throne-inheritance

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A kingdom consists of a king, his children, his grandchildren, and so on. Every once in a while, someone in the family dies or a child is born.

The kingdom has a well-defined order of inheritance that consists of the king as the first member. Let&#39;s define the recursive function <code>Successor(x, curOrder)</code>, which given a person <code>x</code> and the inheritance order so far, returns who should be the next person after <code>x</code> in the order of inheritance.

<pre>
Successor(x, curOrder):
 if x has no children or all of x&#39;s children are in curOrder:
 if x is the king return null
 else return Successor(x&#39;s parent, curOrder)
 else return x&#39;s oldest child who&#39;s not in curOrder
</pre>

For example, assume we have a kingdom that consists of the king, his children Alice and Bob (Alice is older than Bob), and finally Alice&#39;s son Jack.

<ol>
	<li>In the beginning, <code>curOrder</code> will be <code>[&quot;king&quot;]</code>.</li>
	<li>Calling <code>Successor(king, curOrder)</code> will return Alice, so we append to <code>curOrder</code> to get <code>[&quot;king&quot;, &quot;Alice&quot;]</code>.</li>
	<li>Calling <code>Successor(Alice, curOrder)</code> will return Jack, so we append to <code>curOrder</code> to get <code>[&quot;king&quot;, &quot;Alice&quot;, &quot;Jack&quot;]</code>.</li>
	<li>Calling <code>Successor(Jack, curOrder)</code> will return Bob, so we append to <code>curOrder</code> to get <code>[&quot;king&quot;, &quot;Alice&quot;, &quot;Jack&quot;, &quot;Bob&quot;]</code>.</li>
	<li>Calling <code>Successor(Bob, curOrder)</code> will return <code>null</code>. Thus the order of inheritance will be <code>[&quot;king&quot;, &quot;Alice&quot;, &quot;Jack&quot;, &quot;Bob&quot;]</code>.</li>
</ol>

Using the above function, we can always obtain a unique order of inheritance.

Implement the <code>ThroneInheritance</code> class:

<ul>
	<li><code>ThroneInheritance(string kingName)</code> Initializes an object of the <code>ThroneInheritance</code> class. The name of the king is given as part of the constructor.</li>
	<li><code>void birth(string parentName, string childName)</code> Indicates that <code>parentName</code> gave birth to <code>childName</code>.</li>
	<li><code>void death(string name)</code> Indicates the death of <code>name</code>. The death of the person doesn&#39;t affect the <code>Successor</code> function nor the current inheritance order. You can treat it as just marking the person as dead.</li>
	<li><code>string[] getInheritanceOrder()</code> Returns a list representing the current order of inheritance excluding dead people.</li>
</ul>

&nbsp;
Example 1:

<pre>
Input
[&quot;ThroneInheritance&quot;, &quot;birth&quot;, &quot;birth&quot;, &quot;birth&quot;, &quot;birth&quot;, &quot;birth&quot;, &quot;birth&quot;, &quot;getInheritanceOrder&quot;, &quot;death&quot;, &quot;getInheritanceOrder&quot;]
[[&quot;king&quot;], [&quot;king&quot;, &quot;andy&quot;], [&quot;king&quot;, &quot;bob&quot;], [&quot;king&quot;, &quot;catherine&quot;], [&quot;andy&quot;, &quot;matthew&quot;], [&quot;bob&quot;, &quot;alex&quot;], [&quot;bob&quot;, &quot;asha&quot;], [null], [&quot;bob&quot;], [null]]
Output
[null, null, null, null, null, null, null, [&quot;king&quot;, &quot;andy&quot;, &quot;matthew&quot;, &quot;bob&quot;, &quot;alex&quot;, &quot;asha&quot;, &quot;catherine&quot;], null, [&quot;king&quot;, &quot;andy&quot;, &quot;matthew&quot;, &quot;alex&quot;, &quot;asha&quot;, &quot;catherine&quot;]]

