34. Search for a Range

本文介绍了一个简单的算法,用于在一维有序整数数组中查找特定目标值的第一个和最后一个位置。通过二分查找确定目标值的位置,并进一步扩展搜索以找到其范围。

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简单题,先找数字的位置,再找范围。

class Solution {
public:
    vector<int> searchRange(vector<int>& nums, int target) {

        vector<int> result;
        result.push_back(-1);
        result.push_back(-1);

        if(nums.size()==0)
            return result;

        int left=0;
        int right=nums.size()-1;
        int mid=0;

        while(right-left>1)
        {
            mid=left+(right-left)/2;

            if(nums[mid]>target)
                right=mid-1;
            else if(nums[mid]<target)
                left=mid+1;
            else
                break;
        }

        int targetIndex=0;
        if(right-left>1)
            targetIndex=mid;
        else
        {
            if(nums[left]==target)
                targetIndex=left;
            else if(nums[right]==target)
                targetIndex=right;
            else
                targetIndex=-1;
        }


        //cout<<targetIndex;
        if(targetIndex>=0)
        {

            int leftRange=targetIndex;
            int rightRange=targetIndex;

            while(leftRange>=0&&nums[leftRange]==target)
                leftRange--;

            while(rightRange<nums.size()&&nums[rightRange]==target)
                rightRange++;
            result[0]=(leftRange+1);
            result[1]=(rightRange-1);
        }

        return result;


    }
};
### Hierarchical Embedding Model for Personalized Product Search In machine learning, hierarchical embedding models aim to capture the intricate relationships between products and user preferences by organizing items within a structured hierarchy. This approach facilitates more accurate recommendations and search results tailored specifically towards individual users' needs. A hierarchical embedding model typically involves constructing embeddings that represent both product features and their positions within a category tree or other organizational structures[^1]. For personalized product searches, this means not only capturing direct attributes of each item but also understanding how these relate across different levels of abstraction—from specific brands up through broader categories like electronics or clothing. To train such models effectively: - **Data Preparation**: Collect data on user interactions with various products along with metadata describing those goods (e.g., price range, brand name). Additionally, gather information about any existing hierarchies used in categorizing merchandise. - **Model Architecture Design**: Choose an appropriate neural network architecture capable of processing multi-level inputs while maintaining computational efficiency during training sessions. Techniques from contrastive learning can be particularly useful here as they allow systems to learn meaningful representations even when labels are scarce or noisy[^3]. - **Objective Function Formulation**: Define loss functions aimed at optimizing performance metrics relevant for ranking tasks; minimizing negative log-likelihood serves well as it encourages correct predictions over incorrect ones[^4]. Here’s a simplified example using Python code snippet demonstrating part of what might go into building one aspect of this kind of system—learning embeddings based off some hypothetical dataset containing customer reviews alongside associated product IDs: ```python import torch from torch import nn class HierarchicalEmbedder(nn.Module): def __init__(self, vocab_size, embed_dim=100): super().__init__() self.embedding = nn.Embedding(vocab_size, embed_dim) def forward(self, x): return self.embedding(x) # Example usage: vocab_size = 5000 # Number of unique words/products embeddings_model = HierarchicalEmbedder(vocab_size) input_tensor = torch.LongTensor([i for i in range(10)]) # Simulated input indices output_embeddings = embeddings_model(input_tensor) print(output_embeddings.shape) # Should output something similar to "torch.Size([10, 100])" ``` This script initializes a simple PyTorch module designed to generate fixed-size vector outputs corresponding to given integer keys representing either textual tokens found within review texts or numeric identifiers assigned uniquely per catalog entry.
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