Timus 1139. City Blocks 题解

The blocks in the city of Fishburg are of square form. N avenues running south to north and Mstreets running east to west bound them. A helicopter took off in the most southwestern
crossroads and flew along the straight line to the most northeastern crossroads. How many blocks did it fly above?

Note. A block is a square of minimum area (without its borders).

Input

The input contains N and M separated by one or more spaces. 1 < N, M < 32000.

Output

The number of blocks the helicopter flew above.

Samples

input	output
4 3	4
3 3	2

Hint

The figures for samples:



Reference - The blog below explaine in detail, but I seem like not quite get it that much：
http://flickeringtubelight.net/blog/2006/08/a-diagonal-through-a-rectangular-grid-of-squares/
But anyway, it's a good explanation. And it should be benefit to read it, maybe you can come up with your own way to understand this approach.

This is a problem that can be approach by many ways. I want to post it because it is very mathematics-related.

I , too, use that formula to solve it.

My suggestion is: if you really have a hard time to deduct that formula, just check the small examples, like n = 2, m = 3, and n = 5, m = 4 and so on.

Below is my C++ solution:

#include <iostream>
using namespace std;

int GCDcityBlocks(int n, int m)
{
	while (m)
	{
		int a = n % m;
		n = m;
		m = a;
	}
	return n;
}

void CityBlocks1139()
{
	int n = 0, m = 0;
	cin>>n>>m;
	n--, m--;
	int k = GCDcityBlocks(n, m);
	int ans = n/k + m/k - 1;
	cout<<ans * k;
}