【Gym - 100947G】Square Spiral Search

BUPT 2017 summer training (for 16) #1C

题意

A new computer scientist is trying to develop a new memory management system called "spiral memory management".

The basic idea of this system is that it represents the memory as a 2D grid with a predefined origin point, and the address of each memory location is represented as its (x,y) coordinates, and it tries to store frequently used data as close to the origin point as possible.

This system needs a search algorithm. Our computer scientist is currently developing an algorithm called "square spiral search".

The algorithm searches the memory locations in the following order (also shown in the figure):

(0,0), (1,0), (1,1), (0,1), (-1,1), (-1,0), (-1,-1), (0,-1), (1,-1), (2,-1), (2,0), (2,1), (2,2), (1,2), (0,2), (-1,2), (-2,2), (-2,1), (-2,0), (-2,-1), (-2,-2,) ,(-1,-2) ... and so on.

Now he is wondering: how many steps would it take to reach a memory location with the address (x, y) using the square spiral search. Can you help him find the answer?

题解

代码

#include <cstdio>
#include <cmath>
#include <algorithm>
#define ll long long
using namespace std;
int main(){
	int t;
	scanf("%d",&t);
	while(t--){
		int x,y;
		scanf("%d%d",&x,&y);
		if(!x&&!y){
			puts("0");continue;		
		}
		ll s=max(abs(x),abs(y)),ans=(s*2+1)*(s*2+1)-1;
		if(y==-s)
			ans-=(s-x);
		else if(x==-s)
			ans-=s*2+(s+y);
		else if(y==s)
			ans-=s*4+(s+x);
		else
			ans-=s*6+(s-y);
		printf("%lld\n",ans);
	}
	return 0;
}