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
public class Trie {
    private Trie[] children = new Trie[26];
    private int val;

    public void Insert(string w, int x) {
        Trie node = this;
        for (int i = 0; i < w.Length; ++i) {
            int idx = w[i] - 'a';
            if (node.children[idx] == null) {
                node.children[idx] = new Trie();
            }
            node = node.children[idx];
            node.val += x;
        }
    }

    public int Search(string w) {
        Trie node = this;
        for (int i = 0; i < w.Length; ++i) {
            int idx = w[i] - 'a';
            if (node.children[idx] == null) {
                return 0;
            }
            node = node.children[idx];
        }
        return node.val;
    }
}

public class MapSum {
    private Dictionary<string, int> d = new Dictionary<string, int>();
    private Trie trie = new Trie();

    public MapSum() {
    }

    public void Insert(string key, int val) {
        int x = val - (d.ContainsKey(key) ? d[key] : 0);
        d[key] = val;
        trie.Insert(key, x);
    }

    public int Sum(string prefix) {
        return trie.Search(prefix);
    }
}

/**
 * Your MapSum object will be instantiated and called as such:
 * MapSum obj = new MapSum();
 * obj.Insert(key,val);
 * int param_2 = obj.Sum(prefix);
 */
