【CodeForces】609B - The Best Gift（水）
Description
Emily's birthday is next week and Jack has decided to buy a present for her. He knows she loves books so he goes to the local bookshop, where there are n books on sale from one of m genres.
In the bookshop, Jack decides to buy two books of different genres.
Based on the genre of books on sale in the shop, find the number of options available to Jack for choosing two books of different genres for Emily. Options are considered different if they differ in at least one book.
The books are given by indices of their genres. The genres are numbered from 1 to m.
Input
The first line contains two positive integers n and m (2 ≤ n ≤ 2·105, 2 ≤ m ≤ 10) — the number of books in the bookstore and the number of genres.
The second line contains a sequence a1, a2, ..., an, where ai (1 ≤ ai ≤ m) equals the genre of the i-th book.
It is guaranteed that for each genre there is at least one book of that genre.
Output
Print the only integer — the number of ways in which Jack can choose books.
It is guaranteed that the answer doesn't exceed the value 2·109.
Sample Input
4 3 2 1 3 1
5
7 4 4 2 3 1 2 4 3
18
Sample Output
Hint
The answer to the first test sample equals 5 as Sasha can choose:
- the first and second books,
- the first and third books,
- the first and fourth books,
- the second and third books,
- the third and fourth books.
简单水题，说说思路给蓝鸟吧：这道题好的地方就是书的类型是按照1-n来排的。举个例子说明下吧：比如有5类书：1 2 3 4 5。其各自的个数存入数组，分别为：
a[1] , a[2] , a[3] ,a[4] , a[5]
下面就开始组合，1和2 3 4 5组合，可能的方法就是 a[1]*a[2]+a[1]*a[3]+a[1]*a[4]+a[1]*a[5]
接着，2和3 4 5组合，方法数为：a[2]*a[3]+a[2]*a[4]+a[2]*a[5]
然后，3和4 5组合，方法数为：a[3]*a[4]+a[3]*a[5]
最后，4和5组合，方法数为：a[4]*a[5]
加起来就是答案了。
用c语言实现，就是两个for循环嵌套，很简单。
代码如下：
#include <stdio.h>
#include <string.h>
int a[11]; //每类书的个数
int main()
{
int n,m;
int t;
int ans;
while (~scanf ("%d%d",&n,&m))
{
memset (a,0,sizeof (a)); //初始化
while (n--)
{
scanf ("%d",&t);
a[t]++; //记录每类书的个数
}
ans=0;
for (int i=1;i<m;i++)
{
for (int j=i+1;j<=m;j++)
{
ans+=a[i]*a[j];
}
}
printf ("%d\n",ans);
}
return 0;
}