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1017. Queueing at Bank (25)Suppose a bank has K windows open for service. There is a yellow line in front of the windows which devides the waiting area into two parts. All the customers have to wait in line behind the yellow line, until it is his/her turn to be served and there is a window available 阅读全文
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1016. Phone Bills (25) A long-distance telephone company charges its customers by the following rules: Making a long-distance call costs a certain amount per minute, depending on the time of day when the call is made. When a customer starts connecting a long-distance call, the tim... 阅读全文
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1015. Reversible Primes (20) A reversible prime in any number system is a prime whose "reverse" in that number system is also a prime. For example in the decimal system 73 is a reversible prime because its reverse 37 is also a prime. Now given any two positive integers N (#include... 阅读全文
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The Sequential Minimal Optimization Algorithm (SMO)本文主要介绍用于解决SVM对偶模型的算法，它于1998年由John Platt在论文“Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines”中提出的。这篇笔记还参考了某篇博客，但由于是一年前的事了，暂时没找到这篇博客，所以没有引用出来，希望该篇博客的主人见谅。（1）解决的问题。 SMO 算法解决的是 soft SVM 对偶问题。其模型为：\begin{align}\matho. 阅读全文
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Soft Margin SVM（1）Recall 之前分析到SVM的模型为：\begin{align}\mathop{\min}&\quad \frac{1}{2}w^\prime w\nonumber\\\mathop{s.t}&\quad y_i(x_i^\prime w+b)\geq 1, i=1,2,\cdots,m\label{model:SVM}\end{align} 利用Lagrange乘子法转化为对偶问题：\begin{align}\mathop{\max}&\quad \theta(\alpha)=\sum_{i}\alpha_i-\frac{1}{2 阅读全文
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1014. Waiting in Line (30) Suppose a bank has N windows open for service. There is a yellow line in front of the windows which devides the waiting area into two parts. The rules for the customers to wait in line are: The space inside the yellow line in front of each window is eno... 阅读全文
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The Solutions of Nonlinear Equation 本文主要介绍几种用于解非线性方程$f(x)=0$的一些方法。（1） Bisection Method. 算法：step 1: 初始化$a,b(b>a)$，使$f(a),f(b)$异号。step 2: while (停止条件不满足) $p=a+\frac{b-a}{2}$； 若 $f(p)f(a)a,g(b)0,\lambda, \lim_{n\to\infty}\frac{\tilde{p_{n+1}}-p}{(\tilde{p_n}-p)^\alpha}=\lambda$$由于Aitken's $\De.. 阅读全文
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1013. Battle Over Cities (25) It is vitally important to have all the cities connected by highways in a war. If a city is occupied by the enemy, all the highways from/toward that city are closed. We must know immediately if we need to repair any other highways to keep the rest of ... 阅读全文
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Kernels 我们首先来回顾kernel函数的定义：一个函数$K(x,y)$为kernel函数当且仅当对$\forall g, \int K(x,y)g(x)g(y)dxdy\geq 0$成立。另外，根据Mercer's theorem，存在一个映射$\Phi$使$K(x,y)=\langle \Phi(x),\Phi(y)\rangle$，并且对任意有限的点，kernel矩阵是半正定的。一、核函数的封闭性 Hadamard product：$$\mathbf{A}\circ\mathbf{B}=\left[\begin{array}&a_{11}b_{11}&a_{ 阅读全文
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Linear & Ridge Regression 对于$n$个数据$\{(x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)\},x_i\in\mathbb{R}^d,y_i\in\mathbb{R}$。我们采用以下矩阵来记上述数据：\begin{equation}\math... 阅读全文
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