From a2b9314d2845652328bdf087e9e5f8e3ffd63cd1 Mon Sep 17 00:00:00 2001 From: Seogeurim Date: Sun, 11 Jul 2021 21:40:45 +0900 Subject: [PATCH 1/3] =?UTF-8?q?[DataStructure]=20=EA=B7=B8=EB=9E=98?= =?UTF-8?q?=ED=94=84=20=EC=9D=B4=EB=A1=A0=20=EC=A0=95=EB=A6=AC?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- contents/data-structure/basic.md | 87 +++++++++++++++++- ...\267\270\353\236\230\355\224\204.001.jpeg" | Bin 0 -> 138173 bytes ...\267\270\353\236\230\355\224\204.002.jpeg" | Bin 0 -> 162939 bytes ...\267\270\353\236\230\355\224\204.003.jpeg" | Bin 0 -> 139769 bytes 4 files changed, 86 insertions(+), 1 deletion(-) create mode 100644 "contents/data-structure/img/\352\267\270\353\236\230\355\224\204.001.jpeg" create mode 100644 "contents/data-structure/img/\352\267\270\353\236\230\355\224\204.002.jpeg" create mode 100644 "contents/data-structure/img/\352\267\270\353\236\230\355\224\204.003.jpeg" diff --git a/contents/data-structure/basic.md b/contents/data-structure/basic.md index b261f1c..f0244ac 100644 --- a/contents/data-structure/basic.md +++ b/contents/data-structure/basic.md @@ -256,4 +256,89 @@ String[] name = {"Stacy", "Tracy", "Dorothy"}; ## Graph (그래프) -### Graph 용어 +## 그래프 정의 + +현실세계의 사물이나 개념 간의 **연결 관계**를 수학적 모델로 단순화하여 표현한 것 + +- V : 정점 (Vertex / Node) +- E : 간선 (Edge / Link / Arc) +- 그래프 G = (V, E) + +## 그래프 용어 + +1. 정점, 노드 (Vertex, Node) +2. 간선 (Edge) + - 무향 간선 (Undirected Edge) : 방향이 존재하지 않는 간선, 양방향 + - 유향 간선 (Directed Edge) : 방향이 존재하는 간선 +3. 인접 (Adjacent) : (정점 관점) 두 정점 A, B 사이에 간선이 존재한다면 A, B는 인접한다. +4. 부속 (Incident) : (간선 관점) 두 정점 A, B 사이에 간선 e가 존재한다면 간선 e는 정점 A, B에 부속한다. +5. 차수 (Degree) : 한 정점에 연결된 간선의 수 + - (방향 그래프) in-degree : 정점에 들어오는 간선의 수, out-degree : 나가는 간선의 수 +6. 자기 간선과 다중 간선 + - 자기 간선 (Self-loop) : 자신으로 다시 돌아오는 간선 + - 다중 간선 (Multiple / Parallel edges) : 두 개 이상의 간선이 똑같은 두 정점에 부속할 때 +7. 경로 (Path) : 정점 + 간선이 교대로 구성된 sequence + - 단순 경로 (Simple Path) : 같은 정점을 두 번 이상 가지 않는 경로 +8. 회로 (Cycle) : A 정점에서 출발했을 때 다시 A 정점으로 돌아오는 경로 + - 단순 회로 (Simple Cycle) : 같은 정점을 두 번 이상 가지 않는 싸이클 +9. 연결됨 (Connected) : 정점 A에서 정점 B로의 경로가 존재할 때 A와 B는 연결되어 있다. + +## 그래프 종류 + +> 별도로 표시된 것은 내가 기억하기 쉬울 것 같은 이름이다. + +1. 무향 그래프 (Undirected Graph) : 무방향 간선으로 이루어진 그래프 +2. 유향 그래프 (Directed Graph) : 방향 간선으로 이루어진 그래프 +3. 가중치 그래프 (Weighted Graph) : 가중치(비용)를 갖는 간선들로 이루어진 그래프 +4. 