From bc092f563b19d4a0522ca6ac93c0873d80593862 Mon Sep 17 00:00:00 2001 From: beombu Date: Wed, 27 Apr 2022 17:03:43 +0900 Subject: [PATCH 1/8] add : tree --- 09/beom/Tree.md | 70 +++++++++++++++++++++++++ 09/beom/asset/complete_binary_tree.png | Bin 0 -> 18985 bytes 09/beom/asset/perfect_binary_tree.png | Bin 0 -> 23083 bytes 09/beom/asset/tree.png | Bin 0 -> 100081 bytes 4 files changed, 70 insertions(+) create mode 100644 09/beom/Tree.md create mode 100644 09/beom/asset/complete_binary_tree.png create mode 100644 09/beom/asset/perfect_binary_tree.png create mode 100644 09/beom/asset/tree.png diff --git a/09/beom/Tree.md b/09/beom/Tree.md new file mode 100644 index 00000000..90281a49 --- /dev/null +++ b/09/beom/Tree.md @@ -0,0 +1,70 @@ +# Tree + +## 목차 +- 트리의 용어 +- 트리의 시간복잡도 +- 트리의 활용 +- Binary Tree + - 정 이진 트리(Full Binary Tree) + - 포화 이진 트리(Perfect Binary Tree) + - 완전 이진 트리(Complete Binary Tree) +- 트리의 순회 + + +## 트리의 용어 +![트리의 용어](asset/tree.png) + +- 트리 : 무방향이면서 사이클이 없는 연결그래프 +- 루트 노드 : 가장 상위 노드를 루트노드라고 한다. +- 부모 노드 : 부모-자식 관계에서 상위 계층의 노드 +- 자식 노드 : 부모-자식 관계에서 하위 계층의 노드 +- 형제 노드 : 부모가 동일한 노드 +- 서브트리 : 전체 트리 내에서 작게 나눠서 보면 또 따른 서브 트리라고 볼 수 있다. +- 노드 : 트리의 구성요소 +- 단말 노드 : 자식 노드가 없는 노드 +- 깊이 : 루트 노드에서 해당 노드까지 도달하는데 사용하는 간선의 수 + - 루트 노드의 깊이는 0 +- 레벨 : 노드의 깊이 + 1 +- 높이 : 루트 노드에서 해당 노드까지 도달하는데 지나간 정점의 개수 + - 트리에 차수 : 해당 트리 내 모든 노드의 높이 중 최댓값 +- 노드의 차수 : 노드의 자식 수 + - 트리에 차수 : 해당 트리 내 모든 노드의 차수 중 최댓값 + +## 트리의 시간복잡도 +- 노드 삽입 : O(1) +- 노드 삭제 : O(1) +- 노드 검색 : O(N) + +## 트리의 활용 +- HTML DOM 트리 +- 파일 시스템 +- DBMS +- 검색 엔진 +- 트라이 알고리즘 + +## Binary Tree +> 트리의 차수가 2 이하인 트리 + +- 비선형 자료구조 +- 자식이 최대 2개이기 때문에 자식을 왼쪽 자식과 오른쪽 자식으로 구분 +- 높이가 `N`인 이진 트리의 최대 노드 갯수는 2^N -1 개이다. + +### 정 이진 트리(Full Binary Tree) +> 모든 노드의 차수가 0 또는 2인 이진 트리 + +### 포화 이진 트리(Perfect Binary Tree) +> 정 이진 트리에서 단말 노드 제외 모든 노드가 두 개의 자식 노드를 가지고 모든 노드의 동일한 깊이 또는 레벨을 가지는 트리 + +![포화 이진 트리](asset/perfect_binary_tree.png) + +### 완전 이진 트리(Complete Binary Tree) +> 마지막 레벨을 제외하고 모든 레벨이 완전히 채워져 있고 마지막 레벨의 모든 노드는 가능한 가장 왼쪽에 있는 트리 + +![완전 이진 트리](asset/complete_binary_tree.png) + + +## 트리의 순회 + +1. 전위 순회(Pre-order) : 현재 노드 방문 -> 왼쪽 자식 탐색 -> 오른쪽 자식 탐색 +2. 중위 순회(In-order) : 왼쪽 자식 탐색 -> 현재 노드 방문 -> 오른쪽 자식 탐색 +3. 후위 순회(Post-order) : 왼쪽 자식 탐색 -> 오른쪽 자식 탐색 -> 현재노드 방문 diff --git a/09/beom/asset/complete_binary_tree.png b/09/beom/asset/complete_binary_tree.png new file mode 100644 index 0000000000000000000000000000000000000000..e75a945d83eea5bcd0ff224006c1d1d1939cc6ac GIT binary patch literal 18985 zcmc$F^$T42MdWH2tQBL#KtJl$p?{IWf#3$J-xf9~wYY$BY znO8Lvln00d099YNfK>n7+fMeTPr$R~y^bdA2o9g~^29ABsgw{B!TtP72rOojtD@|K7X@^fBlK zgbW6Q`|{E0Ah_@71DGJVGS0Hnp|~=N?+6(YKO)Qhe?K7Hy?q!8mtx@H_y{MU+nN)$ z>MsB;xNW&h$d3zkePm9fm7qg4N++?{o(_;Z=(}^5k)c8X;N!2D(oC4y^-6W$(;bTW zC+E;4bcka$8j=OC>`@HumjPAcy*+(I>zk_3*Mr=INkD~k$?9P_5H1XSx!IN@ijzPn zeEn8!)53!)J?$VljS9O}{JiPZ{a!