NYOJ--319-Splitting plane

NYOJ--319-Splitting plane

Splitting plane

1000 ms  |  内存限制： 65535

2

We have seen many problems about straight line splitting plane.Today ours problem has little difference with before.Because this time we don't use a straight line to splitting plane,we use a broken line to splitting plane.

For example , a broken line can divided a plane to two parts,  two broken line can divided a plane to seven parts.

The first line input an integer N(1

Then N trip test data

Each test data have a integer M. M represents the number of broken lines.(0

输出 For each test case, please output plane's biggest segmentation number, the output of each instance of one line. 样例输入

21 2

样例输出

27

来源

​​HDOJ​​

推规律题：

分割平面的个数=交点个数+顶点个数+1。 令f(n-1)为前n-1条折线分割的平面数，当添加第n条折线时。 因为每一条边与前n-1条折线的两条边都相交，故增加的交点数为2*2*(n-1)，顶点增加1，故 f(n)=f(n-1)+4(n-1)+1，再累加。

参考代码;

/************NYOJ319Result:AcceptedTimes:164ms;Author:jiabeimuwei*************/#includeint f(int n){ int i,j=1; for(i=1; i<=n; i++) { j+=4*i-3; } return j;}int main(){ int t, n, m, i = 0; scanf("%d",&t); while(t--) { scanf("%d",&m); printf("%d\n",f(m)); } return 0;}

公式套用：

#includeint main(){ long long n,m; scanf("%lld",&m); while(m--) { scanf("%lld",&n); printf("%lld\n",(4*n*n+2*n)/2+1-2*n); } return 0;}

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