정규 그래프 (Regular Graph) : 모든 정점이 동일한 차수를 가지는 그래프 +5. 완전 그래프 (Complete Graph) : 모든 정점이 서로 인접해있는 그래프, 완전 그래프는 정규 그래프 +6. 연결 그래프 (Connected Graph) : 모든 정점이 연결되어 있어서 모든 정점끼리 경로가 존재하는 그래프 +7. 부분 그래프 : 어떤 그래프의 부분 부분 +8. 트리 그래프 : 싸이클을 가지지 않는 연결 그래프, 모든 정점에 대해서 경로가 정확히 1개 존재한다. + +## 그래프 표현 + +**간선 리스트, 인접 행렬, 인접 리스트** 이렇게 3가지 방식이 있다. + +정점 개수 : V개, 간선 개수 : E개 + +### 간선 리스트 (Edge List) + +- E x 2 (or E x 3) 이차원 배열 A에 정보를 저장한다. +- 두 정점 x, y 를 연결하는 간선 k에 대해서 A[k][0] = x, A[k][1] = y +- 가중치 그래프의 경우 A[k][2] 에 가중치 정보를 저장한다. + +![간선리스트](./img/그래프.001.jpeg) + + +### 인접 행렬 (Adjacency Matrix) + +- V x V 이차원 배열 A에 정보를 저장한다. +- Vi, Vj를 연결하는 간선이 존재한다면 A[i][j] = 1, 존재하지 않는다면 A[i][j] = 0 +- 가중치 그래프의 경우 1 대신 가중치 정보를 저장한다. + +> 메모리 복잡도가 V2 이기 때문에 V의 값이 클 경우 쓰지 않는 것이 좋다. +> 100 이하의 값일 때 사용하는 것이 좋다. + +![인접행렬](./img/그래프.002.jpeg) + +### 인접 리스트 (Adjacent List) + +- V 개의 Linked List로 그래프 정보를 저장한다. +- 가중치 그래프의 경우 (정점 정보, 가중치 정보)를 함께 저장한다. (C++ : pair, Java : class) + +![인접리스트](./img/그래프.003.jpeg) + +### 그래프 표현 방식 비교 + +정점 개수 : V개, 간선 개수 : E개 + +| | 간선 리스트 | 인접 행렬 | 인접 리스트 | +| :---: | :------: | :-------------: | :------------: | +| 공간 | E | V2 | V + E | +| 정점 Va 의 부속 간선 | E | V | Va 차수 | +| 정점 Va, Vb 의 인접 여부 | E | 1 | min(Va 차수, Vb 차수) | +| 정점 삽입 | 1 | V2 | 1 | +| 간선 삽입 | 1 | 1 | 1 | + + diff --git "a/contents/data-structure/img/\352\267\270\353\236\230\355\224\204.001.jpeg" "b/contents/data-structure/img/\352\267\270\353\236\230\355\224\204.001.jpeg" new file mode 100644 index 0000000000000000000000000000000000000000..ab7ea0418602ee5320518bd6529c0dd6b66577fd GIT binary patch literal 138173 zcmeFZ2|UzazX$#ml58Q$I?9r)$-a(~Em>NSb&{PJOGJhdA$tf>mO{!l*_CB5cG-6l zGm41JSO;U~|Lym?&wcLickg}O|9zh4{$Kz5yzbHYc6{eJb3W&MzVGu{zm!SJJaFQw zj=l~+MFjwQ;158-0-D+Zu1)}8Xb6Y_0B{VTigE>Lz!umA;07xI9LYWMmpgQ!xzvAY z(tv*Y`^@~cK*Hn{#X0%@9nnV`rNvq1@@T) z+XD73cHkIPM6fM!_ut%i{x|J^`ChOKz;MOY*Xy2Lpn!?&uV4SM<-TJ8NCyCD!My@~ 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z8v&mOaIODNhHk_2%oM;1;t`tKAUD;Rwj_=^ZOg4#>N86*tneWWSxcU&I>fGdyxc&4 z*jKX5m1kfXAW#a!`IlQTl6RTj3fW>+)Q&yC%{_l!(Cw((d7e#=3I@GpkL=%i*}Pym zO1x_Be?)xZO9zKac7SyBV?eP$X4$y<4D+Fdnfv`2zhY<@8m6rL?RuEb8z{+6vF^*s z^?x*)r`OeG6tpkin1xFwE7WMNKdiB&a0T2AnGKYv2MOw*gWh4EA^qkF{(D`4Z* z4_L$4Xa^|JXYmCKezGR{>S0YA=n*=SNLy8 z>nFGp(8ty+ouS(CdA!9&lEy$&s2p_bx!gs&oVFv6>k)Q_$a7NOUbj2nto+l`(Q^&RGOC`e z_T2Laa{p-uMrR|(FB9U276+(9W=Ay&B9hPS-@vJrWtqoDALxj ziP986-Xk~tw#QUCN$SM|Vn9#pzr3>^Hd^w) Date: Sun, 11 Jul 2021 21:47:07 +0900 Subject: [PATCH 2/3] =?UTF-8?q?