// License: GPLv3 Copyright: 2026, Kovid Goyal, <kovid at kovidgoyal.net>

package hints

// hints_to_skip calculates how many hints to skip based on the given n and
// alphabet size so that the next n hints generated by expanding the prefix tree
// of an alphabet of size alphabetSize will be prefix-free.
//
// The result is 1-based, meaning that the first hint to be skipped is the first
// non-empty hint.
//
// For example, if alphabet was "abc" and n was 5, the first non-empty hints
// from that alphabet would be: "a", "b", "c", "aa", "ab", "ac", ...
// the result of hints_to_skip would be 1, and this would mean that if you skip
// "a" from the list above, the next 5 hints are prefix-free:
// "b", "c", "aa", "ab", "ac".
//
// See issue #10195 for an informal proof on why this function works.
func hints_to_skip(n int, alphabetSize int) int {
	if n < 2 {
		n = 2
	}
	return (n - 2) / (alphabetSize - 1)
}

// generate_prefix_free_hint generates the hint corresponding to the given index
// in the breadth-first traversal of the prefix tree generated by the given
// alphabet.
//
// For example, given the alphabet "abc", the hints would be generated in
// the following order:
// 1. "a"
// 2. "b"
// 3. "c"
// 4. "aa"
// 5. "ab"
// 6. "ac"
// 7. "ba"
// 8. "bb"
// 9. "bc"
// 10. "ca"
// 11. "cb"
// 12. "cc"
// 13. "aaa"
// ...
//
// Indices are 1-based on non-empty hints; index=0 returns an empty (invalid)
// hint.
func generate_prefix_free_hint(index int, alphabet string) string {
	l := len(alphabet)

	hint := ""
	index -= 1
	for index >= 0 {
		mod := index % l
		char := string(alphabet[mod])
		index /= l
		hint = char + hint
		index -= 1
	}
	return hint
}