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 {
public:
    Trie()
        : children(26, nullptr) {
    }

    void insert(string& w, int x) {
        Trie* node = this;
        for (char c : w) {
            c -= 'a';
            if (!node->children[c]) {
                node->children[c] = new Trie();
            }
            node = node->children[c];
            node->val += x;
        }
    }

    int search(string& w) {
        Trie* node = this;
        for (char c : w) {
            c -= 'a';
            if (!node->children[c]) {
                return 0;
            }
            node = node->children[c];
        }
        return node->val;
    }

private:
    vector<Trie*> children;
    int val = 0;
};

class MapSum {
public:
    MapSum() {
    }

    void insert(string key, int val) {
        int x = val - d[key];
        d[key] = val;
        trie->insert(key, x);
    }

    int sum(string prefix) {
        return trie->search(prefix);
    }

private:
    unordered_map<string, int> d;
    Trie* trie = new Trie();
};

/**
 * Your MapSum object will be instantiated and called as such:
 * MapSum* obj = new MapSum();
 * obj->insert(key,val);
 * int param_2 = obj->sum(prefix);
 */