[DataStructure]=20=EA=B7=B8=EB=9E=98?= =?UTF-8?q?=ED=94=84=20=EC=9D=B4=EB=A1=A0=20=EC=A0=95=EB=A6=AC=20=EC=88=98?= =?UTF-8?q?=EC=A0=95?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- contents/data-structure/basic.md | 42 +++++++++--------- ...\267\270\353\236\230\355\224\204.003.jpeg" | Bin 139769 -> 144961 bytes 2 files changed, 20 insertions(+), 22 deletions(-) diff --git a/contents/data-structure/basic.md b/contents/data-structure/basic.md index f0244ac..b386e1a 100644 --- a/contents/data-structure/basic.md +++ b/contents/data-structure/basic.md @@ -266,41 +266,39 @@ String[] name = {"Stacy", "Tracy", "Dorothy"}; ## 그래프 용어 -1. 정점, 노드 (Vertex, Node) -2. 간선 (Edge) +1. **정점, 노드 (Vertex, Node)** +2. **간선 (Edge)** - 무향 간선 (Undirected Edge) : 방향이 존재하지 않는 간선, 양방향 - 유향 간선 (Directed Edge) : 방향이 존재하는 간선 -3. 인접 (Adjacent) : (정점 관점) 두 정점 A, B 사이에 간선이 존재한다면 A, B는 인접한다. -4. 부속 (Incident) : (간선 관점) 두 정점 A, B 사이에 간선 e가 존재한다면 간선 e는 정점 A, B에 부속한다. -5. 차수 (Degree) : 한 정점에 연결된 간선의 수 +3. **인접 (Adjacent)** : (정점 관점) 두 정점 A, B 사이에 간선이 존재한다면 A, B는 인접한다. +4. **부속 (Incident)** : (간선 관점) 두 정점 A, B 사이에 간선 e가 존재한다면 간선 e는 정점 A, B에 부속한다. +5. **차수 (Degree)** : 한 정점에 연결된 간선의 수 - (방향 그래프) in-degree : 정점에 들어오는 간선의 수, out-degree : 나가는 간선의 수 -6. 자기 간선과 다중 간선 +6. **자기 간선과 다중 간선** - 자기 간선 (Self-loop) : 자신으로 다시 돌아오는 간선 - 다중 간선 (Multiple / Parallel edges) : 두 개 이상의 간선이 똑같은 두 정점에 부속할 때 -7. 경로 (Path) : 정점 + 간선이 교대로 구성된 sequence +7. **경로 (Path)** : 정점 + 간선이 교대로 구성된 sequence - 단순 경로 (Simple Path) : 같은 정점을 두 번 이상 가지 않는 경로 -8. 회로 (Cycle) : A 정점에서 출발했을 때 다시 A 정점으로 돌아오는 경로 +8. **회로 (Cycle)** : A 정점에서 출발했을 때 다시 A 정점으로 돌아오는 경로 - 단순 회로 (Simple Cycle) : 같은 정점을 두 번 이상 가지 않는 싸이클 -9. 연결됨 (Connected) : 정점 A에서 정점 B로의 경로가 존재할 때 A와 B는 연결되어 있다. +9. **연결됨 (Connected)** : 정점 A에서 정점 B로의 경로가 존재할 때 A와 B는 연결되어 있다. ## 그래프 종류 -> 별도로 표시된 것은 내가 기억하기 쉬울 것 같은 이름이다. - -1. 무향 그래프 (Undirected Graph) : 무방향 간선으로 이루어진 그래프 -2. 유향 그래프 (Directed Graph) : 방향 간선으로 이루어진 그래프 -3. 가중치 그래프 (Weighted Graph) : 가중치(비용)를 갖는 간선들로 이루어진 그래프 -4. 정규 그래프 (Regular Graph) : 모든 정점이 동일한 차수를 가지는 그래프 -5. 완전 그래프 (Complete Graph) : 모든 정점이 서로 인접해있는 그래프, 완전 그래프는 정규 그래프 -6. 연결 그래프 (Connected Graph) : 모든 정점이 연결되어 있어서 모든 정점끼리 경로가 존재하는 그래프 -7. 