Association for the Country of Mububa(dp)

本文介绍了一个算法问题,目标是将一组数字划分成尽可能多的区间,每个后续区间的和需大于等于前一个。通过动态规划,文章详细解释了如何确定每个数作为区间结尾时的最优解,最终达到最大化区间数量。

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题目链接:Association for the Country of Mububa

题意:将这些数划分成n个区间,使得后一个区间里数字的和大于等于前一个区间里数字的和,求最大可以划分多少区间。

思路(gxj大佬的):

  1. 我们知道所有数到最后都会属于某一个区间,某个数结尾的序列最后一个区间值是最大的
  2. 我们可以这样想,每个数相当于插入到他前一个数形成的序列结尾,然后就变成了一个一个数插入不断取最优值的过程
  3. 对于当前这个数来说,插入他之后要么自己构成一个区间,要么把前面一个区间从某个位置截断,截断位置后面的元素与他组成一个区间。
  4. 对于某状态形成的区间来说最后一个区间值越小越有利于后面的值插入(因为我们要形成的区间数最多),也就是说以某个数结尾的区间最后一个区间越短越好,那么我们插入这个值的时候从当前位置往前一直找到能够满足条件(该数形成的区间大于序列末尾的区间)的数的时候,这个位置一定是当前位置能够形成的最优解。
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#include<queue>
#include<stack>
#include<vector>
#include<map>
#include<set>
#define inf 0x3f3f3f3f
using namespace std;

typedef long long ll;

const int N = 3010;

ll n;
ll sum[N];//前缀和
ll num[N];//当前位置所能形成的最大区间数量,dp数组
ll best[N];//以这个数结尾的最后一个区间的值

int main()
{
    ll x;
    scanf("%lld",&n);
    for(ll i = 1; i <= n; i++)
    {
        scanf("%lld",&x);
        sum[i] = sum[i-1] + x;
    }
    for(ll i = 1; i <= n; i++)
    {
        for(ll j = i-1; j >= 0; j--)
        {
            if(sum[i]-sum[j] >= best[j])
            {
                num[i] = num[j]+1;
                best[i] = sum[i]-sum[j];
                break;//找到的第一个符合条件的肯定就是最大区间数了
            }
        }
    }
    printf("%lld",num[n]);
    return 0;
}

Certainly! Here's an example of fuzzy association rule mining using the Python library scikit-fuzzy: ```python import numpy as np import pandas as pd import skfuzzy as fuzz from sklearn.preprocessing import LabelEncoder # Load the dataset dataset = pd.read_csv('your_dataset.csv') # Preprocess the dataset label_encoder = LabelEncoder() dataset['Item'] = label_encoder.fit_transform(dataset['Item']) # Fuzzify the dataset fuzzy_dataset = fuzz.interp_membership(dataset['Item'], np.arange(len(dataset['Item'])), dataset['Support'], np.max) # Generate frequent itemsets frequent_itemsets = fuzz.frequent_itemsets(fuzzy_dataset, min_support=0.3, min_confidence=0.6) # Generate fuzzy association rules fuzzy_rules = fuzz.generate_association_rules(frequent_itemsets, min_confidence=0.6) # Print the fuzzy association rules for rule in fuzzy_rules: print(rule) ``` In this example, we assume that you have a dataset stored in a CSV file. The dataset contains two columns: 'Item' and 'Support'. 'Item' represents the items or products, and 'Support' represents their support values. First, we preprocess the dataset by encoding the categorical 'Item' column using LabelEncoder. Next, we fuzzify the dataset using `interp_membership` function, which assigns degrees of membership to each item based on their support values. Then, we generate frequent itemsets using the `frequent_itemsets` function. We specify the minimum support threshold (min_support) to determine which itemsets are frequent. Finally, we generate fuzzy association rules using the `generate_association_rules` function. We specify the minimum confidence threshold (min_confidence) to filter out weak rules. The generated fuzzy association rules are then printed out for further analysis. Please note that you need to adjust the parameters and adapt this code to your specific dataset and requirements. Also, ensure that you have the scikit-fuzzy library installed (`pip install scikit-fuzzy`) before running this code.
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