In the latest trend of skin-tight jeans and slimline handbags, having a bulging wallet or purse is simply a fashion crime. You are faced with a dilemma: either you find yourself disowned by your fashion-conscious friends, or risk carrying too little money for your taxi ride home.
You wish to carry the exact amount of money for your taxi ride (in case you are mugged or otherwise lose it). However, you also wish to use as few notes as possible to avoid being ridiculed by your friends. The notes available to you come in denominations of $1, $5, $20 and $100 (you never carry coins, which are simply far too bulky).
For example, if your taxi fare costs $67, the smallest number of notes you can carry is six — this is achieved by carrying three $20 notes, one $5 note and two $1 notes (20+20+20+5+1+1 = 67).
Your task is to determine the smallest number of notes you need to carry in order to make up a given taxi fare.
You really like ladybugs. This is fortunate, as dozens of ladybugs have recently taken up residence in your garden. Every day they emerge into the sunlight and climb your garden fence. The fence is a series of regularly spaced posts which gleam brightly in the sun. The ladybugs settle into their favourite resting spots atop these posts.
Winter is nigh and you wish to protect the ladybugs from the rain. You set out to construct a rain shelter using a single length of ribbon propped up with toothpicks. To protect all the ladybugs, the ribbon must be long enough to cover all their favourite resting spots. Ribbon is not cheap, so you wish to use the shortest length of ribbon you possibly can. A ribbon of length k will cover precisely k adjacent fence posts.
For example, on the fence in the diagram above there are two ladybugs sitting on fence post 3 and one ladybug on each of 2, 6, 7 and 9. The ribbon rain shelter must cover all the posts from 2 through to 9 inclusive, so the shortest possible length of ribbon that covers all the ladybugs is 8.
Your task is to write a program to calculate the minimum length of ribbon that will cover all the ladybugs.