Python里面有内置(Built-in)的平方根函数:sqrt(),可以方便计算正数的平方根.那么,如果要自己定义一个sqrt函数,该怎么解决呢? 解决思路:  1. 大于等于1的正数n的方根,范围肯定在0~n之间:小于1的正数n的方根,范围肯定在0~1之间  2. 用二分法(Bisection method, Binary search)从中间开始找n的方根.  3. 对于大于等于1的正数n,先假设n/2是n的方根,如果n/2的平方大于n,那么说明n的方根在0~n/2之间:如果n/2的平方小…

牛顿法(Newton’s method)又称为牛顿-拉弗森法(Newton-Raphson method),是一种近似求解实数方程式的方法.(注:Joseph Raphson在1690年出版的<一般方程分析>中提出了后来被称为“牛顿-拉弗森法”的数学方法,牛顿于1671年写成的著作<流数法>中亦包括了这个方法,但该书在1736年才出版.) 之前的一篇博客中提到的二分法可以求解方根(用二分法定义平方根函数),而使用牛顿迭代法可以更快地解出方根.现在,人们使用的计算器里面大多数都是运用…

Tiny Wong the chef used to be a mathematics teacher in a senior high school. At that time, he always used to tell his students that when there is a square root of some number in one’s final result, it should be simplified by factoring out the largest…

A. Plus and Square Root time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) an…

Square root digital expansion It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all. The square root of two i…

E. Square Root of Permutation A permutation of length n is an array containing each integer from 1 to n exactly once. For example, q = [4, 5, 1, 2, 3] is a permutation. For the permutation q the square of permutation is the permutation p that p[i] = …

ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) and '' (square root). Initially, the number 2 is displayed on the screen. There are n + 1 levels in the game and ZS the Coder start at t…

C. Plus and Square Root time limit per test 2 seconds memory limit per test 256 megabytes input standard input output standard output ZS the Coder is playing a game. There is a number displayed on the screen and there are two buttons, ' + ' (plus) an…

It is possible to show that the square root of two can be expressed as an infinite continued fraction.  2 = 1 + 1/(2 + 1/(2 + 1/(2 + ... ))) = 1.414213... By expanding this for the first four iterations, we get: 1 + 1/2 = 3/2 = 1.51 + 1/(2 + 1/2) = 7…

Square RootWhen the square root functional configuration is selected, a simplified CORDIC algorithm isused to calculate the positive square root of the input. The input, X_IN, and the output,X_OUT, are always positive and are both expressed as either…