chpt10_graph_theory_review.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "74714a39",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "expected an indented block after 'else' statement on line 14 (3096443045.py, line 15)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"/var/folders/kn/gg6frwt12s7gcf_n79d00hy80000gn/T/ipykernel_747/3096443045.py\"\u001b[0;36m, line \u001b[0;32m15\u001b[0m\n\u001b[0;31m    v, e = map(int, input().split())\u001b[0m\n\u001b[0m                                    ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m expected an indented block after 'else' statement on line 14\n"
     ]
    }
   ],
   "source": [
    "# 1. 서로소 알고리즘을 통한 사이클 판별\n",
    "\n",
    "def find_parent(parent, x):\n",
    "    if parent[x] != x:\n",
    "        parent[x] = find_parent(parent, parent[x])\n",
    "    # 경로 압축을 통해 조금 더 효율적으로!\n",
    "    return parent[x]\n",
    "\n",
    "# parent를 같게 만드는데, 둘 중 큰 것의 부모를 더 작은 것의 부모로 지정\n",
    "def union_parent(parent, a, b):\n",
    "    a = find_parent(parent, a)\n",
    "    b = find_parent(parent, b)\n",
    "    if a > b:\n",
    "        parent[a] = b\n",
    "    else:\n",
    "        parent[b] = a\n",
    "        \n",
    "v, e = map(int, input().split())\n",
    "\n",
    "parent = [0]*(v+1)\n",
    "edges = []\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    parent[i] = i\n",
    "\n",
    "for _ in range(e):\n",
    "    a, b = map(int, input().split())\n",
    "    edges.append((a, b))\n",
    "    \n",
    "cycle = False\n",
    "\n",
    "# 서로소 판별 알고리즘!\n",
    "for edge in edges:\n",
    "    a, b = edge\n",
    "    if find_parent(parent, a) == find_parent(parent, b):\n",
    "        cycle = True\n",
    "    else:\n",
    "        union_parent(parent, a, b)\n",
    "        \n",
    "print(cycle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dd737ab8",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3 3\n",
      "3 1 2\n",
      "2 2 3\n",
      "1 1 3\n",
      "3\n"
     ]
    }
   ],
   "source": [
    "# kruskal algorithm\n",
    "# 그리디 알고리즘의 일종으로, 간선들을 비용에 따라 정렬 후 사이클이 형성된다면 넘어가고, 아니라면 parent를 합침\n",
    "\n",
    "def find_parent(parent, x):\n",
    "    if parent[x] != x:\n",
    "        parent[x] = find_parent(parent, parent[x])\n",
    "    return parent[x]\n",
    "\n",
    "def union_parent(parent, a, b):\n",
    "    a = find_parent(parent, a)\n",
    "    b = find_parent(parent, b)\n",
    "    if a > b:\n",
    "        parent[a] = b\n",
    "    else:\n",
    "        parent[b] = a\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "edges = []\n",
    "result = 0\n",
    "\n",
    "parent = [0]*(v+1)\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    parent[i] = i\n",
    "    \n",
    "for _ in range(e):\n",
    "    cost, a, b = map(int, input().split())\n",
    "    edges.append((cost, a, b))\n",
    "    \n",
    "edges.sort()\n",
    "\n",
    "for edge in edges:\n",
    "    cost, a, b = edge\n",
    "    if find_parent(parent, a) == find_parent(parent, b):\n",
    "        continue\n",
    "    else:\n",
    "        union_parent(parent, a, b)\n",
    "        result+=cost\n",
    "        \n",
    "print(cost)\n",
    "        \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1390734d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 8\n",
      "1 2\n",
      "1 5\n",
      "2 3\n",
      "2 6\n",
      "3 4\n",
      "4 7\n",
      "5 6\n",
      "6 4\n",
      "[1]\n",
      "[1, 2]\n",
      "[1, 2, 5]\n",
      "[1, 2, 5, 3]\n",
