GCD and LCM Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65535/65535 K (Java/Others)Total Submission(s): 1460    Accepted Submission(s): 653Problem DescriptionGiven two positive

Problem AExpression BracketingInput: standard inputOutput: standard outputTime Limit: 1 secondMemory Limit: 32 MB Inthis problem you will have to find in how many waysn letters can be

Problem JBits Input: Standard InputOutput: StandardOutput  A bit is a binary digit,taking a logical value of either "1" or "0" (also referredto as "true" or "false" respectively).  And every

``Pinary" number is a positive number using only two digits ``0" and ``1" with usual rule that it must not begin with a 0, and the additional rule that two successive digits must not be both ``1". Thi

A cellular automaton is a collection of cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules that describe the new state of a cell based

Consider an n-by-n matrixA. We define Ak = A *A * ... * A (k times). Here, * denotes the usual matrix multiplication.You are to write a program that computes the matrix A + A2 + A3 + ... + Ak.

Do you know how to compute the mean (or average) of n numbers?Well, that's not good enough for me. I want the supermean! "What's asupermean," you ask? I'll tell you. List then given numbers innon-

A square root of a number x is a number r such that r2 = x. A discrete square root of a non-negative integerx is a non-negative integer r such that r2 x mod N , 0r <N , where N is a specific

What do researchers working at ICPC (Institute for Cryptographic Programming and Computing) do for fun? Well, as you probably have expected, in addition to solving algorithm-related problems on online

Now a days a very common problem is:“The coordinate of two points in Cartesian coordinate system is (200, 300) and(4000, 5000). If these two points are connected we get a line segment. How manylattice

Hackerland is a happy democratic country with m×n cities, arranged in a rectangularm by n grid and connected bym roads in the east-west direction and n roads in the north-south direction. By pub

We are given a rooted tree of n vertices. The vertices are to be labeled with numbers1, 2,..., n so that each label is unique and the heap condition holds, i.e. the label of any vertex is less than

DescriptionWe say that integer x, 0 i mod p) | 1 <= i <= p-1 } is equal to { 1, ..., p-1 }. For example, the consecutive powers of 3 modulo 7 are 3, 2, 6, 4, 5, 1, and thus 3 is a primitive root m

double getRotateAngle(double x1, double y1, double x2, double y2){ const double epsilon = 1.0e-6; const double nyPI = acos(-1.0); double dist, dot, degree, angle; // normalize dist

233 MatrixTime Limit: 10000/5000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)Total Submission(s): 409    Accepted Submission(s): 273Problem DescriptionIn our daily life we

A suspension bridge suspends the roadway from huge main cables, which extend from one end of the bridge to the other. These cables rest on top of high towers and are secured at each end by anchorages.

Problem C - NecklaceOnce upon a time, three girls - Winnie, Grace and Bonnie - owned a large number of pearls. However, each of them only had a single color of pearls. Winnie had white pearls, G

Problem BCubes You are given 12 rods of equal length. Each of them is coloredin certain color. Your task is to determine in how many different ways one canconstruct a cube using these rods a

I just bought Leonardo's secret notebook! Rare objectcollector Stan Ucker was really agitated but his friend,special investigator Sarah Keptic was unimpressed.| How do you know it is genui

Problem ALights inside a 3D GridInput: Standard InputOutput: Standard Output  You are given a 3Dgrid, which have dimensions N, M andP. Each of the M xN x P cells has a light. Initially all

之前只做了快速幂取模，这次是矩阵。  就因为线代没怎么学，今天还花了一些时间去想为什么矩阵A^k+A^l=A^(k+l)，是因为A^n=A^(n-1)*A=A^(n-2)*A*A=.....由于矩阵相乘满足结合律（可以以三个为例证明一下），所以可以任意取位置先后结合，所以有A^k+A^l=A^(k+l)。  两个矩阵相乘，复杂度是O（N^3），再乘M次，所以一个矩阵的M次方时间复杂度是O（

