Solution.go

func numberOfBeautifulIntegers(low int, high int, k int) int {
	s := strconv.Itoa(high)
	f := g(len(s), k, 21)

	var dfs func(pos, mod, diff int, lead, limit bool) int
	dfs = func(pos, mod, diff int, lead, limit bool) int {
		if pos >= len(s) {
			if mod == 0 && diff == 10 {
				return 1
			}
			return 0
		}
		if !lead && !limit && f[pos][mod][diff] != -1 {
			return f[pos][mod][diff]
		}
		up := 9
		if limit {
			up = int(s[pos] - '0')
		}
		ans := 0
		for i := 0; i <= up; i++ {
			if i == 0 && lead {
				ans += dfs(pos+1, mod, diff, true, limit && i == up)
			} else {
				nxt := diff + 1
				if i%2 == 0 {
					nxt -= 2
				}
				ans += dfs(pos+1, (mod*10+i)%k, nxt, false, limit && i == up)
			}
		}
		if !lead && !limit {
			f[pos][mod][diff] = ans
		}
		return ans
	}

	a := dfs(0, 0, 10, true, true)
	s = strconv.Itoa(low - 1)
	f = g(len(s), k, 21)
	b := dfs(0, 0, 10, true, true)
	return a - b
}

func g(m, n, k int) [][][]int {
	f := make([][][]int, m)
	for i := 0; i < m; i++ {
		f[i] = make([][]int, n)
		for j := 0; j < n; j++ {
			f[i][j] = make([]int, k)
			for d := 0; d < k; d++ {
				f[i][j][d] = -1
			}
		}
	}
	return f
}