codeforces 1038C. Gambling(思维，模拟)

Posted 2021-01-04 wangxwws

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Two players A and B have a list of $\mathrm{nn integers\; each.\; They\; both\; want\; to\; maximize\; the\; subtraction\; between\; their\; score\; and\; their\; opponent‘s\; score.}$

In one turn, a player can either add to his score any element from his list (assuming his list is not empty), the element is removed from the list afterward. Or remove an element from his opponent‘s list (assuming his opponent‘s list is not empty).

Note, that in case there are equal elements in the list only one of them will be affected in the operations above. For example, if there are elements $\{1,2,2,3\}\{1,2,2,3\} in\; a\; list\; and\; you\; decided\; to\; choose 22 for\; the\; next\; turn,\; only\; a\; single\; instance\; of 22 will\; be\; deleted\; (and\; added\; to\; the\; score,\; if\; necessary).$

The player A starts the game and the game stops when both lists are empty. Find the difference between A‘s score and B‘s score at the end of the game, if both of the players are playing optimally.

Optimal play between two players means that both players choose the best possible strategy to achieve the best possible outcome for themselves. In this problem, it means that each player, each time makes a move, which maximizes the final difference between his score and his opponent‘s score, knowing that the opponent is doing the same.

Input

The first line of input contains an integer $\mathrm{nn (1\le n\le 1000001\le n\le 100000) —\; the\; sizes\; of\; the\; list.}$

The second line contains $\mathrm{nn integers aiai (1\le ai\le 1061\le ai\le 106),\; describing\; the\; list\; of\; the\; player\; A,\; who\; starts\; the\; game.}$

The third line contains $\mathrm{nn integers bibi (1\le bi\le 1061\le bi\le 106),\; describing\; the\; list\; of\; the\; player\; B.}$

Output

Output the difference between A‘s score and B‘s score ($\mathrm{A?BA?B)\; if\; both\; of\; them\; are\; playing\; optimally.}$

Examples

input

Copy

2
1 4
5 1

output

Copy

0

input

Copy

3
100 100 100
100 100 100

output

Copy

0

input

Copy

2
2 1
5 6

output

Copy

-3

Note

In the first example, the game could have gone as follows:

• A removes $\mathrm{55 from\; B‘s\; list.}$
• B removes $\mathrm{44 from\; A‘s\; list.}$
• A takes his $11.$
• B takes his $11.$

Hence, A‘s score is $\mathrm{11,\; B‘s\; score\; is 11 and\; difference\; is 00.}$

There is also another optimal way of playing:

• A removes $\mathrm{55 from\; B‘s\; list.}$
• B removes $\mathrm{44 from\; A‘s\; list.}$
• A removes $\mathrm{11 from\; B‘s\; list.}$
• B removes $\mathrm{11 from\; A‘s\; list.}$

The difference in the scores is still $00.$

In the second example, irrespective of the moves the players make, they will end up with the same number of numbers added to their score, so the difference will be $00.$

$\mathrm{题目大意：有A,B两个竞赛者各自拥有一个序列，他们可以在每一个回合中进行两种操作，第一种操作是在对方的序列中删除一个元素，第二种操作是把自己序列中的一个元素加入自己的得分中，A,B都想要自己的得分较高，输出A-B的值。}$

$\mathrm{思路：将两个序列排序，进行操作模拟。}$

#include <cstdio>
#include <iostream>
#include <string.h>
#include <queue>
#include <algorithm>
using namespace std;
int a[100010];
int b[100010];

int main()
{
    int n;
    scanf("%d",&n);
    for(int i=0; i<n; i++)
        scanf("%d",&a[i]);
    for(int i=0; i<n; i++)
        scanf("%d",&b[i]);
    sort(a,a+n);
    sort(b,b+n);
    long long sum=0;
    int t=0;
    int x=n-1;
    int y=n-1;
    while(x>=0||y>=0)
    {
        if(t%2==0)
        {
            if(a[x]>b[y]) sum+=a[x],x--;
            else y--;
        }
        else
        {
            if(a[x]>=b[y]) x--;
            else sum-=b[y],y--;
        }
        t++;
    }
    printf("%I64d
",sum);
    return 0;
}