Things you think computers are good at Calculations Processing Data Following Instructions Not making mistakes Doing the same thing many many times Searching Multitasking Worldwide communications Streaming video Storing Information Playing chess Word processing Solving algorithms Using electricity Editing graphics

Peter Denning’s article on Computation lists some of the things that computers find difficult to do in real time…. Entscheidungsproblem

The “3000 club” of problems includes… Finding the capacities of Internet links to avoid congestion Finding shortest shipping routes in a transportation system. Packing transistors on to a silicon wafer to minimize waste. Rendering a scene in a movie. Finding good algorithms for these problems is worth billions of dollars to the economy in resources not wasted by suboptimal solutions. (Denning PJ 2007)

Rucksack Problem (a well known computationally hard problem) 5 kg £5 12 kg £10 3 kg £3 10 kg £8 8 kg £12 Given a set of items, each with a cost and a value, determine the number of each item to include in a collection so that the total cost is less than some given cost and the total value is as large as possible. The problem is to fill the rucksack with no more than 20kg of weight, whilst giving the maximum value of the items possible,

Answer Put the yellow and the blue boxes into the rucksack only.

Simulations Multiplication of two numbers. Input – Process – Output sequence. Tower of Hanoi The rings from the left pole must be moved to the right pole. They must end up in the right order with the largest on the bottom and the smallest on the top. Once solved write down the moves they made then – write down the moves you would make for a four-peg towers of Hanoi puzzle. Finally – can you abstract the problem sufficiently to write a general algorithm (in words) for the problem…

Answers Finding a solution is not essential, the process of abstracting to a general algorithm is very useful if you can do it. However, it is useful to have looked at this sort of problem as an introduction to the problem- solving aspect of Computing. The TOH puzzle can be solved iteratively or recursively. Solutions are on the www (wikipedia) or (Plus magazine)