I occasionally do coding challenges, so I decided to start recording my solutions here (well, at least the successful ones).

I'm definitely not an algorithms guy. My computer science theory is leaky at best. I can usually put together a naive programming-oriented solution, but rarely figure out the mathy trick to do it in a reasonable amount of time.

That said, for this particular challenge, programming solution seems to have been enough.

The challenge

There is a new alien language which uses the latin alphabet. However, the order among letters are unknown to you. You receive a list of words from the dictionary, wherewords are sorted lexicographically by the rules of this new language. Derive the order of letters in this language.

For example,
Given the following words in dictionary,

[ "wrt", "wrf", "er", "ett", "rftt" ]

The correct order is: "wertf".


You may assume all letters are in lowercase.
If the order is invalid, return an empty string.
There may be multiple valid order of letters, return any one of them is fine.

Original paywalled link

Thought process

I figured this can be done in three steps.

1. Extract letter ordering rules

The format is key: list of letters that come after the key. For the example word list, you would get something like this:

    t: ['f'],
    w: ['e'],
    e: ['r'],
    r: ['t']

So 't' comes before 'f', 'w' is before 'e' and so forth.

2. Using this information, assign weights to each letter

Higher weight means the letter will come later in the sequence. I just go through these rules over and over again and adjust weights, until everything is consistent. Example output for this step:

    w: 0,
    r: 2,
    t: 3,
    f: 4,
    e: 1

If any of these weights go over total number of letters, I presume something is wrong and exit.

3. Generate the sequence

In the last step, I just sort the letters using these weights and create a sequence.


function order(words) {
    const rules = {};
    const weights = {};

    // 1. Extract ordering rules from input words
    for (let row = 0; row < words.length - 1; row++) {
        const thisWord = words[row];
        const nextWord = words[row + 1];

        let col = 0, before, after;
        do {
            before = thisWord[col];
            after = nextWord[col];

            if (!before || !after)  {
                continue wordLoop;
        } while (before === after);

        if (rules[after] && rules[after].indexOf(before) !== -1) {
            // Invalid input. Conflicting rule
            return '';

        // Prefill weights
        weights[before] = 0;
        weights[after] = 0;

        const afterList = rules[before] = rules[before] || [];
        if (afterList.indexOf(after) ===  -1) {

    // 2. Resolve weights
    let changed;
    const alphabetLength = Object.keys(weights).length;
    do {
        changed = false;
        for (let before in rules) {
            const afterList = rules[before];
            for (let i = 0; i < afterList.length; i++) {
                const after = afterList[i];
                if (weights[after] <= weights[before]) {
                    weights[after] = weights[before] + 1;

                    // Check if infinite loop:
                    // I will assume in a solvable alphabet the highest index will never
                    // be greater than total number of letters
                    if (weights[after] > alphabetLength) {
                        return '';

                    changed = true;
                    break ruleLoop;
    } while (changed);

    // 3. Order results according to weights
    const result = Object.keys(weights);
    result.sort((a, b) => {
        return weights[a] - weights[b];

    return result.join('');

Full code is available here: solution.js

See it in action here: alien-dictionary