Data Structure＝（D，S）

在计算机科学中，Data Structure（数据结构）是一种组织数据的方式，它将数据以特定的形式存储和管理，以便高效地访问、插入和删除。公式（D，S）可以理解为描述数据结构的一般形式：

- D（Data）代表数据，即存储的对象，可能是数字、字符串、数组、列表、图等各种类型的元素。
- S（Structure）则是指如何组织这些数据，也就是数据的存储方式和数据之间的关联规则。这包括各种数据结构的算法设计，如数组（Array）、链表（Linked List）、堆（Heap）、栈（Stack）、队列（Queue）、树（Tree）、图（Graph）、哈希表（Hash Table）等。

不同的数据结构适用于不同的场景，选择合适的数据结构可以大大提高程序的效率。例如，如果需要快速查找某个元素，可能选择哈希表；如果需要按顺序访问元素并保持元素的插入顺序，那么双向链表会是个好选择。

相关问题

翻译这段程序并自行赋值调用：import matplotlib.pyplot as plt import numpy as np import sklearn import sklearn.datasets import sklearn.linear_model def plot_decision_boundary(model, X, y): # Set min and max values and give it some padding x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1 y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1 h = 0.01 # Generate a grid of points with distance h between them xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) # Predict the function value for the whole grid Z = model(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Plot the contour and training examples plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) plt.ylabel('x2') plt.xlabel('x1') plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral) def sigmoid(x): s = 1/(1+np.exp(-x)) return s def load_planar_dataset(): np.random.seed(1) m = 400 # number of examples N = int(m/2) # number of points per class print(np.random.randn(N)) D = 2 # dimensionality X = np.zeros((m,D)) # data matrix where each row is a single example Y = np.zeros((m,1), dtype='uint8') # labels vector (0 for red, 1 for blue) a = 4 # maximum ray of the flower for j in range(2): ix = range(Nj,N(j+1)) t = np.linspace(j3.12,(j+1)3.12,N) + np.random.randn(N)0.2 # theta r = anp.sin(4t) + np.random.randn(N)0.2 # radius X[ix] = np.c_[rnp.sin(t), rnp.cos(t)] Y[ix] = j X = X.T Y = Y.T return X, Y def load_extra_datasets(): N = 200 noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3) noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2) blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6) gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None) no_structure = np.random.rand(N, 2), np.random.rand(N, 2) return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure

这段程序是一个分类模型的辅助函数，包括了绘制决策边界、sigmoid函数和加载数据集的函数。具体实现如下：

import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model

def plot_decision_boundary(model, X, y):
    # 设置最小值和最大值，并给它们一些填充
    x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
    y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
    h = 0.01

    # 生成一个网格，网格中点的距离为h
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

    # 对整个网格预测函数值
    Z = model(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)

    # 绘制轮廓和训练样本
    plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
    plt.ylabel('x2')
    plt.xlabel('x1')
    plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)

def sigmoid(x):
    s = 1 / (1 + np.exp(-x))
    return s

def load_planar_dataset():
    np.random.seed(1)
    m = 400  # 样本数量
    N = int(m / 2)  # 每个类的样本数量

    # 生成数据集
    D = 2  # 特征维度
    X = np.zeros((m, D))  # 特征矩阵
    Y = np.zeros((m, 1), dtype='uint8')  # 标签向量

    a = 4  # 花的最大半径

    for j in range(2):
        ix = range(N*j, N*(j+1))
        t = np.linspace(j*3.12, (j+1)*3.12, N) + np.random.randn(N)*0.2  # theta
        r = a*np.sin(4*t) + np.random.randn(N)*0.2  # radius
        X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
        Y[ix] = j

    X = X.T
    Y = Y.T

    return X, Y

def load_extra_datasets():
    N = 200
    noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3)
    noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2)
    blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6)
    gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None)
    no_structure = np.random.rand(N, 2), np.random.rand(N, 2)

    return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure

这段程序中包含了以下函数：

- `plot_decision_boundary(model, X, y)`：绘制分类模型的决策边界，其中`model`是分类模型，`X`是特征矩阵，`y`是标签向量。
- `sigmoid(x)`：实现sigmoid函数。
- `load_planar_dataset()`：加载一个二维的花瓣数据集。
- `load_extra_datasets()`：加载五个其他数据集。

Implement the hash table (with chaining) data structure. Your table should be able to grow and shrink based on how many items are there. contain at least the following methods: * __init__: initialize the data structure * hash: implement a hash function that is chosen from a universal hash family * search: search for a key in the table, return True if found, False otherwise * insert: insert a key into the table if it is not already in there * delete: delete a key from the table * size: return the number of buckets in your hash table

Sure, I can help you with that. Here's a possible implementation of a hash table with chaining:

import random

class HashTable:
    def __init__(self, initial_size=10, load_factor=0.7):
        self.buckets = [[] for _ in range(initial_size)]
        self.load_factor = load_factor
        self.size = 0
    
    def hash(self, key):
        # A simple universal hash function using random parameters
        a = random.randint(1, 10**9)
        b = random.randint(0, 10**9)
        p = 10**9 + 7
        return (a * hash(key) + b) % p % len(self.buckets)
    
    def search(self, key):
        bucket = self.buckets[self.hash(key)]
        for k, v in bucket:
            if k == key:
                return True
        return False
    
    def insert(self, key, value=None):
        if self.size / len(self.buckets) >= self.load_factor:
            self._resize(2 * len(self.buckets))
        bucket = self.buckets[self.hash(key)]
        for i, (k, v) in enumerate(bucket):
            if k == key:
                bucket[i] = (key, value)
                return
        bucket.append((key, value))
        self.size += 1
    
    def delete(self, key):
        bucket = self.buckets[self.hash(key)]
        for i, (k, v) in enumerate(bucket):
            if k == key:
                del bucket[i]
                self.size -= 1
                if self.size / len(self.buckets) <= 1 - self.load_factor:
                    self._resize(len(self.buckets) // 2)
                return
        raise KeyError(key)
    
    def _resize(self, new_size):
        new_buckets = [[] for _ in range(new_size)]
        for bucket in self.buckets:
            for k, v in bucket:
                new_buckets[self.hash(k)].append((k, v))
        self.buckets = new_buckets
    
    def __len__(self):
        return self.size

This implementation uses a list of buckets, where each bucket is a list of key-value pairs. The hash function is a simple universal hash function that uses random parameters to avoid collisions. The load factor determines when the table should be resized (either doubled or halved) to maintain a reasonable level of occupancy. The `search`, `insert`, `delete`, and `size` methods are straightforward operations on the buckets. The `__len__` method returns the number of key-value pairs in the table.

Note that this implementation doesn't handle collisions beyond chaining, and doesn't support efficient iteration over all key-value pairs in the table. There are many possible improvements and variations depending on the specific use case and performance requirements.