Task: Esthetic numbers





Java: import java.util.ArrayList;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

public class EstheticNumbers {
    interface RecTriConsumer<A, B, C> {
        void accept(RecTriConsumer<A, B, C> f, A a, B b, C c);
    }

    private static boolean isEsthetic(long n, long b) {
        if (n == 0) {
            return false;
        }
        var i = n % b;
        var n2 = n / b;
        while (n2 > 0) {
            var j = n2 % b;
            if (Math.abs(i - j) != 1) {
                return false;
            }
            n2 /= b;
            i = j;
        }
        return true;
    }

    private static void listEsths(long n, long n2, long m, long m2, int perLine, boolean all) {
        var esths = new ArrayList<Long>();
        var dfs = new RecTriConsumer<Long, Long, Long>() {
            public void accept(Long n, Long m, Long i) {
                accept(this, n, m, i);
            }

            @Override
            public void accept(RecTriConsumer<Long, Long, Long> f, Long n, Long m, Long i) {
                if (n <= i && i <= m) {
                    esths.add(i);
                }
                if (i == 0 || i > m) {
                    return;
                }
                var d = i % 10;
                var i1 = i * 10 + d - 1;
                var i2 = i1 + 2;
                if (d == 0) {
                    f.accept(f, n, m, i2);
                } else if (d == 9) {
                    f.accept(f, n, m, i1);
                } else {
                    f.accept(f, n, m, i1);
                    f.accept(f, n, m, i2);
                }
            }
        };

        LongStream.range(0, 10).forEach(i -> dfs.accept(n2, m2, i));

        var le = esths.size();
        System.out.printf("Base 10: %d esthetic numbers between %d and %d:%n", le, n, m);
        if (all) {
            for (int i = 0; i < esths.size(); i++) {
                System.out.printf("%d ", esths.get(i));
                if ((i + 1) % perLine == 0) {
                    System.out.println();
                }
            }
        } else {
            for (int i = 0; i < perLine; i++) {
                System.out.printf("%d ", esths.get(i));
            }
            System.out.println();
            System.out.println("............");
            for (int i = le - perLine; i < le; i++) {
                System.out.printf("%d ", esths.get(i));
            }
        }
        System.out.println();
        System.out.println();
    }

    public static void main(String[] args) {
        IntStream.rangeClosed(2, 16).forEach(b -> {
            System.out.printf("Base %d: %dth to %dth esthetic numbers:%n", b, 4 * b, 6 * b);
            var n = 1L;
            var c = 0L;
            while (c < 6 * b) {
                if (isEsthetic(n, b)) {
                    c++;
                    if (c >= 4 * b) {
                        System.out.printf("%s ", Long.toString(n, b));
                    }
                }
                n++;
            }
            System.out.println();
        });
        System.out.println();

        
        listEsths(1000, 1010, 9999, 9898, 16, true);
        listEsths((long) 1e8, 101_010_101, 13 * (long) 1e7, 123_456_789, 9, true);
        listEsths((long) 1e11, 101_010_101_010L, 13 * (long) 1e10, 123_456_789_898L, 7, false);
        listEsths((long) 1e14, 101_010_101_010_101L, 13 * (long) 1e13, 123_456_789_898_989L, 5, false);
        listEsths((long) 1e17, 101_010_101_010_101_010L, 13 * (long) 1e16, 123_456_789_898_989_898L, 4, false);
    }
}



Python: from collections import deque
from itertools import dropwhile, islice, takewhile
from textwrap import wrap
from typing import Iterable, Iterator


Digits = str  


def esthetic_nums(base: int) -> Iterator[int]:
    
    queue: deque[tuple[int, int]] = deque()
    queue.extendleft((d, d) for d in range(1, base))
    while True:
        num, lsd = queue.pop()
        yield num
        new_lsds = (d for d in (lsd - 1, lsd + 1) if 0 <= d < base)
        num *= base  
        queue.extendleft((num + d, d) for d in new_lsds)


def to_digits(num: int, base: int) -> Digits:
    
    digits: list[str] = []
    while num:
        num, d = divmod(num, base)
        digits.append("0123456789abcdef"[d])
    return "".join(reversed(digits)) if digits else "0"


def pprint_it(it: Iterable[str], indent: int = 4, width: int = 80) -> None:
    
    joined = ", ".join(it)
    lines = wrap(joined, width=width - indent)
    for line in lines:
        print(f"{indent*' '}{line}")
    print()


def task_2() -> None:
    nums: Iterator[int]
    for base in range(2, 16 + 1):
        start, stop = 4 * base, 6 * base
        nums = esthetic_nums(base)
        nums = islice(nums, start - 1, stop)  
        print(
            f"Base-{base} esthetic numbers from "
            f"index {start} through index {stop} inclusive:\n"
        )
        pprint_it(to_digits(num, base) for num in nums)


def task_3(lower: int, upper: int, base: int = 10) -> None:
    nums: Iterator[int] = esthetic_nums(base)
    nums = dropwhile(lambda num: num < lower, nums)
    nums = takewhile(lambda num: num <= upper, nums)
    print(
        f"Base-{base} esthetic numbers with "
        f"magnitude between {lower:,} and {upper:,}:\n"
    )
    pprint_it(to_digits(num, base) for num in nums)


if __name__ == "__main__":
    print("======\nTask 2\n======\n")
    task_2()

    print("======\nTask 3\n======\n")
    task_3(1_000, 9_999)

    print("======\nTask 4\n======\n")
    task_3(100_000_000, 130_000_000)