=wll=Quz@(E&BDZ)K^^|D5YiiOT8R^g{;`T;v zVXv(@XsLM$nYv*`n5Nfl^_xg&IZA+-}ZQ$z7p2FAbYNwkGt#jO-CXD3fl zAAIP7d!K$G+t(VHpU!NkhM^;a>;MO%ouu0NhkNn 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HI!6CrC2%@z literal 0 HcmV?d00001 From 4eb19c7db7dc8aed7629c567f0c9f8a64d8c03bb Mon Sep 17 00:00:00 2001 From: beombu Date: Wed, 27 Apr 2022 19:44:57 +0900 Subject: [PATCH 2/8] add : bintree.java --- ADT/beom/Tree/binTree.java | 216 +++++++++++++++++++++++++++++++++++++ 1 file changed, 216 insertions(+) create mode 100644 ADT/beom/Tree/binTree.java diff --git a/ADT/beom/Tree/binTree.java b/ADT/beom/Tree/binTree.java new file mode 100644 index 00000000..4d5de619 --- /dev/null +++ b/ADT/beom/Tree/binTree.java @@ -0,0 +1,216 @@ +```java +package algorithmStudyTree; + +import java.security.PublicKey; +import java.util.Comparator; +import java.util.LinkedList; +import java.util.Queue; + +public class BinTree { + static class Node{ + private K key; + private V data; + private Node left; + private Node right; + + public Node(K key, V data, Node left, Node right) { + this.key = key; + this.data = data; + this.left = left; + this.right = right; + } + + public K getKey() { + return key; + } + + public V getData() { + return data; + } + + void print(){ + System.out.println(data); + } + } + + private Node root; + private Comparator comparator =null; //비교자 + + public BinTree() { + root = null; + } + + public BinTree(Comparator c) { + this(); + this.comparator = c; + } + + private int comp(K key1, K key2){ + return (comparator == null) ? ((Comparable) key1).compareTo(key2) + : comparator.compare(key1, key2); + } + + public V search(K key){ + Node p = root; + + while(true){ + if(p==null) + return null; + int cond = comp(key, p.getKey()); + if(cond == 0){ + //System.out.println(p.getData()); + return p.getData(); + } + else if(cond <0) + p = p.left; + else + p=p.right; + } + } + + private void addNode(Node node, K key, V data){ + int cond = comp(key, node.getKey()); + if(cond ==0) + return; + else if(cond < 0){ + if(node.left == null) + node.left = new Node(key, data,null,null); + else + addNode(node.left, key,data); + } else{ + if(node.right == null) + node.right = new Node(key, data,null,null); + else + addNode(node.right, key,data); + } + } + + //addNode는 private로 외부에서 사용x + public void add(K key, V data){ + if(root == null) + root = new Node(key,data,null,null); + else + addNode(root, key, data); + } + + public boolean remove(K key){ + Node p = root; + Node parent = null; + boolean isLeftChild = true; + + while (true){ + if(p==null) + return false; + int cond = comp(key,p.getKey()); + if (cond == 0) + break; + else{ + parent = p; + if(cond < 0){ + isLeftChild = true; + p = p.left; + } else { + isLeftChild = false; + p = p.right; + } + } + } + + if(p.left == null){ + if(p == root) + root = p.right; + else if(isLeftChild) + parent.left = p.right; + else + parent.right = p.right; + } else if(p.right ==null){ + if(p == root) + root = p.left; + else if(isLeftChild) + parent.left = p.left; + else + parent.right = p.left; + } else{ + parent = p; + Node left = p.left; + isLeftChild = true; + while(left.right != null){ + parent = left; + left = left.right; + isLeftChild = false; + } + p.key = left.key; + p.data = left.data; + if(isLeftChild) + parent.left = left.left; + else + parent.right = left.left; + } + return true; + } + + private void preOrder(Node