We have many polynomials modulo p (p is a prime number). An interesting issue would be to determine whether they have some roots in common. Notice roots we mention here are integers in modulo p system

In the late 1700s', Gauss, a famous mathematician, found a special kind ofnumbers. These integers are all in the form:a + b.The sum and multiplicationofthese integers can be naturally defined as the

Emoogle Grid You have to color an M x N (1M,N108) two dimensional grid. You will be providedK (2K108) different colors to do so. You will also be provided a list of B (0B500)list

Problem ESimple AdditionInput: Standard InputOutput: Standard Output Let’s define a simple recursivefunction F (n), where  Let’s define another function S (p,q),  In this problem

Cipher Bob and Alice started to use a brand-new encoding scheme. Surprisingly it is not a Public Key Cryptosystem, but their encoding and decoding is based on secret keys. They chose the

Problem A: So you want to be a 2n-aire?The player starts with a prize of $1, and is asked a sequence of n questions. For each question, he mayquit and keep his prize. answer the question. If wro

Burger When Mr. and Mrs. Clinton's twin sons Ben and Bill had their tenth birthday, the party was held at the McDonald's restaurant at South Broadway 202, New York. There were 20 kids at

Problem GProbability|GivenInput: Standard InputOutput: Standard Output  N friends go to the local super market together. The probability of their buying something from the market is respecti

Ferrers图像图像概念一个从上而下的n层格子，mi 为第i层的格子数，当mi>=mi+1(i=1,2,,n-1) ，即上层的格子数不少于下层的格子数时，称之为Ferrers图像。[1]图像性质（1）每一层至少有一个格子；　　（2）第一行与第一列互换，第二行与第二列互换，…，所得到的图象仍然是Ferrers图象，这两个 Ferrers图象称为是一对共轭的Ferrers图象。

佩尔方程若一个丢番图方程具有以下的形式：且为正整数，则称此二元二次不定方程为佩尔方程(英文：Pell's equation 德文：Pellsche Gleichung)若是完全平方数，则这个方程式只有解（实际上对任意的，都是解）。对于其余情况，拉格朗日证明了佩尔方程总有解。而这些解可由的连分数求出。佩尔方程的解设 是的连分数表示:的渐近分数列，由连分数理

Problem ASend a TableInput: Standard InputOutput: Standard Output When participating inprogramming contests, you sometimes face the following problem: You know how tocalcutale the output for

Fermat vs. Pythagoras BackgroundComputer generated and assisted proofs and verification occupy a small niche in the realm of Computer Science. The first proof of the four-color probl

前几天做一个题都快做出来了，结果就是不会快速算幂导致超时。。  快速幂取模我看了2种方法。  首先有公式:  (a+b)%m=(a%m+b%m)%m   (a*b)%m=(a%m*b%m)%m  1.算法导论里的，算a^b mod n，设b[k]是b二进制的最高位（不算符号位）。Modular-Exponentiation(a, b, n) 1.

Problem CLeading and TrailingTime limit: 2 seconds Apart from the novice programmers, all others know that you can’t exactly represent numbers raised to some high power.

线性筛素数的思想：

Hooray!  Agent Bauer has shot the terrorists, blown upthe bad guy base, saved the hostages, exposed the moles in the government,prevented an environmental catastrophe, and found homes for three orphan

Problem XHuge ModInput: standard inputOutput: standard outputTime Limit: 1 secondThe operator for exponentiation is different from the addition, subtraction, multiplication or division ope

Problem APlay with Floor and CeilInput: standard inputOutput: standard outputTime Limit: 1 second TheoremFor any two integers x and k there exists two more integersp and q such that:

Problem IBack to Kernighan-RitchieInput: Standard InputOutput: Standard Output Youmust have heard the name of Kernighan and Ritchie, the authors ofThe C Programming Language. While cod