30thAug_higher_order_2

// rick the rabbit

/*

2 stairs
hop hop skip

3 stairs
skip hop
hop skip
jump

*/

function rick_the_rabbit(n){
    return n < 0
           ? 0
           : n === 0
           ? 1
           : rick_the_rabbit(n - 1) // rick hops
           +
           rick_the_rabbit(n - 2) // rick skips
           +
           rick_the_rabbit(n - 3); // rick jumps
}

// coin change problem

/*

given: different kinds of coins
given: amount of money in cents
wanted: number of ways to change amt into coins

order of coins dont matter
cents: 5,10,20,50, 100

*/

/*

120 cents

highest coin is either 100 or not

*/

function first_denomination ( kinds_of_coins ) {
    return kinds_of_coins === 1 ? 5 :
           kinds_of_coins === 2 ? 10 :
           kinds_of_coins === 3 ? 20 :
           kinds_of_coins === 4 ? 50 :
           kinds_of_coins === 5 ? 100 : 0;
}

function cc(amount, kind_of_coins){
    return amount === 0
           ? 1
           : amount < 0 || kind_of_coins === 0
           ? 0
           : cc(amount - first_denomination(kind_of_coins), kind_of_coins)
             +
             cc(amount, kind_of_coins - 1);
    
}

cc(20, 3);