node){ + if(node != null){ + System.out.print(node.data + " " ); + preOrder(node.left); + preOrder(node.right); + } + } + + public void printPreOrder(){ + preOrder(root); + } + + private void inOrder(Node node){ + if(node != null){ + inOrder(node.left); + System.out.print(node.data + " "); + inOrder(node.right); + } + } + + public void printInOrder(){ + inOrder(root); + } + + private void postOrder(Node node){ + if(node != null){ + postOrder(node.left); + postOrder(node.right); + System.out.print(node.data + " "); + } + } + + public void printPostOrder(){ + postOrder(root); + } + + private void levelOrder(Node a){ + Queue queue= new LinkedList<>(); + queue.offer(a); + Node p = root; + + while(!queue.isEmpty()){ + Node node = queue.poll(); + System.out.print(node.getData()+ " "); + + if(node.left != null){ + p = p.left; + queue.offer(p); + } + + if(node.right != null){ + p = p.right; + queue.offer(p); + } + } + } + + public void printLevelOrder(){ + levelOrder(root); + } + + +} + +``` From 5cc26df4ed35e021b79b71f30bcad698136345a8 Mon Sep 17 00:00:00 2001 From: beombu Date: Thu, 28 Apr 2022 16:40:20 +0900 Subject: [PATCH 3/8] finish : implement Tree --- 09/beom/TreeTest.java | 26 ++++++++++++++++++++++++++ ADT/beom/Tree/binTree.java | 20 +++++++++----------- 2 files changed, 35 insertions(+), 11 deletions(-) create mode 100644 09/beom/TreeTest.java diff --git a/09/beom/TreeTest.java b/09/beom/TreeTest.java new file mode 100644 index 00000000..4ed515a4 --- /dev/null +++ b/09/beom/TreeTest.java @@ -0,0 +1,26 @@ +package algorithmStudyTree; + +public class implementTree { + + public static void main(String[] args) { + BinTree binTree = new BinTree<>(); + + binTree.add(30,30); + binTree.add(25,25); + binTree.add(90,90); + binTree.add(19,19); + binTree.add(26,26); + binTree.add(77,77); + binTree.add(99,99); + binTree.add(5,5); + + binTree.printPreOrder(); + System.out.println(); + binTree.printInOrder(); + System.out.println(); + binTree.printPostOrder(); + System.out.println(); + binTree.printLevelOrder(); + System.out.println(); + } +} \ No newline at end of file diff --git a/ADT/beom/Tree/binTree.java b/ADT/beom/Tree/binTree.java index 4d5de619..efb8ad28 100644 --- a/ADT/beom/Tree/binTree.java +++ b/ADT/beom/Tree/binTree.java @@ -152,8 +152,8 @@ else if(isLeftChild) private void preOrder(Node node){ if(node != null){ System.out.print(node.data + " " ); - preOrder(node.left); - preOrder(node.right); + if(node.left != null) preOrder(node.left); + if(node.right != null) preOrder(node.right); } } @@ -163,9 +163,9 @@ public void printPreOrder(){ private void inOrder(Node node){ if(node != null){ - inOrder(node.left); + if(node.left != null) inOrder(node.left); System.out.print(node.data + " "); - inOrder(node.right); + if(node.right != null) inOrder(node.right); } } @@ -175,8 +175,8 @@ public void printInOrder(){ private void postOrder(Node node){ if(node != null){ - postOrder(node.left); - postOrder(node.right); + if(node.left != null) postOrder(node.left); + if(node.right != null) postOrder(node.right); System.out.print(node.data + " "); } } @@ -188,20 +188,17 @@ public void printPostOrder(){ private void levelOrder(Node a){ Queue queue= new LinkedList<>(); queue.offer(a); - Node p = root; while(!queue.isEmpty()){ Node node = queue.poll(); System.out.print(node.getData()+ " "); if(node.left != null){ - p = p.left; - queue.offer(p); + queue.offer(node.left); } if(node.right != null){ - p = p.right; - queue.offer(p); + queue.offer(node.right); } } } @@ -213,4 +210,5 @@ public void printLevelOrder(){ } + ``` From 44e2d0d0a5ebf7262a8a98a172f454f62d3c25c7 Mon Sep 17 00:00:00 2001 From: beombu Date: Thu, 28 Apr 2022 18:23:36 +0900 Subject: [PATCH 4/8] add : Leetcode 99 --- 09/beom/Leetcode.md | 91 +++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 91 insertions(+) create mode 100644 09/beom/Leetcode.md diff --git a/09/beom/Leetcode.md b/09/beom/Leetcode.md new file mode 100644 index 00000000..4f83c35a --- /dev/null +++ b/09/beom/Leetcode.md @@ -0,0 +1,91 @@ +# Tree +## 목차 +- 99. Recover Binary Search Tree + + +## 99. Recover Binary Search Tree +### 문제 요약 +BST의 순서가 잘못된 것을 복원하시오 + +> 풀이
+> 주어진 root를 중위순회 방식으로 하여 오름차순 또는 내림차순으로 정렬된 배열을 바꿔야할 것같다는 생각까지만 들었다. 하지만 그 이후로는 생각이 나지 않아 discuss의 도움을 받았다. + +### 시간 복잡도 공간복잡도 +| time | space | +|------|-------| +| O(n) | O(n) | + +### 코드 +```java +class Solution { + TreeNode prev = null; + TreeNode first = null; + TreeNode second = null; + + public void recoverTree(TreeNode root) { + inOrder(root); + int temp = first.val; + first.val = second.val; + second.val = temp; + } + + public void inOrder(TreeNode root){ + if(root==null)return; + inOrder(root.left); + + if(prev!=null&&root.val Date: Fri, 29 Apr 2022 10:59:48 +0900 Subject: [PATCH 5/8] add : treeset, treemap & ppt --- 09/beom/Tree.md | 31 ++++++++++++++++++++++++++----- 09/beom/Tree.pptx | Bin 0 -> 1172644 bytes 2 files changed, 26 insertions(+), 5 deletions(-) create mode 100644 09/beom/Tree.pptx diff --git a/09/beom/Tree.md b/09/beom/Tree.md index 90281a49..45d5af3e 100644 --- a/09/beom/Tree.md +++ b/09/beom/Tree.md @@ -30,11 +30,6 @@ - 노드의 차수 : 노드의 자식 수 - 트리에 차수 : 해당 트리 내 모든 노드의 차수 중 최댓값 -## 트리의 시간복잡도 -- 노드 삽입 : O(1) -- 노드 삭제 : O(1) -- 노드 검색 : O(N) - ## 트리의 활용 - HTML DOM 트리 - 파일 시스템 @@ -68,3 +63,29 @@ 1. 전위 순회(Pre-order) : 현재 노드 방문 -> 왼쪽 자식 탐색 -> 오른쪽 자식 탐색 2. 중위 순회(In-order) : 왼쪽 자식 탐색 -> 현재 노드 방문 -> 오른쪽 자식 탐색 3. 후위 순회(Post-order) : 왼쪽 자식 탐색 -> 오른쪽 자식 탐색 -> 현재노드 방문 + +## Java에서의 Tree + +자바의 Collection Framework는 `treeset`과 `treemap`을 지원한다. + +`treeset`과 `treemap`은 내부적으로 어떤 자료구조를 사용하고 있을까? + +바로 `레드블랙트리(Red-Black-Tree)`를 사용한다. + +레드블랙트리의 자세한 내용은 아래 링크를 참고하자 + +[레드블랙트리링크](https://devlog-wjdrbs96.tistory.com/159?category=882242) + +간단하게 설명하자면 데이터가 한쪽으로 편향되는 경우를 방지하기 위해 삽입시에 레드 블랙트리의 조건에 의해 균형이 맞춰진 트리가 만들어진다. + +중요한 것은 BST의 연산의 시간복잡도는 트리의 높이만큼 증가하는데 편향된 트리(O(n))에서 균형이 잡힌 트리(O(logn))으로 줄였다는 것이다. + +`treeset`과 `treemap`의 **차이점**은 + +`treeset`은 그냥 값만 저장한다면 `treemap`은 키와 값이 저장된 Map, Entry를 저장한다는 것이다. + +## 트리의 시간복잡도\ +- treeset, treemap 동일 +- 노드 삽입 : O(log n) +- 노드 삭제 : O(log n) +- 노드 검색 : O(log n) diff --git a/09/beom/Tree.pptx b/09/beom/Tree.pptx new file 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