【Educational Codeforces Round 3 B】【水题 基本容斥】The Best Gift n本书任选两个不能同一类型的方案数

B. The Best Gift

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

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 test(s)

input

4 3
2 1 3 1

output

5

input

7 4
4 2 3 1 2 4 3

output

18

Note
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.

#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
void fre(){freopen("c://test//input.in","r",stdin);freopen("c://test//output.out","w",stdout);}
#define MS(x,y) memset(x,y,sizeof(x))
#define MC(x,y) memcpy(x,y,sizeof(x))
#define MP(x,y) make_pair(x,y)
#define ls o<<1
#define rs o<<1|1
typedef long long LL;
typedef unsigned long long UL;
typedef unsigned int UI;
template <class T1,class T2>inline void gmax(T1 &a,T2 b){if(b>a)a=b;}
template <class T1,class T2>inline void gmin(T1 &a,T2 b){if(b<a)a=b;}
const int N=0,M=0,Z=1e9+7,ms63=0x3f3f3f3f;
int n,m,x;
int a[12];
LL C(LL x)
{
return x*(x-1)/2;
}
int main()
{
while(~scanf("%d%d",&n,&m))
{
MS(a,0);
for(int i=1;i<=n;++i)
{
scanf("%d",&x);
++a[x];
}
LL ans=C(n);
for(int i=1;i<=m;++i)ans-=C(a[i]);
printf("%lld\n",ans);
}
return 0;
}
/*
【trick&&吐槽】
注意不要爆int

【题意】
有n（2<=n<=2e5）本书，书有共计m（2<=m<=10）个类型。依次告诉你每本书的类型。
我们想选出两本书，要求这两本书不能类型相同，问你有多少种选法。

【类型】
水题 简单容斥

【分析】
显然 C（tot,2）- ∑(i=1~m)C（typei，2）就是答案了。

【时间复杂度&&优化】
O(n)

*/