throne-inheritance

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Algorithms

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>