/btqUzwxoQAU/okhUIqaZuQUVGEagXi4B1k/img.png](https://blog.kakaocdn.net/dn/ce4PpK/btqUzwxoQAU/okhUIqaZuQUVGEagXi4B1k/img.png) + +**step 4.**  큐에서 노드 ‘3’을 꺼내고 방문하지 않은 인접 노드 ‘4’와 ‘5’를 모두 큐에 삽입하고 방문 처리한다. + +![https://blog.kakaocdn.net/dn/BTsbO/btqUsd0qG4H/qoKj8boq0MeWnCir9ZwXxK/img.png](https://blog.kakaocdn.net/dn/BTsbO/btqUsd0qG4H/qoKj8boq0MeWnCir9ZwXxK/img.png) + +step 5.  큐에서 노드 ‘8’을 꺼내고 방문하지 않은 인접 노드가 없으므로 무시한다. + +![https://blog.kakaocdn.net/dn/tCzKL/btqUvD4O2Bf/oCi82kI7RdCkrkY2AcoL11/img.png](https://blog.kakaocdn.net/dn/tCzKL/btqUvD4O2Bf/oCi82kI7RdCkrkY2AcoL11/img.png) + +**step 6.**  큐에서 노드 ‘7’을 꺼내고 방문하지 않은 인접 노드 ‘6’을 큐에 삽입하고 방문 처리를 한다. + +![https://blog.kakaocdn.net/dn/8z2Ah/btqUEy9fjiT/9qJImYpNda9RIVArN5ts2K/img.png](https://blog.kakaocdn.net/dn/8z2Ah/btqUEy9fjiT/9qJImYpNda9RIVArN5ts2K/img.png) + +**step 7.**  남아 있는 노드에 방문하지 않은 인접 노드가 없다. 따라서 모든 노드를 차례로 꺼낸다. + +![https://blog.kakaocdn.net/dn/5pP0v/btqUuNGCarJ/kXYrVPGc9SKmqwmVixlGxk/img.png](https://blog.kakaocdn.net/dn/5pP0v/btqUuNGCarJ/kXYrVPGc9SKmqwmVixlGxk/img.png) + +**노드의 탐색 순서**(큐에 들어간 순서) 1 -> 2 -> 3 -> 8 -> 7 -> 4 -> 5 -> 6 + +**·** 너비 우선 탐색 알고리즘인 BFS는 **큐 자료구조**에 기초한다. + +**·** 구현할 때는 언어에서 제공하는 **큐 라이브러리**를 사용하자. + +**·** 탐색 수행 시간은 O(N)의 시간이 소요되고, 일반적인 경우 실제 **수행 시간**은 DFS보다 좋다. + +**-** 재귀 함수로 DFS를 구현하면 컴퓨터 시스템의 동작 특성상 실제 프로그램의 수행 시간이 느려질 수 있기 때문이다. + +```java +import java.util.LinkedList; +import java.util.Queue; + +public class BFS { + public static void main(String[] args){ +//각 노드가 연결된 정보를 2차원 배열 자료형으로 표현int [][]graph = {{}, + {2, 3, 8}, + {1, 7}, + {1, 4, 5}, + {3, 5}, + {3, 4}, + {7}, + {2, 6, 8}, + {1, 7}}; + +//각 노드가 방문된 정보를 1차원 배열 자료형으로 표현boolean [] visited = {false, false, false ,false ,false ,false ,false ,false, false}; + + int start = 1;// 시작 노드// 큐 구현 + Queue queue = new LinkedList<>(); + queue.add(start); + +// 현재 노드를 방문 처리 + visited[start] = true; + +// 큐가 빌때까지 반복while(!queue.isEmpty()){ +// 큐에서 하나의 원소를 뽑아 출력int v = queue.poll(); + System.out.println(v + " "); + +// 인접한 노드 중 아직 방문하지 않은 원소들을 큐에 삽입for (int i : graph[v]){ + if (visited[i] == false){ + queue.add(i); + visited[i] = true; + } + } + } + } + } +``` + +**결과** + +![https://blog.kakaocdn.net/dn/b3hwex/btrnuWIzmX5/8tkwzlRIkFDGKYXlGuvtP1/img.png](https://blog.kakaocdn.net/dn/b3hwex/btrnuWIzmX5/8tkwzlRIkFDGKYXlGuvtP1/img.png) + +
+ +
+ +* * * + +
