Topswops is a card game created by John Conway in the 1970's.



Assume you have a particular permutation of a set of   n   cards numbered   1..n   on both of their faces, for example the arrangement of four cards given by   [2, 4, 1, 3]   where the leftmost card is on top.

A round is composed of reversing the first   m   cards where   m   is the value of the topmost card.

Rounds are repeated until the topmost card is the number   1   and the number of swaps is recorded.



For our example the swaps produce:

    
    [2, 4, 1, 3]    # Initial shuffle
    [4, 2, 1, 3]
    [3, 1, 2, 4]
    [2, 1, 3, 4]
    [1, 2, 3, 4]

For a total of four swaps from the initial ordering to produce the terminating case where   1   is on top.



For a particular number    n    of cards,    topswops(n)    is the maximum swaps needed for any starting permutation of the   n   cards.



Task

The task is to generate and show here a table of    n    vs    topswops(n)    for    n    in the range   1..10   inclusive.



Note

Topswops   is also known as   Fannkuch   from the German word   Pfannkuchen   meaning   pancake.



Related tasks

   Number reversal game
   Sorting algorithms/Pancake sort


 
use itertools::Itertools;
 
fn solve(deck: &[usize]) -> usize {
    let mut counter = 0_usize;
    let mut shuffle = deck.to_vec();
    loop {
        let p0 = shuffle[0];
        if p0 == 1 {
            break;
        }
        shuffle[..p0].reverse();
        counter += 1;
    }
 
    counter
}
 
// this is a naive method which tries all permutations and works up to ~12 cards
fn topswops(number: usize) -> usize {
    (1..=number)
        .permutations(number)
        .fold(0_usize, |mut acc, p| {
            let steps = solve(&p);
            if steps > acc {
                acc = steps;
            }
            acc
        })
}
fn main() {
    (1_usize..=10).for_each(|x| println!("{}: {}", x, topswops(x)));
}
 