cf1141f2 greedy

本文介绍了一种使用C++解决区间覆盖问题的方法,通过结构体存储区间信息,运用vector容器进行区间管理,实现对区间进行排序和合并,以找到最小的区间覆盖集合。

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#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#include <string>
#include <map>
#include <vector>
using namespace std;
int n;
struct node
{
    int l,r;
    friend bool operator<(node x,node y)
    {
        return x.r<y.r;
    }
};

long long sum[1505];
long long a[1505];

vector<node> v[1501*1501];
int cnt;

int get(int id,int f)
{
    int len=v[id].size();
    int ans=0;
    int pre=0;
    for(int i=0;i<len;i++)
    {
        if(v[id][i].l>pre)
        {
            ans++;
            pre=v[id][i].r;
            if(f==1)
                printf("%d %d\n",v[id][i].l,v[id][i].r);
        }
    }
    return ans;
}
int main() {

    while(~scanf("%d",&n))
    {
        memset(sum,0, sizeof(sum));
        map<long long,int> mp;
        cnt=0;

        for(int i=1;i<=n;i++)
            scanf("%lld",&a[i]),sum[i]=sum[i-1]+a[i];

        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=i;j++)
            {
                long long tp=sum[i]-sum[j-1];
                if(mp[tp]==0)
                    mp[tp]=++cnt;
                int id=mp[tp];
                node cur;cur.l=j;cur.r=i;
                v[id].push_back(cur);
            }
        }

        int ans=0,ansid;
        for(int i=1;i<=cnt;i++)
        {
            //sort(v[i].begin(),v[i].end());
            int tans=get(i,0);
            if(tans>ans)
                ans=tans,ansid=i;
        }
        printf("%d\n",ans);
        get(ansid,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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