+ +## 정리 + +| | DFS | BFS | +| --- | --- | --- | +| 동작 원리 | 스택 | 큐 | +| 구현 | 재귀 함수 또는 스택 자료구조 이용 | 큐 자료구조 이용 | + +**·**  앞서 DFS와 BFS를 설명하는 데 전형적인 그래프 그림을 이용했다. + +**1차원 배열**이나 **2차원 배열** 또한 **그래프 형태로 생각**하면 수월하게 문제를 풀 수 있다. + +**·**  예를 들어 게임 맵이 3 x 3 형태의 2차원 배열이고 각 데이터를 좌표라고 생각해보자. + +이때 각 표로 상하좌우로만 이동할 수 있다면, 모든 좌표의 형태를 다음처럼 그래프의 형태로 바꿔서 생각할 수 있다. + +![https://blog.kakaocdn.net/dn/bBK37H/btqUBvrpSa7/61307GU3iXkyNArV0cgk70/img.png](https://blog.kakaocdn.net/dn/bBK37H/btqUBvrpSa7/61307GU3iXkyNArV0cgk70/img.png) + +**·** 코딩 테스트 중 2차원 배열에서의 탐색 문제를 만나면 이렇게 그래프 형태로 바꿔서 생각하자. 풀이 방법을 더 쉽게 떠올릴 수 있다. From 704874b419a098dfe0000bc9583d21f334d81ab6 Mon Sep 17 00:00:00 2001 From: JiYong Kim <81874493+JiYongKim-A@users.noreply.github.com> Date: Sat, 16 Apr 2022 16:58:12 +0900 Subject: [PATCH 5/8] Update DFS_BFS.md --- 07/JiYongKim/DFS_BFS.md | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/07/JiYongKim/DFS_BFS.md b/07/JiYongKim/DFS_BFS.md index dba800d7..173c940e 100644 --- a/07/JiYongKim/DFS_BFS.md +++ b/07/JiYongKim/DFS_BFS.md @@ -31,7 +31,8 @@ Ex) 특정 도시에서 다른 도시로 갈 수 있는지 없는지, 전자 회 **※ 깊이 우선 탐색(DFS)의 과정** -[https://t1.daumcdn.net/cfile/tistory/9983A7335BD0156910](https://t1.daumcdn.net/cfile/tistory/9983A7335BD0156910) + +스크린샷 2022-04-16 오후 4 56 58
@@ -76,13 +77,14 @@ ex) 지구 상에 존재하는 모든 친구 관계를 그래프로 표현한 - 깊이가 1인 모든 노드를 방문하고 나서 그 다음에는 깊이가 2인 모든 노드를, 그 다음에는 깊이가 3인 모든 노드를 방문하는 식으로 계속 방문하다가 더 이상 방문할 곳이 없으면 탐색을 마친다. -[https://t1.daumcdn.net/cfile/tistory/99960F405BD01A8D18](https://t1.daumcdn.net/cfile/tistory/99960F405BD01A8D18) + +스크린샷 2022-04-16 오후 4 57 04
**※ DFS 와 BFS 의 차이** -[https://t1.daumcdn.net/cfile/tistory/997C3C3E5BD01AF41D](https://t1.daumcdn.net/cfile/tistory/997C3C3E5BD01AF41D) +997C3C3E5BD01AF41D](https://t1.daumcdn.net/cfile/tistory/997C3C3E5BD01AF41D)
From de1582d85d4543ba41e9453a11c04c3f0b945cc9 Mon Sep 17 00:00:00 2001 From: JiYongKim Date: Mon, 9 May 2022 21:44:30 +0900 Subject: [PATCH 6/8] Create Leetcode.md & ADT --- 07/JiYongKim/Leetcode.md | 84 ++++++++++++++++++++++++++++++ ADT/JiYongKim/Graph/ArrGraph.java | 36 +++++++++++++ ADT/JiYongKim/Graph/ListGraph.java | 49 +++++++++++++++++ 3 files changed, 169 insertions(+) create mode 100644 07/JiYongKim/Leetcode.md create mode 100644 ADT/JiYongKim/Graph/ArrGraph.java create mode 100644 ADT/JiYongKim/Graph/ListGraph.java diff --git a/07/JiYongKim/Leetcode.md b/07/JiYongKim/Leetcode.md new file mode 100644 index 00000000..68c28953 --- /dev/null +++ b/07/JiYongKim/Leetcode.md @@ -0,0 +1,84 @@ +

