Frog Position After T Seconds
<p>Given an undirected tree consisting of <code>n</code> vertices numbered from <code>1</code> to <code>n</code>. A frog starts jumping from <strong>vertex 1</strong>. In one second, the frog jumps from its current vertex to another <strong>unvisited</strong> vertex if they are directly connected. The frog can not jump back to a visited vertex. In case the frog can jump to several vertices, it jumps randomly to one of them with the same probability. Otherwise, when the frog can not jump to any unvisited vertex, it jumps forever on the same vertex.</p>

<p>The edges of the undirected tree are given in the array <code>edges</code>, where <code>edges[i] = [a<sub>i</sub>, b<sub>i</sub>]</code> means that exists an edge connecting the vertices <code>a<sub>i</sub></code> and <code>b<sub>i</sub></code>.</p>

<p><em>Return the probability that after <code>t</code> seconds the frog is on the vertex <code>target</code>. </em>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/12/21/frog1.jpg" style="width: 338px; height: 304px;" />
<pre>
<strong>Input:</strong> n = 7, edges = [[1,2],[1,3],[1,7],[2,4],[2,6],[3,5]], t = 2, target = 4
<strong>Output:</strong> 0.16666666666666666 
<strong>Explanation:</strong> The figure above shows the given graph. The frog starts at vertex 1, jumping with 1/3 probability to the vertex 2 after <strong>second 1</strong> and then jumping with 1/2 probability to vertex 4 after <strong>second 2</strong>. Thus the probability for the frog is on the vertex 4 after 2 seconds is 1/3 * 1/2 = 1/6 = 0.16666666666666666. 
</pre>

<p><strong class="example">Example 2:</strong></p>
<strong><img alt="" src="https://assets.leetcode.com/uploads/2021/12/21/frog2.jpg" style="width: 304px; height: 304px;" /></strong>

<pre>
<strong>Input:</strong> n = 7, edges = [[1,2],[1,3],[1,7],[2,4],[2,6],[3,5]], t = 1, target = 7
<strong>Output:</strong> 0.3333333333333333
<strong>Explanation: </strong>The figure above shows the given graph. The frog starts at vertex 1, jumping with 1/3 = 0.3333333333333333 probability to the vertex 7 after <strong>second 1</strong>. 
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 100</code></li>
	<li><code>edges.length == n - 1</code></li>
	<li><code>edges[i].length == 2</code></li>
	<li><code>1 &lt;= a<sub>i</sub>, b<sub>i</sub> &lt;= n</code></li>
	<li><code>1 &lt;= t &lt;= 50</code></li>
	<li><code>1 &lt;= target &lt;= n</code></li>
</ul>

['longest-special-path']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    double frogPosition(int n, vector<vector<int>>& edges, int t, int target) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public double frogPosition(int n, int[][] edges, int t, int target) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def frogPosition(self, n, edges, t, target):\n        \"\"\"\n        :type n: int\n        :type edges: List[List[int]]\n        :type t: int\n        :type target: int\n        :rtype: float\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def frogPosition(self, n: int, edges: List[List[int]], t: int, target: int) -> float:\n        "}, {"value": "c", "text": "C", "defaultCode": "double frogPosition(int n, int** edges, int edgesSize, int* edgesColSize, int t, int target) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public double FrogPosition(int n, int[][] edges, int t, int target) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number} n\n * @param {number[][]} edges\n * @param {number} t\n * @param {number} target\n * @return {number}\n */\nvar frogPosition = function(n, edges, t, target) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function frogPosition(n: number, edges: number[][], t: number, target: number): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer $n\n     * @param Integer[][] $edges\n     * @param Integer $t\n     * @param Integer $target\n     * @return Float\n     */\n    function frogPosition($n, $edges, $t, $target) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func frogPosition(_ n: Int, _ edges: [[Int]], _ t: Int, _ target: Int) -> Double {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun frogPosition(n: Int, edges: Array<IntArray>, t: Int, target: Int): Double {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  double frogPosition(int n, List<List<int>> edges, int t, int target) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func frogPosition(n int, edges [][]int, t int, target int) float64 {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer} n\n# @param {Integer[][]} edges\n# @param {Integer} t\n# @param {Integer} target\n# @return {Float}\ndef frog_position(n, edges, t, target)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def frogPosition(n: Int, edges: Array[Array[Int]], t: Int, target: Int): Double = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn frog_position(n: i32, edges: Vec<Vec<i32>>, t: i32, target: i32) -> f64 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (frog-position n edges t target)\n  (-> exact-integer? (listof (listof exact-integer?)) exact-integer? exact-integer? flonum?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec frog_position(N :: integer(), Edges :: [[integer()]], T :: integer(), Target :: integer()) -> float().\nfrog_position(N, Edges, T, Target) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec frog_position(n :: integer, edges :: [[integer]], t :: integer, target :: integer) :: float\n  def frog_position(n, edges, t, target) do\n    \n  end\nend"}]
{
  "name": "frogPosition",
  "params": [
    {
      "name": "n",
      "type": "integer"
    },
    {
      "type": "integer[][]",
      "name": "edges"
    },
    {
      "type": "integer",
      "name": "t"
    },
    {
      "type": "integer",
      "name": "target"
    }
  ],
  "return": {
    "type": "double"
  }
}
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Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. 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Adding an item to a hash.</b>\r\n<pre>\r\nstruct hash_entry {\r\n    int id;            /* we'll use this field as the key */\r\n    char name[10];\r\n    UT_hash_handle hh; /* makes this structure hashable */\r\n};\r\n\r\nstruct hash_entry *users = NULL;\r\n\r\nvoid add_user(struct hash_entry *s) {\r\n    HASH_ADD_INT(users, id, s);\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>2. Looking up an item in a hash:</b>\r\n<pre>\r\nstruct hash_entry *find_user(int user_id) {\r\n    struct hash_entry *s;\r\n    HASH_FIND_INT(users, &user_id, s);\r\n    return s;\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>3. 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If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. 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You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Tree', 'Depth-First Search', 'Breadth-First Search', 'Graph']