34. Search for a Range

本文介绍了一种在有序整数数组中查找指定目标值起始和结束位置的方法,算法复杂度为O(log n),并提供了两种实现方案,一种是手动实现二分查找逻辑,另一种是利用标准库函数。

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Given an array of integers sorted in ascending order, find the starting and ending position of a given target value.

Your algorithm's runtime complexity must be in the order of O(log n).

If the target is not found in the array, return [-1, -1].

For example,
Given [5, 7, 7, 8, 8, 10] and target value 8,
return [3, 4].

法一:

类似使用二分法,分别找出target的起始和终点

https://leetcode.com/problems/search-for-a-range/discuss/

class Solution {
public:
    vector<int> searchRange(vector<int>& nums, int target) {
        vector<int> ind(2, -1);
        if(nums.capacity() == 0) return ind;
        int l = 0, r = nums.capacity() - 1;
        while(r > l){    //寻找左边缘
            int m = (r + l)/2;
            if(nums[m] < target) l = m + 1;
            else r = m;
        }
        if(nums[l] != target) return ind;
        ind[0] = l;
        r = nums.capacity() - 1;
        while(r > l){     //寻找右边缘
            int m = (r + l)/2 + 1;    //加一使m更接近右边缘
            if(nums[m] > target) r = m - 1;
            else l = m;
        }
        ind[1] = r;
        return ind;
    }
};

 

法二:

使用函数库:

vector<int> searchRange(vector<int>& nums, int target) {
    auto bounds = equal_range(nums.begin(), nums.end(), target);
    if (bounds.first == bounds.second)
        return {-1, -1};
    return {bounds.first - nums.begin(), bounds.second - nums.begin() - 1};
}

 

### 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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