Search for a Range

此博客介绍了如何在一个已排序的整数数组中找到给定目标值的起始和结束索引,算法的时间复杂度必须为 O(log n)。如果目标值未出现在数组中,则返回 [-1, -1]。通过实例演示了查找过程,并提供了相应的代码实现。

Given a sorted array of integers, 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].

#include<iostream>
#include<vector>
using namespace std;

vector<int> searchRange(int A[], int n, int target) {
	int first = 0;
	int last  = n - 1;
	vector<int>result(2, -1);
	while (first<=last)
	{
		int mid = (first + last) / 2;
		if (A[mid] == target)
		{
			result[0] = mid;
			result[1] = mid;
			while (result[0]-1 >= first&&A[result[0]-1] == target)//当一位是重复位时才对范围跟新
				--result[0];	
			while (result[1]+1 <= last&&A[result[1]+1] == target)
				++result[1];
			return result;
		}
		else if (A[mid] < target)
			first = mid + 1;
		else
			last = mid - 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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