# 2013 AIO(Senior) 赛题

## The Troublesome Frog

Input File: frogin.txt
Output File: frogout.txt
Time Limit: 1 second

Bazza and Shazza do not like bugs. They wish to clear out all the bugs on their garden fence. They come up with a brilliant idea: they buy some sugar frogs and release them near the fence, letting them eat up all the bugs.

The plan is a great success and the bug infestation is gone. But strangely, they now have a sugar frog infestation. Instead of getting rid of the frogs, Bazza and Shazza decide to set up an obstacle course and watch the frogs jump along it for their enjoyment.

The fence is a series of N fence posts of varying heights. Bazza and Shazza will select three fence posts to create the obstacle course, where the middle post is strictly higher than the other two. The frogs are to jump up from the left post to the middle post, then jump down from the middle post to the right post. The three posts do not have to be next to each other as frogs can jump over other fence posts, regardless of the height of those other posts.

The difficulty of an obstacle course is the height of the first jump plus the height of the second jump. The height of a jump is equal to the difference in height between its two fence posts. Your task is to help Bazza and Shazza find the most difficult obstacle course for the frogs to jump.

### Input

Your program should read from the file . The file will describe a single fence.

• The first line of input will contain one integer N: the number of fence posts.
• The next N lines will each contain one integer hi: the height of the ith fence post.

You are guaranteed that there will be at least one valid obstacle course: that is, there will be at least one combination of three fence posts where the middle post is strictly higher than the other two.

### Output

Your program should write to the file . Your output file should contain one line with one integer: the greatest difficulty of any possible obstacle course.

## Save-It

Input File: savein.txt
Output File: saveout.txt
Time Limit: 1 second

The United Bakers of Australia (UBA) is once again in hot water. Profits have been crumbling recently due to a new tax on an invisible poisonous ingredient underpinning cake manufacturing. Rather than adapt their recipes to use healthier alternatives, the UBA has employed analysts from PwC (People with Cupcakes) to find a way to cut costs.

Upon inspection of UBA's purchasing practices, the analysts found that when a group of ingredients is ordered, the cost of the group is rounded to the nearest 5 cents. That is, a group's cost is the multiple of 5 that has the smallest difference with the sum of its ingredient costs.

For instance, two items costing 32c and 47c can be bought in separate groups for 30c and 45c, or 75c in total, whereas purchasing them in one group together would cost 80c (rounded up from 79c).

Your task is to put the required ingredients into groups for purchasing in order to minimise their total cost.

### Input

Your program should read from the file . The file will describe a single list of ingredients.

• The first line of input will contain one integer N: the number of ingredients.
• The next N lines each contain one integer ci: the cost of the ith ingredient in cents.

### Output

Your program should write to the file . Your output file should contain one line with one integer: the minimum total cost for the ingredients.

## Art Class

Input File: artin.txt
Output File: artout.txt
Time Limit: 1 second

You are attending a highly exclusive seminar run by the famous artist known only as Leo.

Leo is said to be highly influential in the art world. In fact, he invented all the genres of art. All of them. Impressionism, post-modernism, and even cave paintings. In this seminar, Leo teaches you about his newest style of art, which he calls post-cubist squarism.

A post-cubist squarist artwork is painted on a rectangular grid, in which each grid cell is either coloured or blank. Two adjacent coloured cells (vertically or horizontally, not diagonally) are connected, and a shape is a group of coloured cells that are directly or indirectly connected to each other.

The diameter of a shape is the greatest distance between any two of its cells.

The distance between two cells is the minimal number of up, down, left or right steps through the grid to get from one to the other. It doesn't matter whether the steps go through blank cells or even part of an entirely different shape.

In a stroke of genius, Leo realised that the most important aspect of a post-cubist squarist painting is the largest diameter of any shape. He announces that there is a reward for whoever can determine this in his newest artwork. Of course, Leo's genius won't help you now. But what about his computer? While no one else is looking, you steal his laptop and begin to code.

### Input

Your program should read from the file . The file will describe a single post-cubist squarist painting.

• The first line of input will contain two space-separated integers H and W, the height and width of the painting.
• The following H lines describe the painting grid. Each of these lines will contain W characters each. Each character will be either `X' or `.', denoting a coloured or blank grid cell respectively.
• It is guaranteed that there will be at least two adjacent coloured cells.

### Output

Your program should write to the file . Your output file should contain one line with one integer: the largest diameter of any shape in the painting.