CSP-S exam various explanations idea huddle

I was so going to test a dish.

I have no mind to maintain a blog. Open a blog post now. You may remember mess.

This may be my last blog post of the OI career? ?

Certainly very, very long.

impossible. Who knows when I'll restore the mentality of the above two sentences deleted at the beginning of the blog in various Hu Lie Lie.

 

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• "Columns" solution to a problem: exgcd

　　Nest planted. Honestly I see $ exgcd $ a. Also written out. But do not use flawed.

　　$ Exgcd $ primarily used to solve linear equations $ ax + $ solutions of a group of specialized gcd (a, b) by =. This particular solution can be extended to our group $ ax + by = c $ in. The PEI Shu theorem, if and only if $ gcd (a, b) | C $ time, equation $ ax + by = c $ solvable.

　　　　$ Exgcd $ proof:

　　　　　　For equation $ ax + by = gcd (a, b) $, so $ a = b, b = a% b $, there are $ b * x + a% b * y = gcd (b, a% b) $ ,

　　　　　　又$gcd(a,b)=gcd(b,a%b)$，所以可得$a*x+b*y=b*x+a%b*b=b*x+(a-a/b*b)*y=a*y+b*(x-a/b*y)$

　　　　　　Proved.

　　　　Code:

int exgcd(rint a,rint b,rint &x,rint &y)
{
	if(!b)
	{
		x = 1; y = 0;
		return a;
	}
	rint res=exgcd(b,a%b,x,y);
	rint t=x;x=y;y=t-a/b*x;
	return res;
}

 　　This question about the number of columns, we need to apply in advance $ exgcd $ solve a particular solution set. Our ultimate goal is that the + abs (y) $ minimum, so that when we assume obtain $ a <b $, then the answer must be made positive or negative maximum value at the minimum $ x $ $ abs (x). If $ a> b $, $ swap $ then be resolved.