Map Sum Pairs
<p>Design a map that allows you to do the following:</p>

<ul>
	<li>Maps a string key to a given value.</li>
	<li>Returns the sum of the values that have a key with a prefix equal to a given string.</li>
</ul>

<p>Implement the <code>MapSum</code> class:</p>

<ul>
	<li><code>MapSum()</code> Initializes the <code>MapSum</code> object.</li>
	<li><code>void insert(String key, int val)</code> Inserts the <code>key-val</code> pair into the map. If the <code>key</code> already existed, the original <code>key-value</code> pair will be overridden to the new one.</li>
	<li><code>int sum(string prefix)</code> Returns the sum of all the pairs&#39; value whose <code>key</code> starts with the <code>prefix</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input</strong>
[&quot;MapSum&quot;, &quot;insert&quot;, &quot;sum&quot;, &quot;insert&quot;, &quot;sum&quot;]
[[], [&quot;apple&quot;, 3], [&quot;ap&quot;], [&quot;app&quot;, 2], [&quot;ap&quot;]]
<strong>Output</strong>
[null, null, 3, null, 5]

<strong>Explanation</strong>
MapSum mapSum = new MapSum();
mapSum.insert(&quot;apple&quot;, 3);  
mapSum.sum(&quot;ap&quot;);           // return 3 (<u>ap</u>ple = 3)
mapSum.insert(&quot;app&quot;, 2);    
mapSum.sum(&quot;ap&quot;);           // return 5 (<u>ap</u>ple + <u>ap</u>p = 3 + 2 = 5)
</pre>

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

<ul>
	<li><code>1 &lt;= key.length, prefix.length &lt;= 50</code></li>
	<li><code>key</code> and <code>prefix</code> consist of only lowercase English letters.</li>
	<li><code>1 &lt;= val &lt;= 1000</code></li>
	<li>At most <code>50</code> calls will be made to <code>insert</code> and <code>sum</code>.</li>
</ul>
Design; Trie; Hash Table; String
class Trie:
    def __init__(self):
        self.children: List[Trie | None] = [None] * 26
        self.val: int = 0

    def insert(self, w: str, x: int):
        node = self
        for c in w:
            idx = ord(c) - ord('a')
            if node.children[idx] is None:
                node.children[idx] = Trie()
            node = node.children[idx]
            node.val += x

    def search(self, w: str) -> int:
        node = self
        for c in w:
            idx = ord(c) - ord('a')
            if node.children[idx] is None:
                return 0
            node = node.children[idx]
        return node.val


class MapSum:
    def __init__(self):
        self.d = defaultdict(int)
        self.tree = Trie()

    def insert(self, key: str, val: int) -> None:
        x = val - self.d[key]
        self.d[key] = val
        self.tree.insert(key, x)

    def sum(self, prefix: str) -> int:
        return self.tree.search(prefix)


# Your MapSum object will be instantiated and called as such:
# obj = MapSum()
# obj.insert(key,val)
# param_2 = obj.sum(prefix)