Explanation
ThroneInheritance t= new ThroneInheritance(&quot;king&quot;); // order: king
t.birth(&quot;king&quot;, &quot;andy&quot;); // order: king &gt; andy
t.birth(&quot;king&quot;, &quot;bob&quot;); // order: king &gt; andy &gt; bob
t.birth(&quot;king&quot;, &quot;catherine&quot;); // order: king &gt; andy &gt; bob &gt; catherine
t.birth(&quot;andy&quot;, &quot;matthew&quot;); // order: king &gt; andy &gt; matthew &gt; bob &gt; catherine
t.birth(&quot;bob&quot;, &quot;alex&quot;); // order: king &gt; andy &gt; matthew &gt; bob &gt; alex &gt; catherine
t.birth(&quot;bob&quot;, &quot;asha&quot;); // order: king &gt; andy &gt; matthew &gt; bob &gt; alex &gt; asha &gt; catherine
t.getInheritanceOrder(); // return [&quot;king&quot;, &quot;andy&quot;, &quot;matthew&quot;, &quot;bob&quot;, &quot;alex&quot;, &quot;asha&quot;, &quot;catherine&quot;]
t.death(&quot;bob&quot;); // order: king &gt; andy &gt; matthew &gt; <s>bob</s> &gt; alex &gt; asha &gt; catherine
t.getInheritanceOrder(); // return [&quot;king&quot;, &quot;andy&quot;, &quot;matthew&quot;, &quot;alex&quot;, &quot;asha&quot;, &quot;catherine&quot;]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= kingName.length, parentName.length, childName.length, name.length &lt;= 15</code></li>
	<li><code>kingName</code>, <code>parentName</code>, <code>childName</code>, and <code>name</code> consist of lowercase English letters only.</li>
	<li>All arguments <code>childName</code> and <code>kingName</code> are distinct.</li>
	<li>All <code>name</code> arguments of <code>death</code> will be passed to either the constructor or as <code>childName</code> to <code>birth</code> first.</li>
	<li>For each call to&nbsp;<code>birth(parentName, childName)</code>, it is guaranteed that&nbsp;<code>parentName</code> is alive.</li>
	<li>At most <code>105</code> calls will be made to <code>birth</code> and <code>death</code>.</li>
	<li>At most <code>10</code> calls will be made to <code>getInheritanceOrder</code>.</li>
</ul>

Throne Inheritance

Operations on Tree

operations-on-tree

树上的操作

Tree

Depth-First Search

Design

Hash Table

一个王国里住着国王、他的孩子们、他的孙子们等等。每一个时间点，这个家庭里有人出生也有人死亡。

这个王国有一个明确规定的王位继承顺序，第一继承人总是国王自己。我们定义递归函数&nbsp;<code>Successor(x, curOrder)</code>&nbsp;，给定一个人&nbsp;<code>x</code>&nbsp;和当前的继承顺序，该函数返回 <code>x</code>&nbsp;的下一继承人。

<pre>
Successor(x, curOrder):
 如果 x 没有孩子或者所有 x 的孩子都在 curOrder 中：
 如果 x 是国王，那么返回 null
 否则，返回 Successor(x 的父亲, curOrder)
 否则，返回 x 不在 curOrder 中最年长的孩子
</pre>

比方说，假设王国由国王，他的孩子&nbsp;Alice 和 Bob （Alice 比 Bob&nbsp;年长）和 Alice 的孩子&nbsp;Jack 组成。

<ol>
	<li>一开始，&nbsp;<code>curOrder</code>&nbsp;为&nbsp;<code>["king"]</code>.</li>
	<li>调用&nbsp;<code>Successor(king, curOrder)</code>&nbsp;，返回 Alice ，所以我们将 Alice 放入 <code>curOrder</code>&nbsp;中，得到&nbsp;<code>["king", "Alice"]</code>&nbsp;。</li>
	<li>调用&nbsp;<code>Successor(Alice, curOrder)</code>&nbsp;，返回 Jack ，所以我们将 Jack 放入&nbsp;<code>curOrder</code>&nbsp;中，得到&nbsp;<code>["king", "Alice", "Jack"]</code>&nbsp;。</li>
	<li>调用&nbsp;<code>Successor(Jack, curOrder)</code>&nbsp;，返回 Bob ，所以我们将 Bob 放入&nbsp;<code>curOrder</code>&nbsp;中，得到&nbsp;<code>["king", "Alice", "Jack", "Bob"]</code>&nbsp;。</li>
	<li>调用&nbsp;<code>Successor(Bob, curOrder)</code>&nbsp;，返回&nbsp;<code>null</code>&nbsp;。最终得到继承顺序为&nbsp;<code>["king", "Alice", "Jack", "Bob"]</code>&nbsp;。</li>
</ol>

