本文给出杨辉三角的几种C语言实现,并简要分析典型方法的复杂度。 本文假定读者具备二项式定理、排列组合、求和等方面的数学知识。 一 基本概念 杨辉三角,又称贾宪三角、帕斯卡三角,是二项式系数在三角形中的一种几何排列。此处引用维基百科上的一张动态图以直观说明(原文链接http://zh.wikipedia.org/wiki/杨辉三角):...
今天介绍数学中一个非常神奇数阵“帕斯卡三角形(Pascal's Triangle)”。 帕斯卡三角形,在中国通常称作杨辉三角,又称贾宪三角形、海亚姆三角形、塔塔利亚三角形等,是二项式系数在的一种写法,形似三角形,在中国首现于南宋杨辉的《详解九章算术》得名,书中杨辉说明是引自贾宪的《释锁算术...
In mathematics, Pascal's triangle is a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as(x + y)n. It is named for the 17th-century French mathematician Blaise Pascal. As an easier explanation for those who are not familiar with...
To build the triangle, start with 1 at the top, then continue placing numbers below it in a triangular pattern. Each number is the numbers directly above it added together.
Leetcode 118.杨辉三角(Pascal's Triangle) Leetcode 118.杨辉三角 1 题目描述(Leetcode题目链接) 给定一个非负整数 numRows,生成杨辉三角的前 numRows 行。在杨辉三角中,每个数是它左上方和右上方的数的和。 2 题解 直接构造。......
The Pascals Triangle is just a triangular pattern of numbers. But what makes it interesting is how each number is built from the two numbers directly above it. The first row starts with a 1 at the top. Each row after that gets wider, and every number in the triangle is the sum of ...
In this C Programming example, you will learn to print half pyramid, pyramid, inverted pyramid, Pascal's Triangle and Floyd's triangle.
[LeetCode] 118. Pascal's Triangle Given an integer numRows, return the first numRows of Pascal's triangle. In Pascal's triangle, each number is the sum of the two numbers directly above it as shown: Example 1: Input: numRows = 5...
Pascal's triangle is a number triangle with numbers arranged in staggered rows such that (1) where is a binomial coefficient. The triangle was studied by B. Pascal, in whose posthumous work it appeared in 1665 (Pascal 1665). However, it had been previously investigated my many other ...
In Part 1 of this series we stated that Pascal is credited with being the founder of probability theory – but credit also needs to be given to other mathematicians, in particular the Italian polymath Girolamo Cardano. The connection between probability and the numbers in Pascal’s triangle can...