chpt10_primary_theory.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "aaac45f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "# kruskal algorithm\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",
    "    \n",
    "    if a > b:\n",
    "        parent[a] = b\n",
    "    else:\n",
    "        parent[b] = a\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "\n",
    "edges = []\n",
    "parent = [0]*(v+1)\n",
    "\n",
    "for _ in range(e):\n",
    "    a, b, cost = map(int, input().split())\n",
    "    edges.append((cost, a, b))\n",
    "    \n",
    "    \n",
    "edges.sort()\n",
    "result = 0\n",
    "\n",
    "for edge in edges:\n",
    "    cost, a, b = edge\n",
    "    \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(result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "234f9ff5",
   "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",
      "2\n",
      "5\n",
      "3\n",
      "6\n",
      "4\n",
      "7\n"
     ]
    }
   ],
   "source": [
    "# Topology sort\n",
    "# 1. 진입 차수가 0인 노드를 큐에 넣음\n",
    "# 2. 큐가 빌 때까지 다음의 과정을 반복\n",
    "# - 큐에서 원소를 꺼내 해당 노드에서 출발하는 간선을 그래프에서 제거\n",
    "# - 새롭게 진입차수가 0이 된 노드를 큐에 넣는다.\n",
    "\n",
    "from collections import deque\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "graph = [[] for _ in range(v+1)]\n",
    "indegree = [0]*(v+1)\n",
    "\n",
    "for _ in range(e):\n",
    "    a, b = map(int, input().split())\n",
    "    graph[a].append(b)\n",
    "    indegree[b]+=1\n",
    "\n",
    "\n",
    "def topology_sort():\n",
    "    q = deque()\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",
    "        print(now)\n",
    "        for ver in graph[now]:\n",
    "            indegree[ver]-=1\n",
    "            if indegree[ver] == 0:\n",
    "                q.append(ver)\n",
    "        \n",
    "\n",
    "topology_sort()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ada09c59",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7 8\n",
      "0 1 3\n",
      "1 1 7\n",
      "YES\n"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "Interrupted by user",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m/var/folders/kn/gg6frwt12s7gcf_n79d00hy80000gn/T/ipykernel_21830/2052386330.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m     18\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     19\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m     \u001b[0mop\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minput\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msplit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     21\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mop\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mfind_parent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparent\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mfind_parent\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparent\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36mraw_input\u001b[0;34m(self, prompt)\u001b[0m\n\u001b[1;32m   1004\u001b[0m                 \u001b[0;34m\"raw_input was called, but this frontend does not support input requests.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1005\u001b[0m             )\n\u001b[0;32m-> 1006\u001b[0;31m         return self._input_request(\n\u001b[0m\u001b[1;32m   1007\u001b[0m             \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mprompt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1008\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_parent_ident\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"shell\"\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Frameworks/Python.framework/Versions/3.10/lib/python3.10/site-packages/ipykernel/kernelbase.py\u001b[0m in \u001b[0;36m_input_request\u001b[0;34m(self, prompt, ident, parent, password)\u001b[0m\n\u001b[1;32m   1049\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1050\u001b[0m                 \u001b[0;31m# re-raise KeyboardInterrupt, to truncate traceback\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1051\u001b[0;31m                 \u001b[0;32mraise\u001b[0m \u001b[0mKeyboardInterrupt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Interrupted by user\"\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1052\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1053\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Invalid Message:\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mexc_info\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: Interrupted by user"
     ]
    }
   ],
   "source": [
    "# 실전 문제 / 팀 결성\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",
    "parent = [0]*(v+1)\n",
    "for i in range(1, v+1):\n",
    "    parent[i] = i\n",
    "    \n",
    "for _ in range(e):\n",
    "    op, a, b = map(int, input().split())\n",
    "    if op == 0:\n",
    "        if find_parent(parent, a) != find_parent(parent, b):\n",
    "            union_parent(parent, a, b)\n",
    "    else:\n",
    "        if find_parent(parent, a) == find_parent(parent, b):\n",
    "            print(\"YES\")\n",
    "        else:\n",
    "            print(\"NO\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8aaee728",
   "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": [
    "# 실전 문제 / 도시 분할 계획\n",
    "\n",
    "v, e = map(int, input().split())\n",
    "edges = []\n",
    "\n",
    "for _ in range(e):\n",
    "    a, b, c = map(int, input().split())\n",
    "    edges.append((c, a, b))\n",
    "    \n",
    "edges.sort()\n",
    "parent = [0]*(v+1)\n",
    "\n",
    "for i in range(1, v+1):\n",
    "    parent[i] = i\n",
    "    \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",
    "    \n",
    "    if a > b:\n",
    "        parent[a] = b\n",
    "    else:\n",
    "        parent[b] = a\n",
    "        \n",
    "result = 0\n",
    "for edge in edges:\n",
    "    cost, a, b = edge\n",
    "    \n",
    "    if find_parent(parent, a) != find_parent(parent, b):\n",
    "        union_parent(parent, a, b)\n",
    "        last = cost\n",
    "        result += cost\n",
    "        \n",
    "print(result - last)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "5ab84bba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n",
      "10 -1\n",
      "10 1 -1\n",
      "4 1 -1\n",
      "4 3 1 -1\n",
      "3 3 -1\n",
      "20\n",
      "24\n",
      "28\n",
      "31\n",
      "0\n"
     ]
    }
   ],
   "source": [
    "# 실전 문제 / 커리큘럼 / 위상 정렬 이용\n",
    "from collections import deque\n",
    "\n",
    "v = int(input())\n",
    "\n",
    "graph = [[] for _ in range(v+1)]\n",
    "indegree = [0]*(v+1)\n",
    "curri = [0]*(v+1)\n",
    "\n",
    "for i in range(v):\n",
    "    lis = list(map(int, input().split()))\n",
    "    curri[i] = lis[0]\n",
    "    graph[i] = lis[1:-1]\n",
    "\n",
    "def topology_sort():\n",
    "    for i in range(1, len(indegree)):\n",
    "        for now in graph[i]:\n",
    "            indegree[i]+=1\n",
    "            curri[i]+=curri[now]\n",
    "        \n",
    "    \n",
    "    q = deque()\n",
    "    for i in range(1,len(indegree)):\n",
    "        if indegree[i] == 0:\n",
    "            q.append(i)\n",
    "    \n",
    "    while q:\n",
    "        now = q.popleft()\n",
    "        for v in graph[now]:\n",
    "            \n",
    "                \n",
    "    for i in range(1, v+1):\n",
    "        print(curri[i])\n",
    "        \n",
    "topology_sort()\n",
    "        \n",
    "# unsolved.. must be review!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4a34109e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 실전 문제 / 커리큘럼 저자\n",
    "\n",
    "from collections import deque\n",
    "import copy\n",
    "\n",
    "v = int(input())\n",
    "\n",
    "indegree = [0]*(v+1)\n",
    "graph = [[] for _ in range(v+1)]\n",
    "\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",
    "        graph[x].append(i)\n",
    "        \n",
    "def top_sort():\n",
    "    result = copy.deepcopy(time)\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])\n",
    "        \n",
    "top_sort()"
   ]
  }
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