bzoj5139 [Usaco2017 Dec]Greedy Gift Takers(二分答案+模拟)

本文介绍了一种通过二分查找确定在特定排列下无法获取礼物的牛的最小编号的方法。利用预处理找出每头牛可能停留的位置,并检查是否存在使得某些牛永远无法前进的死循环。若存在死循环,则采用二分法找到首头受影响的牛。

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首先我们发现如果第x头牛不能拿到礼物,则x之后的所有牛也不能拿到礼物。因此我们可以二分来找到这第一头不能拿到礼物的牛。满足什么条件的牛不能拿到礼物呢?我们预处理出每头牛拿到礼物之后会出现在哪里,如果在第x头牛之前的牛们形成了一个死循环,则第x头牛就永远也拿不到礼物了。怎么样会形成一个死循环呢?出现在前i个位置的牛有多于i头,则这i头牛就会一直卡在这前i个位置。因此我们模拟一下这个过程看有没有死循环出现就好了。

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define N 100010
inline int read(){
    int x=0,f=1;char ch=getchar();
    while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*f;
}
int n,a[N],cnt[N];
inline bool jud(int mid){//判断mid是不是不能拿到礼物
    memset(cnt,0,sizeof(cnt));int sum=0;
    for(int i=1;i<mid;++i) cnt[a[i]]++;
    for(int i=1;i<mid;++i){
        sum+=cnt[i];if(sum>=i) return 1;
    }return 0;
}
int main(){
//  freopen("a.in","r",stdin);
    n=read();for(int i=1;i<=n;++i) a[i]=n-read();
    int l=1,r=n;//找第一个不能拿到礼物的牛
    while(l<=r){
        int mid=l+r>>1;
        if(jud(mid)) r=mid-1;else l=mid+1;
    }++r;printf("%d\n",n-r+1);
    return 0;
}
### Epsilon-Greedy Algorithm Implementation and Use Cases The epsilon-greedy algorithm is a strategy commonly used in reinforcement learning to balance exploration and exploitation. In this context, exploration refers to trying out new actions to discover potentially better outcomes, while exploitation involves selecting the action that has historically provided the best reward. #### Algorithm Implementation The epsilon-greedy policy selects a random action with probability ε (epsilon) and the greedy action (the one with the highest estimated value) with probability 1 - ε. This ensures that the agent does not always exploit known information but also explores other options to avoid getting stuck in suboptimal strategies[^2]. Below is an implementation of the epsilon-greedy algorithm in Python: ```python import numpy as np def epsilon_greedy_policy(Q, state, epsilon): if np.random.rand() < epsilon: # Exploration: Select a random action return np.random.choice(len(Q[state])) else: # Exploitation: Select the action with the highest value return np.argmax(Q[state]) ``` In this code snippet, `Q` represents the action-value function estimate for each state-action pair, `state` is the current state, and `epsilon` determines the likelihood of choosing a random action over the optimal one. #### Use Cases Epsilon-greedy algorithms are widely applied in various domains where decision-making under uncertainty is required. Some prominent use cases include: 1. **Reinforcement Learning**: The algorithm is fundamental in training agents to solve Markov Decision Processes (MDPs). For instance, it can be employed in games like chess or Go, where the agent must decide between exploring new moves or exploiting known winning strategies[^1]. 2. **Multi-Armed Bandit Problems**: These problems involve maximizing rewards by selecting among multiple options (or "arms") with unknown payoff distributions. Epsilon-greedy policies help determine which arm to pull next by balancing exploration and exploitation. 3. **Recommendation Systems**: In online recommendation systems, such as those used by streaming platforms or e-commerce websites, epsilon-greedy algorithms can suggest items to users. By occasionally recommending less popular items, the system can discover new preferences while primarily offering top-rated suggestions[^3]. 4. **Autonomous Driving**: Self-driving cars use reinforcement learning techniques to navigate roads safely. An epsilon-greedy approach might allow the vehicle to experiment with different driving styles during testing phases before settling on optimal behaviors[^4]. 5. **Resource Allocation**: In cloud computing environments, epsilon-greedy methods can optimize server allocation by dynamically adjusting resources based on historical performance metrics while exploring alternative configurations[^3].
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