      "[1, 2, 5, 3, 6]\n",
      "[1, 2, 5, 3, 6, 4]\n",
      "[1, 2, 5, 3, 6, 4, 7]\n"
     ]
    }
   ],
   "source": [
    "# topology sort\n",
    "# 선수 과목과 같은 앞의 것이 충족되어야 뒤의 것을 할 수 있는 것을 할 때 유용\n",
    "\n",
    "from collections import deque\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "\n",
    "graph = [[] for _ in range(v+1)]\n",
    "edges = []\n",
    "indegree = [0]*(v+1)\n",
    "for _ in range(e):\n",
    "    a, b = map(int, input().split())\n",
    "    edges.append((a, b))\n",
    "    \n",
    "for edge in edges:\n",
    "    a, b = edge\n",
    "    graph[a].append(b)\n",
    "    indegree[b]+=1\n",
    "    \n",
    "q = deque()\n",
    "visited = []\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    if indegree[i] == 0:\n",
    "        q.append(i)\n",
    "        \n",
    "while q:\n",
    "    now = q.popleft()\n",
    "    visited.append(now)\n",
    "    \n",
    "    for v in graph[now]:\n",
    "        indegree[v]-=1\n",
    "        if indegree[v] == 0:\n",
    "            q.append(v)\n",
    "            \n",
    "\n",
    "print(visited)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "250921bb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 8\n",
      "0 1 3\n",
      "1 1 7\n",
      "NO\n",
      "0 7 6\n",
      "1 7 1\n",
      "NO\n",
      "0 3 7\n",
      "0 4 2\n",
      "0 1 1\n",
      "1 1 1\n",
      "YES\n"
     ]
    }
   ],
   "source": [
    "# 10-2 / 실전 문제 / 팀 결성\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "parent = [0]*(v+1)\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    parent[i] = i\n",
    "    \n",
    "# 경로 압축 방식의 서로소 집합 자료 구조\n",
    "def find_parent(parent, x):\n",
    "    if parent[x] != x:\n",
    "        parent[x] = find_parent(parent, parent[x])\n",
    "    return parent[x]\n",
    "\n",
    "def union_parent(parent, a, b):\n",
    "    a = find_parent(parent, a)\n",
    "    b = find_parent(parent, b)\n",
    "    if a > b:\n",
    "        parent[a] = b\n",
    "    else:\n",
    "        parent[b] = a\n",
    "        \n",
    "# 사이클 확인은 딱히 필요 없음!\n",
    "\n",
    "for _ in range(e):\n",
    "    oper, a, b = map(int, input().split())\n",
    "    if oper == 0:\n",
    "        union_parent(parent, a, b)\n",
    "    elif oper == 1:\n",
    "        if find_parent(parent, a) == find_parent(parent, b):\n",
    "            print(\"YES\")\n",
    "        else:\n",
    "            print(\"NO\")\n",
    "    else:\n",
    "        print(\"unappropriate input!\")\n",
    "        \n",
    "# solve!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b2b57ae1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 12\n",
      "1 2 3\n",
      "1 3 2\n",
      "3 2 1\n",
      "2 5 2\n",
      "3 4 4\n",
      "7 3 6\n",
      "5 1 5\n",
      "1 6 2\n",
      "6 4 1\n",
      "6 5 3\n",
      "4 5 3\n",
      "6 7 4\n",
      "8\n"
     ]
    }
   ],
   "source": [
    "# 10-3 / 실전 문제 / 도시 분할 계획\n",
    "# kruskal algorithm use!\n",
    "\n",
    "def find_parent(parent, x):\n",
    "    if parent[x] != x:\n",
    "        parent[x] = find_parent(parent, parent[x])\n",
    "        \n",
    "    return parent[x]\n",
    "\n",
    "def union_parent(parent, a, b):\n",
    "    a = find_parent(parent, a)\n",
    "    b = find_parent(parent, b)\n",
    "    \n",
    "    if a > b:\n",
    "        parent[a] = b\n",
    "    else:\n",
    "        parent[b] = a\n",
    "\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "parent = [0]*(v+1)\n",
    "for i in range(1, v+1):\n",