通过以上的函数，我们总是能得到一个唯一的继承顺序。

请你实现&nbsp;<code>ThroneInheritance</code>&nbsp;类：

<ul>
	<li><code>ThroneInheritance(string kingName)</code> 初始化一个&nbsp;<code>ThroneInheritance</code>&nbsp;类的对象。国王的名字作为构造函数的参数传入。</li>
	<li><code>void birth(string parentName, string childName)</code>&nbsp;表示&nbsp;<code>parentName</code>&nbsp;新拥有了一个名为&nbsp;<code>childName</code>&nbsp;的孩子。</li>
	<li><code>void death(string name)</code>&nbsp;表示名为&nbsp;<code>name</code>&nbsp;的人死亡。一个人的死亡不会影响&nbsp;<code>Successor</code>&nbsp;函数，也不会影响当前的继承顺序。你可以只将这个人标记为死亡状态。</li>
	<li><code>string[] getInheritanceOrder()</code>&nbsp;返回 除去&nbsp;死亡人员的当前继承顺序列表。</li>
</ul>

&nbsp;

示例：

<pre>
输入：
["ThroneInheritance", "birth", "birth", "birth", "birth", "birth", "birth", "getInheritanceOrder", "death", "getInheritanceOrder"]
[["king"], ["king", "andy"], ["king", "bob"], ["king", "catherine"], ["andy", "matthew"], ["bob", "alex"], ["bob", "asha"], [null], ["bob"], [null]]
输出：
[null, null, null, null, null, null, null, ["king", "andy", "matthew", "bob", "alex", "asha", "catherine"], null, ["king", "andy", "matthew", "alex", "asha", "catherine"]]

解释：
ThroneInheritance t= new ThroneInheritance("king"); // 继承顺序：king
t.birth("king", "andy"); // 继承顺序：king &gt; andy
t.birth("king", "bob"); // 继承顺序：king &gt; andy &gt; bob
t.birth("king", "catherine"); // 继承顺序：king &gt; andy &gt; bob &gt; catherine
t.birth("andy", "matthew"); // 继承顺序：king &gt; andy &gt; matthew &gt; bob &gt; catherine
t.birth("bob", "alex"); // 继承顺序：king &gt; andy &gt; matthew &gt; bob &gt; alex &gt; catherine
t.birth("bob", "asha"); // 继承顺序：king &gt; andy &gt; matthew &gt; bob &gt; alex &gt; asha &gt; catherine
t.getInheritanceOrder(); // 返回 ["king", "andy", "matthew", "bob", "alex", "asha", "catherine"]
t.death("bob"); // 继承顺序：king &gt; andy &gt; matthew &gt; bob（已经去世）&gt; alex &gt; asha &gt; catherine
t.getInheritanceOrder(); // 返回 ["king", "andy", "matthew", "alex", "asha", "catherine"]
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= kingName.length, parentName.length, childName.length, name.length &lt;= 15</code></li>
	<li><code>kingName</code>，<code>parentName</code>，&nbsp;<code>childName</code>&nbsp;和&nbsp;<code>name</code>&nbsp;仅包含小写英文字母。</li>
	<li>所有的参数&nbsp;<code>childName</code> 和&nbsp;<code>kingName</code>&nbsp;互不相同。</li>
	<li>所有&nbsp;<code>death</code>&nbsp;函数中的死亡名字 <code>name</code>&nbsp;要么是国王，要么是已经出生了的人员名字。</li>
	<li>每次调用 <code>birth(parentName, childName)</code> 时，测试用例都保证 <code>parentName</code> 对应的人员是活着的。</li>
	<li>最多调用&nbsp;<code>105</code>&nbsp;次<code>birth</code> 和&nbsp;<code>death</code>&nbsp;。</li>
	<li>最多调用&nbsp;<code>10</code>&nbsp;次&nbsp;<code>getInheritanceOrder</code>&nbsp;。</li>
</ul>