test

个人赛向

设函数f定义在一个点p_{0}的某个领域U_{p_{0}}内，若对于任何p\in U_{p_{0}},有f(p)\le f_{p_{0}}，此时称f在p_{0}取到极大值，若不等号反向，则称f在p_{0}取到极小值。设f(x,y)在点P(x_{0},y_{0})取到极值，则对任何实数h，考虑两个一元函数\varphi(t)=f(x_{0}+th,y_{0}),\psi(t)=f(x_{0},y_{0}+th)(要求偏导数存在)均在t=0取极值，有Fermat引理\varphi'(0)=f_{x}(x_{0},y_{0})h=0,\psi'(0)=f_{y}(x_{0},y_{0})h=0由于h的任意性，f_{x}(x_{0},y_{0})=f_{y}(x_{0},y_{0})=0

f(x)=\sum_{i=0}^{n}a_{i}x^{i}

正定：正惯性指数=rank（有min）负定：负惯性指数=rank（有max）不定：其他情况（无最值）

z=f(x,y)\frac{\partial z}{\partial x}=f_{x}(x,y)\frac{\partial}{\partial x}(\frac{\partial z}{\partial x})=\frac{\partial^2 z}{\partial x^{2}}=f_{xx}(x,y)=f_{11}\frac{\partial}{\partial x}(\frac{\partial z}{\partial y})=\frac{\partial^2 z}{\partial x\partial y}=f_{xy}(x,y)=f_{12}\frac{\partial}{\partial y}(\frac{\partial z}{\partial y})=\frac{\partial^2 z}{\partial y^{2}}=f_{yy}(x,y)=f_{22}\frac{\partial}{\partial y}(\frac{\partial z}{\partial x})=\frac{\partial^2 z}{\partial y\partial x}=f_{yx}(x,y)=f_{21}

求SCC的Tarjan