problem_261.js

// This problem was asked by Amazon.

// Huffman coding is a method of encoding characters based on their frequency. Each letter is assigned a variable-length binary string, such as `0101` or `111110`, where shorter lengths correspond to more common letters. To accomplish this, a binary tree is built such that the path from the root to any leaf uniquely maps to a character. When traversing the path, descending to a left child corresponds to a `0` in the prefix, while descending right corresponds to `1`.

// Here is an example tree (note that only the leaf nodes have letters):

// ```
//         *
//       /   \
//     *       *
//    / \     / \
//   *   a   t   *
//  /             \
// c               s
// ```

// With this encoding, cats would be represented as `0000110111`.

// Given a dictionary of character frequencies, build a Huffman tree, and use it to determine a mapping between characters and their encoded binary strings.