UVA10213 How Many Pieces of Land数学+大数

Posted 2021-06-14 海岛Blog

You are given an elliptical shaped land and you are asked to choose n arbitrary points on its boundary. Then you connect all these points with one another with straight lines (that’s n ∗ (n−1)/2 connections for n points). What is the maximum number of pieces of land you will get by choosing the points on the boundary carefully?

Fig: When the value of n is 6

Input
The first line of the input file contains one integer S (0 < S < 3500), which indicates how many sets of input are there. The next S lines contain S sets of input. Each input contains one integer N (0 ≤ N < 2³¹).
Output
For each set of input you should output in a single line the maximum number pieces of land possible to get for the value of N.
Sample Input
4
1
2
3
4
Sample Output
1
2
4
8

问题链接：UVA10213 How Many Pieces of Land
问题简述：一个椭圆形的平面，在边界上有n个点，连接这些点构成内接多边形，问最多把平面分成几块？
问题分析：大数计算问题，用Python来解决，不解释。
程序说明：（略）
参考链接：（略）
题记：（略）

AC的Python语言程序如下：

# UVA10213 How Many Pieces of Land

t = int(input())
for i in range(t):
	n = int(input())
	print(n * (n ** 3 - 6 * n ** 2 + 23 * n - 18) // 24 + 1)