Sawtooth Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 422    Accepted Submission(s): 134 Problem Description Think about a plane: ● One straight line can divide a plane into two regions. ● Tw…

题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=5047 解题报告:问一个“M”型可以把一个矩形的平面最多分割成多少块. 输入是有n个“M",现在已经推出这个公式应该是8 * n^2 - 7 * n + 1,但是这个n的范围达到了10^12次方,只要平方一次就超出long long  的范围了,怎么办呢,用大数? 都试过了,很奇怪,会超时,按照估算的话感觉不会,可能是中间结果比较大吧,这个还在思考,但是10^12平方一次乘以八也只达到了10^25次方…

http://acm.hdu.edu.cn/showproblem.php?pid=5047 题目大意: 给n条样子像“m”的折线,求它们能把二维平面分成的面最多是多少. 解题思路: 我们发现直线1条:2平面:2直线:4平面:3直线:7平面......因为第n条直线要与前面n-1条直线都相交,才能使分的平面最多,则添加第n条直线,平面增加n个: 所以公式是面F = 2 + 2 + 3 + ......+ n = (1+n)*n/2 + 1 因为题目的是“M”的折线,一个“M”有4条线将平面分成2…

题意:求n个'M'型的折线将一个平面分成的最多的面数! 思路:我们都知道n条直线将一个平面分成的最多平面数是 An = An-1 + n+1 也就是f(n) = (n*n + n +2)/2 对于一个'M'型的折线呢?它有四条线,但是由于三个顶点的关系导致划分的平面 的数目减少了9个!所以有递推公式 f(n) = (m*m + m + 2)/2 - 9*n; m = 4*n 最后 f(n) = (8*n+1)*(n-1)+2) 由于 n<=1e12 , 所以回报 long long!那么对于大于…

Hard problem 题目链接: http://acm.split.hdu.edu.cn/showproblem.php?pid=5858 Description cjj is fun with math problem. One day he found a Olympic Mathematics problem for primary school students. It is too difficult for cjj. Can you solve it? Give you the…

  Sawtooth Think about a plane: ● One straight line can divide a plane into two regions. ● Two lines can divide a plane into at most four regions. ● Three lines can divide a plane into at most seven regions. ● And so on... Now we have some figure con…

Problem Description A frog has just learned some number theory, and can't wait to show his ability to his girlfriend. Now the frog ,,⋯ from the bottom, so are the columns. At first the frog is sitting at grid (sx,sy), and begins his journey. To show…

题意: 给出一个\(n(0 \leq n \leq 10^{12})\),问\(n\)个\(M\)形的折线最多可以把平面分成几部分. 分析: 很容易猜出来这种公式一定的关于\(n\)的一个二次多项式. 不妨设\(f(n)=an^2+bn+c\). 结合样例我们可以列出\(3\)个方程: \(f(0)=1,f(1)=2,f(2)=19\) 解出三个系数\(a,b,c\),然后用高精度做即可. #include <cstdio> #include <cstring> #include…

Galaxy Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 262144/262144 K (Java/Others) Total Submission(s): 556    Accepted Submission(s): 127 Special Judge Problem Description Good news for us: to release the financial pressure, the government…

Friend HDU - 1719 Friend number are defined recursively as follows. (1) numbers 1 and 2 are friend number; (2) if a and b are friend numbers, so is ab+a+b; (3) only the numbers defined in (1) and (2) are friend number. Now your task is to judge wheth…