    "    parent[i] = i\n",
    "    \n",
    "edges = []\n",
    "\n",
    "for _ in range(e):\n",
    "    a, b, cost = map(int, input().split())\n",
    "    edges.append((cost, a, b))\n",
    "\n",
    "edges.sort()\n",
    "\n",
    "result = 0\n",
    "last = 0\n",
    "\n",
    "for edge in edges:\n",
    "    cost, a, b = edge\n",
    "    if find_parent(parent, a) == find_parent(parent, b):\n",
    "        continue\n",
    "    else:\n",
    "        union_parent(parent, a, b)\n",
    "        result+=cost\n",
    "        last = cost\n",
    "        \n",
    "print(result-last)\n",
    "\n",
    "# solve!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "115bb7e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 10-4 / 실전 문제 / 커리큘럼 curriculum\n",
    "import copy\n",
    "from collections import deque\n",
    "\n",
    "v = int(input())\n",
    "indegree = [0]*(v+1)\n",
    "time = [0]*(v+1)\n",
    "graph = [[] for _ in range(v+1)]\n",
    "for i in range(1, n+1):\n",
    "    data = list(map(int, input().split()))\n",
    "    time[i] = data[0]\n",
    "    pre = data[1:-1]\n",
    "    graph[i].append(pre)\n",
    "    indegree[i]+=len(pre)\n",
    "\n",
    "q = deque()\n",
    "cur_time = copy.deepcopy(time)\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    if indegree[i] == 0:\n",
    "        q.append(i)\n",
    "    \n",
    "#.. review"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a3e2baf0",
   "metadata": {},
   "outputs": [
    {
     "ename": "IndentationError",
     "evalue": "expected an indented block after 'for' statement on line 37 (2313297534.py, line 37)",
     "output_type": "error",
     "traceback": [
      "\u001b[0;36m  File \u001b[0;32m\"/var/folders/kn/gg6frwt12s7gcf_n79d00hy80000gn/T/ipykernel_815/2313297534.py\"\u001b[0;36m, line \u001b[0;32m37\u001b[0m\n\u001b[0;31m    for i in range(1, v+1):\u001b[0m\n\u001b[0m                           ^\u001b[0m\n\u001b[0;31mIndentationError\u001b[0m\u001b[0;31m:\u001b[0m expected an indented block after 'for' statement on line 37\n"
     ]
    }
   ],
   "source": [
    "from collections import deque\n",
    "import copy\n",
    "\n",
    "v = int(input())\n",
    "indegree = [0]*(v+1)\n",
    "\n",
    "graph = [[] for _ in range(v+1)]\n",
    "time = [0]*(v+1)\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    data = list(map(int, input().split()))\n",
    "    time[i] = data[0]\n",
    "    for x in data[1:-1]:\n",
    "        indegree[i]+=1\n",
    "        # x에 i를 넣는 이유는 그 이후에 수강해야 하기 때문!\n",
    "        graph[x].append(i)\n",
    "\n",
    "        \n",
    "def topology_sort():\n",
    "    # 순수 강의 하나의 시간과 총 강의 시간 계산을 위해 따로 분리!\n",
    "    result = copy.deepcopy(result) # algorithm result를 담을 리스트\n",
    "    q = deque()\n",
    "    \n",
    "    for i in range(1, v+1):\n",
    "        if indegree[i] == 0:\n",
    "            q.append(i)\n",
    "        \n",
    "    while q:\n",
    "        now = q.popleft()\n",
    "        for i in graph[now]:\n",
    "            result[i] = max(result[i], result[now]+time[i])\n",
    "            indegree[i]-=1\n",
    "            \n",
    "            if indegree[i] == 0:\n",
    "                q.append(i)\n",
    "                \n",
    "    for i in range(1, v+1):\n",
    "        print(result[i], end=' ')\n",
    "        \n",
    "topology_sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c9e6dfcd",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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