AtCoder Beginner Contest 116 D - Various Sushi 【貪心+棧】

Problem Statement

There are $\mathrm{NN}$ pieces of sushi. Each piece has two parameters: "kind of topping" ${\mathrm{titi}}^{}$ and "deliciousness" ${\mathrm{didi}}^{}$. You are choosing $\mathrm{KK}$ among these $\mathrm{NN}$ pieces to eat. Your "satisfaction" here will be calculated as follows:

• The satisfaction is the sum of the "base total deliciousness" and the "variety bonus".
• The base total deliciousness is the sum of the deliciousness of the pieces you eat.
• The variety bonus is $\mathrm{x\ast xx\ast x}$, where $\mathrm{xx}$ is the number of different kinds of toppings of the pieces you eat.

You want to have as much satisfaction as possible. Find this maximum satisfaction.

Constraints

• $\mathrm{1\le K\le N\le 1051\le K\le N\le 105}$
• $\mathrm{1\le ti\le N1\le ti\le N}$
• $\mathrm{1\le di\le 1091\le di\le 109}$
• All values in input are integers.

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Input

Input is given from Standard Input in the following format:

$\mathrm{NN}$ $\mathrm{KK}$
${\mathrm{t1t1}}^{}$ ${\mathrm{d1d1}}^{}$
${\mathrm{t2t2}}^{}$ ${\mathrm{d2d2}}^{}$
$..$
$..$
$..$
${\mathrm{tNtN}}^{}$ ${\mathrm{dNdN}}^{}$

Output

Print the maximum satisfaction that you can obtain.

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Sample Input 1 Copy

Copy

5 3
1 9
1 7
2 6
2 5
3 1

Sample Output 1 Copy

Copy

26

If you eat Sushi $\mathrm{1,21,2}$ and $33$:

• The base total deliciousness is $\mathrm{9+7+6=229+7+6=22}$.
• The variety bonus is $\mathrm{2\ast 2=42\ast 2=4}$.

Thus, your satisfaction will be $2626$, which is optimal.

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Sample Input 2 Copy

Copy

7 4
1 1
2 1
3 1
4 6
4 5
4 5
4 5

Sample Output 2 Copy

Copy

25

It is optimal to eat Sushi $\mathrm{1,2,31,2,3}$ and $44$.

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Sample Input 3 Copy

Copy

6 5
5 1000000000
2 990000000
3 980000000
6 970000000
6 960000000
4 950000000

Sample Output 3 Copy

Copy

4900000016

Note that the output may not fit into a $3232$-bit integer type.

題意：給定N個結構體，每個結構體有兩個信息，分別是type  和 x，讓你從中選出K個結構體，使之type的類型數的平方+sum{ xi } 最大。

思路：【貪心】將X從大到小排序，而後按順序取前K個，在取前K個過程當中，將已經出現的類型放入棧中。而後，開始遍歷K+1----N的元素，使得不斷加入沒有出現的元素的類型。在此過程當中經過彈棧更新最值。

AC代碼：

 1 #include<bits/stdc++.h>
 2 
 3 using namespace std;
 4 #define int long long
 5 #define N 150000
 6 struct str{
 7     int x,y;
 8 }st[N];
 9 bool cmp(str a,str b){
10     return a.y>b.y;
11 }
12 map<int,int> mp;
13 stack<int> s;
14 signed  main(){
15     int n,k;
16     cin>>n>>k;
17     for(int i=1;i<=n;i++){
18         cin>>st[i].x>>st[i].y;
19     }
20     sort(st+1,st+1+n,cmp);
21     int maxn=0;
22     int type=0;
23     int sum=0;
24     for(int i=1;i<=k;i++){
25         if(!mp[st[i].x]){
26             mp[st[i].x]=1;
27             type++;
28         }else{
29             s.push(st[i].y);
30         }
31         sum+=st[i].y;
32         maxn=max(maxn,type*type+sum);    
33     }
34     for(int i=k+1;i<=n;i++){
35         if(s.empty())
36             break;
37         if(mp[st[i].x])
38             continue;
39         mp[st[i].x]=1;
40         type++;
41         sum-=s.top();
42         s.pop();
43         sum+=st[i].y;
44         maxn=max(maxn,type*type+sum);    
45     }
46     cout<<maxn;
47     return 0;
48 }