Floyd's Triangle Floyd's triangle is a right-angled triangular array of natural numbers. Floyd's triangle是自然数的直角三角形数组 It is defined by filling the rows of the triangle with consecutive numbers, starting with a 1 in the top left corner. 它是通过用连续的数字填充三角…

To master any programming languages, you need to definitely solve/practice the below-listed problems. These problems range from easy to advanced difficulty level. I have collected these questions from various websites. For solutions refer this - http…

算法思路 路径矩阵 通过一个图的权值矩阵求出它的每两点间的最短路径矩阵.从图的带权邻接矩阵A=[a(i,j)] n×n开始,递归地进行n次更新,即由矩阵D(0)=A,按一个公式,构造出矩阵D(1):又用同样地公式由D(1)构造出D(2),以此类推.最后又用同样的公式由D(n-1)构造出矩阵D(n).矩阵D(n)的i行j列元素便是i号顶点到j号顶点的最短路径长度,称D(n)为图的距离矩阵,同时还可引入一个后继节点矩阵path来记录两点间的最短路径. 状态转移方程 其状态转移方程如下: map[i,…

Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below. For example, given the following triangle [ [], [,4], [6,,7], [4,,8,3] ] The minimum path sum from top to bottom is 11 (i.e.,…

Given an index k, return the kth row of the Pascal's triangle. For example, given k = 3,Return [1,3,3,1]. Note:Could you optimize your algorithm to use only O(k) extra space? 杨辉三角想必大家并不陌生,应该最早出现在初高中的数学中,其实就是二项式系数的一种写法. 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1…

Given numRows, generate the first numRows of Pascal's triangle. For example, given numRows = 5,Return [ [1], [1,1], [1,2,1], [1,3,3,1], [1,4,6,4,1] ] 杨辉三角是二项式系数的一种写法,如果熟悉杨辉三角的五个性质,那么很好生成,可参见我的上一篇博文: http://www.cnblogs.com/grandyang/p/4031536.html 具体生…

关于最短的先记下了 Floyd算法: 1.比较精简准确的关于Floyd思想的表达:从任意节点A到任意节点B的最短路径不外乎2种可能,1是直接从A到B,2是从A经过若干个节点X到B.所以,我们假设maze(AB)为节点A到节点B的最短路径的距离,对于每一个节点X,我们检查maze(AX) + maze(XB) < maze(AB)是否成立,如果成立,证明从A到X再到B的路径比A直接到B的路径短,我们便设置maze(AB) = maze(AX) + maze(XB),这样一来,当我们遍历完所有节点X…

题目简述: Given an index k, return the kth row of the Pascal's triangle. For example, given k = 3, Return [1,3,3,1]. Note: Could you optimize your algorithm to use only O(k) extra space? 解题思路: 这里的关键是空间的使用,既然只能用O(K)很容易就想到我们要进行回卷(名字好像不对).我的做法是每一次都在后面新加入一个数…

题目简述: Given numRows, generate the first numRows of Pascal's triangle. For example, given numRows = 5, Return [ [1], [1,1], [1,2,1], [1,3,3,1], [1,4,6,4,1]] 解题思路: 很简单的问题,只要把两头的一拿出来,中间就是两个数相加了. class Solution: # @return a list of lists of integers def…

http://poj.org/problem?id=1163 The Triangle Time Limit: 1000MS   Memory Limit: 10000K Total Submissions: 32923   Accepted: 19514 Description 73 88 1 02 7 4 44 5 2 6 5 (Figure 1) Figure 1 shows a number triangle. Write a program that calculates the hi…