// Package q1415 implements a solution for https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/
package q1415

import (
	"math"
	"strings"
)

func getHappyString(n, k int) string {
	// The base is ababababab...
	// Behaves like binary, except the first character, which has three choices: a, b, c.
	// Max of k is 2^n + 2^(n-1)

	if k > int(math.Pow(2, float64(n))+math.Pow(2, float64(n-1))) {
		return ""
	}
	k -= 1

	sb := strings.Builder{}
	var last byte
	switch k >> (n - 1) {
	case 0:
		last = 'a'
	case 1:
		last = 'b'
	case 2:
		last = 'c'
	}
	sb.WriteByte(last)

	lut := [][2]byte{
		{'b', 'c'},
		{'a', 'c'},
		{'a', 'b'},
	}

	for i := n - 1; i > 0; i-- {
		lookup := k >> (i - 1) & 1
		c := lut[last-'a'][lookup]
		sb.WriteByte(c)
		last = c
	}
	return sb.String()
}

var _ = getHappyString