E2. Game with Marbles (Hard Version)

合集 - codeforces(57)

1.C. Insert and Equalize2023-12-062.C. Removal of Unattractive Pairs2023-12-063.D. Jumping Through Segments2023-12-084.E. Good Triples2023-12-085.F. Shift and Reverse2023-12-086.D. Yet Another Monster Fight2023-12-117.A. Constructive Problems2023-12-188.C. Game with Multiset2023-12-199.A. Rating Increase2023-12-1910.B. Swap and Delete2023-12-1911.A. Problemsolving Log2023-12-2012.B. Preparing for the Contest2023-12-2013.C. Quests2023-12-2014.D. Three Activities2023-12-20

15.E2. Game with Marbles (Hard Version)2023-12-20

16.cf刷题有感2023-12-2017.A. Anonymous Informant2023-12-2118.A. Forked!2023-12-2319.B. Make Almost Equal With Mod2023-12-2720.C. Heavy Intervals2023-12-2721.D. Split Plus K2023-12-2822.A. 20232023-12-3123.B. Two Divisors2023-12-3124.C. Training Before the Olympiad2023-12-3125.D. Mathematical Problem2024-01-0226.F. Greetings2024-01-0227.C. Partitioning the Array2024-01-1528.G. Bicycles2024-01-1629.E. Eat the Chip2024-01-1730.G. Lights2024-01-1731.D. Array Repetition2024-01-1732.D. Berserk Monsters2024-01-2233.E. Increasing Subsequences2024-01-2334.D. Very Different Array2024-01-2435.G. Mischievous Shooter2024-01-2536.B. Plus-Minus Split2024-01-2737.B. A Balanced Problemset2024-01-2838.C. Did We Get Everything Covered2024-01-2839.D. Find the Different Ones!2024-02-0840.C. Grouping Increases2024-02-1041.D. Good Trip2024-02-1242.C. Physical Education Lesson2024-02-1243.E. Final Countdown2024-02-1844.D. Divisible Pairs2024-02-1945.G. Vlad and Trouble at MIT2024-02-2046.A. Brick Wall2024-02-2847.B. Minimize Inversions2024-02-2848.C. XOR-distance2024-02-2849.A. Moving Chips2024-02-2850.B. Monsters Attack!2024-02-2851.C. Find B2024-02-2852.D. Slimes2024-02-2853.C. Turtle Fingers: Count the Values of k2024-02-2854.D. Turtle Tenacity: Continual Mods2024-02-2855.D. Vlad and Division2024-02-2856.C. LR-remainders2024-02-2857.D. Lonely Mountain Dungeons2024-03-12

收起

原题链接

导论，有点博弈论的感觉？

每个人轮流选一个大家都有的球，然后自己扣一个球，对方扣完。问女生剩下的球减去男生剩下的球，最大值是多少？

一些条件

1.初始每个人每种球都有
2.女生想使答案值大一点，男生想使答案值小一点，换句话说，女生想使$A$值大一点，男生想使$B$值大一点，每个人都尽量多扣对面的球，多保留自己的球。
3.如果选择扣掉对面的球 $i$，那么自己的球 $i$ 将会得到保留。

总述

每个人选择的最优策略是选择 $a[i]+b[i]$ 最大的那个。

代码

#include<bits/stdc++.h>
#define ll long long
using namespace std;
ll a[200005]={0};
ll b[200005]={0};
struct unit
{
    int v;
    int id;
}sum[200005];
bool cmp(unit x,unit y)
{
    return x.v>y.v;
}
int main()
{
    ll t;
    cin>>t;
    while(t--)
    {
        ll n;
        cin>>n;
        for(int i=1;i<=n;i++) cin>>a[i];
        for(int i=1;i<=n;i++)
        {
            cin>>b[i];
            sum[i].v=a[i]+b[i];//又要扣除，又要保留
            sum[i].id=i;
        }
        sort(sum+1,sum+n+1,cmp);
        ll who=0;
        for(int i=1;i<=n;i++)
        {
            int index=sum[i].id;
            if(who==0)
            {
                a[index]--;
                b[index]=0;
            }
            else
            {
                a[index]=0;
                b[index]--;
            }
            who=1-who;
        }
        ll ans=0;
        for(int i=1;i<=n;i++)ans=ans+a[i]-b[i];
        printf("%lld\n",ans);
    }
    return 0;
}