Multi-level counter iteration - algorithm

Question

I'm stuck on creating an algorithm as follows. I know this shouldn't be too difficult, but I simply can't get my head around it, and can't find the right description of this kind of pattern.
Basically I need a multi-level counter, where when a combination exist in the database, the next value is tried by incrementing from the right.
1 1 1 - Start position. Does this exist in database? YES -> Extract this and go to next
1 1 2 - Does this exist in database? YES -> Extract this and go to next
1 1 3 - Does this exist in database? YES -> Extract this and go to next
1 1 4 - Does this exist in database? NO -> Reset level 1, move to level 2
1 2 1 - Does this exist in database? YES -> Extract this and go to next
1 2 2 - Does this exist in database? NO -> Reset level 2 and 1, move to level 3
2 1 1 - Does this exist in database? YES -> Extract this and go to next
2 1 2 - Does this exist in database? YES -> Extract this and go to next
2 1 3 - Does this exist in database? NO -> Reset level 1 and increment level 2
2 2 1 - Does this exist in database? YES -> Extract this and go to next
2 2 2 - Does this exist in database? YES -> Extract this and go to next
2 2 3 - Does this exist in database? YES -> Extract this and go to next
2 3 1 - Does this exist in database? NO -> Extract this and go to next
3 1 1 - Does this exist in database? NO -> Extract this and go to next
3 2 1 - Does this exist in database? NO -> End, as all increments tried
There could be more than three levels, though.
In practice, each value like 1, 2, etc is actually a $value1, $value2, etc. containing a runtime string being matched against an XML document. So it's not just a case of pulling out every combination already existing in the database.

Answer 1

Assuming, the length of the DB key is known upfront, here's one way how it can be implemented. I'm using TypeScript but similar code can be written in your favorite language.
First, I declare some type definitions for convenience.
export type Digits = number[];
export type DbRecord = number;
Then I initialize fakeDb object which works as a mock data source. The function I wrote will work against this object. This object's keys are representing the the database records' keys (of type string). The values are simple numbers (intentionally sequential); they represent the database records themselves.
export const fakeDb: { [ dbRecordKey: string ]: DbRecord } = {
'111': 1,
'112': 2,
'113': 3,
'211': 4,
'212': 5,
'221': 6,
'311': 7,
};
Next, you can see the fun part, which is the function that uses counterDigits array of "digits" to increment depending on whether the record presence or absence.
Please, do NOT think this is the production-ready code! A) there are unnecessary console.log() invocations which only exist for demo purposes. B) it's a good idea to not read a whole lot of DbRecords from the database into memory, but rather use yield/return or some kind of buffer or stream.
export function readDbRecordsViaCounter(): DbRecord[] {
const foundDbRecords: DbRecord[] = [];
const counterDigits: Digits = [1, 1, 1];
let currentDigitIndex = counterDigits.length - 1;
do {
console.log(`-------`);
if (recordExistsFor(counterDigits)) {
foundDbRecords.push(extract(counterDigits));
currentDigitIndex = counterDigits.length - 1;
counterDigits[currentDigitIndex] += 1;
} else {
currentDigitIndex--;
for (let priorDigitIndex = currentDigitIndex + 1; priorDigitIndex < counterDigits.length; priorDigitIndex++) {
counterDigits[priorDigitIndex] = 1;
}
if (currentDigitIndex < 0) {
console.log(`------- (no more records expected -- ran out of counter's range)`);
return foundDbRecords;
}
counterDigits[currentDigitIndex] += 1;
}
console.log(`next key to try: ${ getKey(counterDigits) }`);
} while (true);
}
The remainings are some "helper" functions for constructing a string key from a digits array, and accessing the fake database.
export function recordExistsFor(digits: Digits): boolean {
const keyToSearch = getKey(digits);
const result = Object.getOwnPropertyNames(fakeDb).some(key => key === keyToSearch);
console.log(`key=${ keyToSearch } => recordExists=${ result }`);
return result;
}
export function extract(digits: Digits): DbRecord {
const keyToSearch = getKey(digits);
const result = fakeDb[keyToSearch];
console.log(`key=${ keyToSearch } => extractedValue=${ result }`);
return result;
}
export function getKey(digits: Digits): string {
return digits.join('');
}
Now, if you run the function like this:
const dbRecords = readDbRecordsViaCounter();
console.log(`\n\nDb Record List: ${ dbRecords }`);
you should see the following output that tells you about the iteration steps; as well as reports the final result in the very end.
-------
key=111 => recordExists=true
key=111 => extractedValue=1
next key to try: 112
-------
key=112 => recordExists=true
key=112 => extractedValue=2
next key to try: 113
-------
key=113 => recordExists=true
key=113 => extractedValue=3
next key to try: 114
-------
key=114 => recordExists=false
next key to try: 121
-------
key=121 => recordExists=false
next key to try: 211
-------
key=211 => recordExists=true
key=211 => extractedValue=4
next key to try: 212
-------
key=212 => recordExists=true
key=212 => extractedValue=5
next key to try: 213
-------
key=213 => recordExists=false
next key to try: 221
-------
key=221 => recordExists=true
key=221 => extractedValue=6
next key to try: 222
-------
key=222 => recordExists=false
next key to try: 231
-------
key=231 => recordExists=false
next key to try: 311
-------
key=311 => recordExists=true
key=311 => extractedValue=7
next key to try: 312
-------
key=312 => recordExists=false
next key to try: 321
-------
key=321 => recordExists=false
next key to try: 411
-------
key=411 => recordExists=false
------- (no more records expected -- ran out of counter's range)
Db Record List: 1,2,3,4,5,6,7
It is strongly recommended to read the code. If you want me to describe the approach or any specific detail(s) -- let me know. Hope, it helps.