hdoj Clarke and points 5626 （數學&變換）

Clarke and points

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)

Total Submission(s): 306    Accepted Submission(s): 219

Problem Description Clarke is a patient with multiple personality disorder. One day he turned into a learner of geometric.  

He did a research on a interesting distance called Manhattan Distance. The Manhattan Distance between point   A(xA,yA)  and point   B(xB,yB)  is   |xA−xB|+|yA−yB| .  

Now he wants to find the maximum distance between two points of   n  points.  

Input The first line contains a integer   T(1≤T≤5) , the number of test case.  

For each test case, a line followed, contains two integers   n,seed(2≤n≤1000000,1≤seed≤109) , denotes the number of points and a random seed.  

The coordinate of each point is generated by the followed code.  

```

long long seed;

inline long long rand(long long l, long long r) {

  static long long mo=1e9+7, g=78125;

  return l+((seed*=g)%=mo)%(r-l+1);

}

// ...

cin >> n >> seed;

for (int i = 0; i < n; i++)

  x[i] = rand(-1000000000, 1000000000),

  y[i] = rand(-1000000000, 1000000000);

```  

Output For each test case, print a line with an integer represented the maximum distance.

Sample Input

2
3 233
5 332
        

Sample Output

1557439953
1423870062
  
  
   
    問題描述
   
          
克拉克是一名精神分裂患者。某一天克拉克變成了一位幾何研究學者。  
他研究一個有趣的距離，曼哈頓距離。點A(x_A, y_A)A(x​A​​,y​A​​)和點B(x_B, y_B)B(x​B​​,y​B​​)的曼哈頓距離為|x_A-x_B|+|y_A-y_B|∣x​A​​−x​B​​∣+∣y​A​​−y​B​​∣。  
現在他有nn個這樣的點，他需要找出兩個點i, ji,j使得曼哈頓距離最大。        
        
  輸入描述         
第一行是一個整數T(1 \le T \le 5)T(1≤T≤5)，表示資料組數。  
每組資料第一行為兩個整數n, seed(2 \le n \le 1000000, 1 \le seed \le 10^9)n,seed(2≤n≤1000000,1≤seed≤10​9​​)，表示點的個數和種子。  

nn個點的坐标是這樣得到的：

long long seed;
inline long long rand(long long l, long long r) {
	static long long mo=1e9+7, g=78125;
	return l+((seed*=g)%=mo)%(r-l+1);
}

// ...

cin >> n >> seed;
for (int i = 0; i < n; i++)
	x[i] = rand(-1000000000, 1000000000),
	y[i] = rand(-1000000000, 1000000000);
      
        
  輸出描述         
對于每組資料輸出一行，表示最大的曼哈頓距離。      
        
  輸入樣例         
2
3 233
5 332      
        
  輸出樣例         
1557439953
1423870062      
        
   //思路：   這塊用到一點數學的知識，就是去絕對值，總共有四種情況（應該都知道），但列出來之後會發現可以合并成兩種情況。   情況一：(Xa+Ya)-(Xb+Yb);   情況二：(Xa-Ya)-(Xb-Yb);   是以隻用求出這兩種情況的最大值即為所求。。          
#include<stdio.h>
#include<string.h>
#include<algorithm>
#define INF 0x3f3f3f3f
#define ll long long
#define N 1000010
using namespace std;
long long seed;
inline long long rand(long long l, long long r) 
{
	static long long mo=1e9+7, g=78125;
	return l+((seed*=g)%=mo)%(r-l+1);
}
int main()
{
	int t,n,i;
	scanf("%d",&t);
	while(t--)
	{
		scanf("%d%lld",&n,&seed);
		ll x1=-INF,x2=-INF;
		ll y1=INF,y2=INF;
		for (i = 0; i < n; i++)
		{
			ll x,y;
			x = rand(-1000000000, 1000000000);
			y = rand(-1000000000, 1000000000);
			x1=max(x1,x+y);x2=max(x2,x-y);
			y1=min(y1,x+y);y2=min(y2,x-y);						
		}
		ll sum=max(x1-y1,x2-y2);
		printf("%lld\n",sum);
	}
	return 0;
}