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IC Introduction - 2 IC What does IC Go? Communication, PC/Computer, Automotive, Consumer, Industrial, Government(Military, Satellite) Logic, Memory, Analog, MPU, Opto, Discrete, MCU, Sensor, DSP A computer is a system that uses physical phenomena to represent and manipulate information, include...

Honors ICS - 4 Design Half - adder Full-Adder Parallel Adders Comparators Decoders To detect a pattern Encoders Change a decimal number to a binary number : Multiplexers Select a particular data line which is determined by the select inputs.

Honors ICS - 3 Gates The Invertor The NOT operator. The AND Gate The OR Gate The NAND Gate Produces a LOW output when all inputs are HIGH. It is even more fundamental ! It can represent all the AND, OR, NOT operation! NOT A = A NAND A A AND B = (A NAND B) NAND (A NDAN B) A+B=A+B‾‾=A‾⋅B‾‾=A⋅...

根号分治 + NTT优化dp转移：ICPC2026网络赛B 考虑一个朴素的dp 定义 cic_ici​ 表示有多少个 aaa 小于等于 iii。显然 iii 只有模这 cic_ici​ 个数才会改变。 设 fif_ifi​ 表示在整个过程中，有多少种排列使得 iii 存在过。显然对于 i<a1i<a_1i<a1​，fif_ifi​ 就是答案。而 i≥a1i\ge a_1i≥a1​，答案是0。 fi×1ci→j∈{a}fi  mod  jf_i\times \frac 1{c_i}\to_{j\in \{a\}}f_{i\,\bmod\, j} fi​×ci​1​→j∈...

Honors ICS - 2 Coding Coding Basic Binary Conversions (decimal fraction) : Subtraction Subtraction (for 2 digits) , for decimal system: 63−27=63+(100−27)=63+(99−27)+1=63+¬27+1=63+72+1=136=3663 - 27 = 63 + (100 - 27) = 63 + (99 - 27) + 1 = 63 + \neg 27 + 1=63+72+1=136=3663−27=63+(100−27)=63+(99−2...

Linear Algebra - 3 Section 1.5 Solution Sets of Linear Systems Homogeneous Linear Systems : Homogeneous if it can be written in Ax=0Ax=0Ax=0 Such Ax=0Ax=0Ax=0 always has at least one solution, called trivial solution Ax=0Ax=0Ax=0 has a nontrivial solution iff the equation has at least one free v...

ICPC2026网络赛1 E. LCM Permutation LCM Permutation - Problem - QOJ.ac 我不知道怎么形容这题好，反正很神。此处只描述做法，因为我也不知道怎么std是怎么想出来的。 首先，对于 n≤13n\le 13n≤13 这个级别的，我们直接 O(n!)O(n!)O(n!) 即可（因为必然有解，所以其实是 O((n−1)!)O((n-1)!)O((n−1)!)） 接下来，我们对 14≤n≤2514\le n\le 2514≤n≤25，我们尝试令这个LCM L=168=23×3×7L=168=2^3\times 3\times 7L=168...

Honors Calculus I - 3 Function Function For f:X→Yf:X\to Yf:X→Y is a mapping domain : Df=XD_f=XDf​=X codomain : YYY range : RfR_fRf​ (The definite numbers) yyy is the image of xxx xxx is the inverse image of yyy If : Rf=YR_f=YRf​=Y, that fff is a surjective f(x1)=f(x2)f(x_1)=f(x_2)f(x1​)=f(x2​)...

Honors Physics I - 2 Force and Motion Relative Motion Galilean transformation : xPA=xPB+xABx_{PA}=x_{PB}+x_{AB}xPA​=xPB​+xAB​ Projectile motion x=v0cos⁡θ ty=y0+v0sin⁡θ t−12gt2=0R=v02gsin⁡2θ0x=v_0\cos\theta\, t\\ y=y_0+v_0\sin\theta\,t-\frac 1 2gt^2=0\\ R=\frac {v_0^2}g\sin2\theta_0 x=v0​cosθty=...

Honors ICS - 1 : Bit Operations Logic is about “Proof” Every step must be very solid and accurate Coherent Bit Operations 3 basic operations (gate): AND OR NOT Voltage -> Bit Problem : Addition (Summation) We will start at 1-bit addition like 1-digit addition If will do not consider the ...