부분 그래프 : 어떤 그래프의 부분 부분 -8. 트리 그래프 : 싸이클을 가지지 않는 연결 그래프, 모든 정점에 대해서 경로가 정확히 1개 존재한다. +1. **무향 그래프 (Undirected Graph)** : 무방향 간선으로 이루어진 그래프 +2. **유향 그래프 (Directed Graph)** : 방향 간선으로 이루어진 그래프 +3. **가중치 그래프 (Weighted Graph)** : 가중치(비용)를 갖는 간선들로 이루어진 그래프 +4. **정규 그래프 (Regular Graph)** : 모든 정점이 동일한 차수를 가지는 그래프 +5. **완전 그래프 (Complete Graph)** : 모든 정점이 서로 인접해있는 그래프, 완전 그래프는 정규 그래프 +6. **연결 그래프 (Connected Graph)** : 모든 정점이 연결되어 있어서 모든 정점끼리 경로가 존재하는 그래프 +7. **부분 그래프** : 어떤 그래프의 부분 부분 +8. **트리 그래프** : 싸이클을 가지지 않는 연결 그래프, 모든 정점에 대해서 경로가 정확히 1개 존재한다. ## 그래프 표현 -**간선 리스트, 인접 행렬, 인접 리스트** 이렇게 3가지 방식이 있다. +그래프의 표현 방식에는 **간선 리스트, 인접 행렬, 인접 리스트** 3가지 방식이 있다. -정점 개수 : V개, 간선 개수 : E개 +> 정점 개수 : V개, 간선 개수 : E개 ### 간선 리스트 (Edge List) @@ -331,7 +329,7 @@ String[] name = {"Stacy", "Tracy", "Dorothy"}; ### 그래프 표현 방식 비교 -정점 개수 : V개, 간선 개수 : E개 +> 정점 개수 : V개, 간선 개수 : E개 | | 간선 리스트 | 인접 행렬 | 인접 리스트 | | :---: | :------: | :-------------: | :------------: | diff --git "a/contents/data-structure/img/\352\267\270\353\236\230\355\224\204.003.jpeg" "b/contents/data-structure/img/\352\267\270\353\236\230\355\224\204.003.jpeg" index 58e153425fcaadae8f0f2ccd7892bf3ec2161dde..a3183a94a15595988915596bea98bd2afea9fdbc 100644 GIT binary patch delta 25401 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Date: Mon, 12 Jul 2021 01:56:42 +0900 Subject: [PATCH 3/3] =?UTF-8?q?[Algorithm]=20DP=EC=99=80=20DAC=EC=9D=98=20?= =?UTF-8?q?=EC=B0=A8=EC=9D=B4=EC=A0=90=20=EC=B6=94=EA=B0=80=20#44?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- contents/algorithm/basic.md | 3 +++ 1 file changed, 3 insertions(+) diff --git a/contents/algorithm/basic.md b/contents/algorithm/basic.md index 799e6cb..c5a75eb 100644 --- a/contents/algorithm/basic.md +++ b/contents/algorithm/basic.md @@ -439,3 +439,6 @@ public class SubsetTest { 동적 계획법은 주어진 문제를 해결하기 위해 여러 개의 하위 문제로 나누어 푼 다음 결합하여 답을 찾는 방법이다. 문제 해결을 위해서는 다양한 방법으로 하위 문제로 나누어 보고 주어진 시간 복잡도 내에서 수행이 가능한 최적의 **점화식**을 찾는 것이 핵심이다. 동적 계획법을 적용한 대표적인 문제로는 배낭 짐싸기 문제(Knapsack Problem), 최장증가수열(LIS, Longest Increasing Subsequence), 외판원 순회 문제(TSP, Traveling Salesman Problem) 등이 있다. 이 밖에도 memoization 및 점화식을 통해 다양한 문제를 훨씬 효율적인 방식으로 해결할 수 있다. + +> **"큰 문제를 여러개의 하위 문제로 나누어 푼다"** 라는 점에서 +> DP는 그 하위의 값이 계속 변하고, DAC는 변하지 않는다는 차이점이 있다. 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