project-euler/Yet to solve/788 Dominating Numbers.sf

#!/usr/bin/ruby

# Dominating numbers
# A dominating number is a positive integer that has more than half of its digits equal.

# https://projecteuler.net/problem=788

# 1e3 ..^ 1e4 -> count { .digits.sort.run_length.map{.tail}.max*2 > .len }
# 1e4 ..^ 1e5 -> count { .digits.sort.run_length.map{.tail}.max*2 > .len }
# 1e5 ..^ 1e6 -> count { .digits.sort.run_length.map{.tail}.max*2 > .len }

func f(n) {

    if (n == 1) {
        return 9
    }

    if (n == 2) {
        return 9
    }

    var j = (n.dec>>1)
    var count = 9

    for i in (1 .. j) {
        count += (9*i * (9**i * n))
    }

    if (n >= 6) {
        for i in (1 .. j+1) {
            count += 9**(j+1)
        }
    }

    count
}

say f(1)
say f(2)
say f(3)
say f(4)
say f(5)
say f(6)

assert_eq(f(1), 9)
assert_eq(f(2), 9)
assert_eq(f(3), 252)
assert_eq(f(4), 333)
assert_eq(f(5), 7704)
assert_eq(f(6), 11430)

assert_eq(f(1)+f(2)+f(3), 270)
assert_eq(f(1)+f(2)+f(3)+f(4), 603)
assert_eq(f(1)+f(2)+f(3)+f(4)+f(5), 8307)

say f(1)+f(2)
say f(1)+f(2)+f(3)
say f(1)+f(2)+f(3)+f(4)

say map(1..10, f)
say map(1..10, f).sum

assert_eq(map(1..10, f).sum, 21893256)