+ +

Graph 태그가 있는 문제들

+
+ 1791. Find Center of Star Graph +- 1791. Find Center of Star Graph + +```java +// 시간 복잡도 O(1) +// 공간 복잡도 O(1) +class Solution { + public int findCenter(int[][] edges) { + + + int a1 = edges[0][0]; + int a2 = edges[0][1]; + + int b1 = edges[1][0]; + int b2 = edges[1][1]; + + if(a1 == b1 || a1 == b2) + return a1; + + else + return a2; + } +} +``` +
+ +
+ +
+ 997 . Find the Town Judge +- 997 . Find the Town Judge + +```java +// 시간 복잡도 O(a+b) .. a = trust의 크기, b = n +// 공간 복잡도 O(a) ... a = n+1 +class Solution { + public int findJudge(int n, int[][] trust) { + int[] count = new int[n + 1]; + for (int[] t : trust) { + count[t[0]]--; + count[t[1]]++; + } + for (int i = 1; i <= n; i++) { + if (count[i] == n - 1) { + return i; + } + } + return -1; + } +} +``` +
+ +
+ +
+ 1971. Find if Path Exists in Graph (미완) +- 1971. Find if Path Exists in Graph +
+ + +
+ +

Graph 순회 `알고리즘` + `사용해본 자료구조`

+ +
+ 653. Two Sum IV - Input is a BST (미완) +- 653. Two Sum IV - Input is a BST + +
+ +
+ +
+ 463. Island Perimeter (미완) +- 463. Island Perimeter + +
+ +
\ No newline at end of file diff --git a/ADT/JiYongKim/Graph/ArrGraph.java b/ADT/JiYongKim/Graph/ArrGraph.java new file mode 100644 index 00000000..c6d0f5e2 --- /dev/null +++ b/ADT/JiYongKim/Graph/ArrGraph.java @@ -0,0 +1,36 @@ +package ADT.JiYongKim.Graph; + +// 그래프(행렬) 클래스 +class ArrGraph { + private int[][] arrGraph; + + // 그래프 초기화 + public ArrGraph(int initSize) { + this.arrGraph = new int[initSize+1][initSize+1]; + } + + // 그래프 return + public int[][] getGraph() { + return this.arrGraph; + } + + // 그래프 추가 (양방향) + public void insertVertexEdge(int x, int y) { + arrGraph[x][y] = arrGraph[y][x] = 1; + } + + // 그래프 추가 (단방향) + public void putVertexEdge(int x, int y) { + arrGraph[x][y] = 1; + } + + // 그래프 출력 (인접행렬) + public void printGraph() { + for(int i=0; i> listGraph; + + + public ListGraph(int initSize) { + this.listGraph = new ArrayList>(); // 그래프 생성 + + for(int i=0; i()); + } + } + + public ArrayList> getGraph() { + return this.listGraph; + } + + + public ArrayList getNode(int i) { + return this.listGraph.get(i); + } + + // 그래프 정점 및 양방향 간선 추가 + public void insertVertexEdge(int x, int y) { + listGraph.get(x).add(y); + listGraph.get(y).add(x); + } + + // 그래프 정점 및 단방향 간선 추가 + public void putVertexEdge(int x, int y) { + listGraph.get(x).add(y); + } + + // 그래프 출력 (인접리스트) + public void printGraph() { + for(int i=1; i " + listGraph.get(i).get(j)); + } + System.out.println(); + } + } +} From 2745c2b2a030db423cd3a2a3b553a20986b8d19f Mon Sep 17 00:00:00 2001 From: JiYongKim Date: Mon, 9 May 2022 21:46:52 +0900 Subject: [PATCH 7/8] Add PPT --- 07/JiYongKim/Graph.pptx | Bin 0 -> 6895873 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 07/JiYongKim/Graph.pptx diff --git a/07/JiYongKim/Graph.pptx b/07/JiYongKim/Graph.pptx new file mode 100644 index 0000000000000000000000000000000000000000..f22751cf4efa5b4da5a1a451c402bbb134b8e7c4 GIT binary patch literal 6895873 zcmeFZRa9l&dbNu~;qDaf?(SZA;qLD4?(XhTxVseY?(SB&yL0$zCpkOWmF%?t;> 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