折線分割平面
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 15828 Accepted Submission(s): 10922
/******************************
*
* acm: hdu-2050
*
* title: 折線分割平面
*
* time : 2014.5.17
*
******************************/
//考察遞推求解
#include <stdio.h>
#include <stdlib.h>
int fun(int n)
{
if (n == 1)
{
n = 2;
}
else
{
n = fun(n-1) + 4 * (n - 1) + 2 - 1;
}
return n;
}
int main()
{
int N;
int i = 0;
scanf("%d", &N);
while (i < N)
{
int n;
scanf("%d", &n);
n = fun(n);
printf("%d\n", n);
i++;
}
return 0;
}
直接求解:
/******************************
*
* acm: hdu-2050
*
* title: 折線分割平面
*
* time : 2014.5.17
*
******************************/
//考察遞推求解
//本題用遞推找規律方法求解
/*
f(n) = f(n - 1) + 4*(n - 1) + 2 - 1
= f(n - 1) + 4*(n - 1) + 1
= f(n - 2) + 4*(n - 2) + 4*(n - 1) + 2
......
= f(1) + 4 + 4*2 + ...... + 4*(n - 1) + (n - 1)
= 2*n^2 - n + 1
*/
#include <stdio.h>
#include <stdlib.h>
int main()
{
int N;
int i = 0;
scanf("%d", &N);
while (i < N)
{
int n;
scanf("%d", &n);
printf("%d\n", 2*n*n - n + 1);
i++;
}
return 0;
}