Find maximum possible time HH:MM by permuting four given digits

Question

I recently took a coding test for a promotion at work. This was one of the tasks I really struggled with and was wondering what is the best way to do this. I used a load of

Answer 1

Here is a non brute force solution that I came up with. Check out the comments in the code to see how it works. If any of it is unclear I can help clarify.

function generate(A, B, C, D) {
    vals = [A, B, C, D];
    counts = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
    for (i = 0; i < vals.length; i++) {
        for (j = vals[i]; j < counts.length; j++) counts[j]++;
    }
    // counts is now populated with the number of values less than or equal to the index it belongs to
    // so counts[2] is the total number of 0's, 1's and 2's
    if (counts[2] === 0) return 'NOT POSSIBLE';
    // if there are no 0's and 1's, then it must start with 2
    mustStartWith2 = counts[1] === 0;
    if (mustStartWith2 && counts[3] === 1) return 'NOT POSSIBLE';
    // We want a count of the number of free digits that are 5 or less (for the minute digit)
    numbersAvailableForMinute = counts[5] - (mustStartWith2 ? 2 : 1); 
    if (numbersAvailableForMinute === 0) return 'NOT POSSIBLE';
    // we now know that it is a valid time
    time = [0, 0, 0, 0];
    // we also know if it starts with 2
    startsWith2 = mustStartWith2 || (numbersAvailableForMinute >= 2 && counts[2] > counts[1]);
    // knowing the starting digit, we know the maximum value for each digit
    maxs = startsWith2 ? [2, 3, 5, 9] : [1, 9, 5, 9];
    for (i = 0; i < maxs.length; i++) {
        // find the first occurrence in counts that has the same count as the maximum
        time[i] = counts.indexOf(counts[maxs[i]]);
        // update counts after the value was removed
        for (j = time[i]; j < counts.length; j++) counts[j]--;
    }
    // create the time
    return time[0]+""+time[1]+":"+time[2]+""+time[3];
}