{
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   "source": [
    "Given a set of `N` people (numbered `1, 2, ..., N`), we would like to split\n",
    "everyone into two groups of **any** size.\n",
    "\n",
    "Each person may dislike some other people, and they should not go into the\n",
    "same group.\n",
    "\n",
    "Formally, if `dislikes[i] = [a, b]`, it means it is not allowed to put the\n",
    "people numbered `a` and `b` into the same group.\n",
    "\n",
    "Return `true` if and only if it is possible to split everyone into two groups\n",
    "in this way.\n",
    "\n",
    "\n",
    "\n",
    "**Example 1:**\n",
    "\n",
    "\n",
    "\n",
    "    Input: N = 4, dislikes = [[1,2],[1,3],[2,4]]\n",
    "    Output: true\n",
    "    **Explanation** : group1 [1,4], group2 [2,3]\n",
    "\n",
    "\n",
    "**Example 2:**\n",
    "\n",
    "\n",
    "\n",
    "    Input: N = 3, dislikes = [[1,2],[1,3],[2,3]]\n",
    "    Output: false\n",
    "\n",
    "\n",
    "**Example 3:**\n",
    "\n",
    "\n",
    "\n",
    "    Input: N = 5, dislikes = [[1,2],[2,3],[3,4],[4,5],[1,5]]\n",
    "    Output: false\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "**Constraints:**\n",
    "\n",
    "  * `1 <= N <= 2000`\n",
    "  * `0 <= dislikes.length <= 10000`\n",
    "  * `dislikes[i].length == 2`\n",
    "  * `1 <= dislikes[i][j] <= N`\n",
    "  * `dislikes[i][0] < dislikes[i][1]`\n",
    "  * There does not exist `i != j` for which `dislikes[i] == dislikes[j]`."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "possible_bipartition (generic function with 1 method)"
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "cell_type": "code",
   "source": [
    "# @lc code=start\n",
    "using LeetCode\n",
    "\n",
    "using DataStructures\n",
    "function possible_bipartition(n::Int, dislikes::Vector{Vector{Int}})\n",
    "    int_ds = IntDisjointSets(n)\n",
    "    graph = [Int[] for _ in 1:n]\n",
    "    for (a, b) in dislikes\n",
    "        push!(graph[a], b)\n",
    "        push!(graph[b], a)\n",
    "    end\n",
    "    for i in 1:n\n",
    "        for j in graph[i]\n",
    "            union!(int_ds, graph[i][1], j)\n",
    "            DataStructures.in_same_set(int_ds, i, j) && return false\n",
    "        end\n",
    "    end\n",
    "    return true\n",
    "end\n",
    "# @lc code=end"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
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