算法导论第三版第29章习题答案

参考文献：

https://walkccc.me/CLRS/Chap29/29.1/
https://sites.math.rutgers.edu/~ajl213/CLRS/

29.Linear Programming

29.1 Standard and slack forms

1.If we express the linear program in (29.24)–(29.28) in the compact notation of (29.19)–(29.21), what are n, m, A, b, and c?

2.Give three feasible solutions to the linear program in (29.24)–(29.28). What is the objective value of each one?

with objective value 9.
with objective value 4.
with objective value −1.

3.For the slack form in (29.38)–(29.41), what are N, B, A, b, c, and v?

4.Convert the following linear program into standard form:

$\begin{array}{lrcrcrcrl} \text{minimize} & 2x_1 & + & 7x_2 & + & x_3 & & \\ \text{subject to} & \\ & x_1 & & & - & x_3 & = & 7 \\ & 3x_1 & + & x_2 & & & \ge & 24 \\ & & & x_2 & & & \ge & 0 \\ & & & & & x_3 & \le & 0 & . \end{array}$

5.Convert the following linear program into slack form:

What are the basic and nonbasic variables?

First, we will multiply the second and third inequalities by minus one to make it so that they are all inequalities. We will introduce the three new variables , and perform the usual procedure for rewriting in slack form

$\begin{array}{rcrcrcrcr} x_4 & = & 7 & - & x_1 & - & x_2 & + & x_3 \\ x_5 & = & -8 & + & 3x_1 & - & x_2 \\ x_6 & = & & - & x_1 & + & 2x_2 & + & 2x_3 \\ x_1, x_2, x_3, x_4, x_5, x_6 & \ge & 0 \end{array}$

where we are still trying to maximize . The basic variables are and the nonbasic variables are .

6.Show that the following linear program is infeasible:

By dividing the second constraint by 2 and adding to the first, we have 0≤−3, which is impossible. Therefore there linear program is unfeasible.

7.Show that the following linear program is unbounded:

$\begin{array}{lrcrcrl} \text{minimize} & x_1 & - & x_2 \\ \text{subject to} & \\ & -2x_1 & + & x_2 & \le & -1 \\ & -x_1 & - & 2x_2 & \le & -2 \\ & & x_1, x_2 & & \ge & 0 & . \end{array}$

8.Suppose that we have a general linear program with n variables and m constraints, and suppose that we convert it into standard form. Give an upper bound on the number of variables and constraints in the resulting linear program.

In the worst case, we have to introduce 2 variables for every variable to ensure that we have nonnegativity constraints, so the resulting program will have 2n variables. If each constraint is an equality, we would have to double the number of constraints to create inequalities, resulting in 2m constraints. Changing minimization to maximization and greater-than signs to less-than signs don't affect the number of variables or constraints, so the upper bound is 2n on variables and 2m on constraints.

9.Give an example of a linear program for which the feasible region is not bounded, but the optimal objective value is finite.

29.2 Formulating problems as linear programs

1.Put the single-pair shortest-path linear program from (29.44)–(29.46) into standard form.

The objective is already in normal form. However, some of the constraints are equality constraints instead of ≤ constraints. This means that we need to rewrite them as a pair of inequality constraints, the overlap of whose solutions is just the case where we have equality. we also need to deal with the fact that most of the variables can be negative. To do that, we will introduce variables for the negative part and positive part, each of which need be positive, and we'll just be sure to subtract the negative part. d_sds need not be changed in this way since it can never be negative since we are not assuming the existence of negative weight cycles.

2.Write out explicitly the linear program corresponding to finding the shortest path from node ss to node y in Figure 24.2(a).

3.In the single-source shortest-paths problem, we want to find the shortest-path weights from a source vertex s to all vertices v∈V. Given a graph G, write a linear program for which the solution has the property that is the shortest-path weight from s to v for each vertex $v \in V$ .

We will follow a similar idea to the way to when we were finding the shortest path between two particular vertices.

The first type of constraint makes sure that we never say that a vertex is further away than it would be if we just took the edge corresponding to that constraint. Also, since we are trying to maximize all of the variables, we will make it so that there is no slack anywhere, and so all the values will correspond to lengths of shortest paths to v. This is because the only thing holding back the variables is the information about relaxing along the edges, which is what determines shortest paths.

4.Write out explicitly the linear program corresponding to finding the maximum flow in Figure 26.1(a).

5.Rewrite the linear program for maximum flow (29.47)–(29.50) so that it uses only O(V+E) constraints.

6.Write a linear program that, given a bipartite graph G = (V, E) solves the maximum-bipartite-matching problem.

7.In the minimum-cost multicommodity-flow problem, we are given directed graph G=(V,E) in which each edge (u,v)∈E has a nonnegative capacityc(u,v)≥0 and a costa(u,v). As in the multicommodity-flow problem, we are given k different commodities, , where we specify commodity ii by the triple . We define the flow for commodity i and the aggregate flow on edge (u,v) as in the multicommodity-flow problem. A feasible flow is one in which the aggregate flow on each edge (u,v) is no more than the capacity of edge (u,v). The cost of a flow is, and the goal is to find the feasible flow of minimum cost. Express this problem as a linear program.

29.3 The simplex algorithm

1.Complete the proof of Lemma 29.4 by showing that it must be the case that c = c' and v = v' .

2.Show that the call to PIVOT in line 12 of SIMPLEX never decreases the value of v.

3.Prove that the slack form given to the PIVOT procedure and the slack form that the procedure returns are equivalent.

To show that the two slack forms are equivalent, we will show both that they have equal objective functions, and their sets of feasible solutions are equal.

First, we'll check that their sets of feasible solutions are equal. Basically all we do to the constraints when we pivot is take the non-basic variable, e, and solve the equation corresponding to the basic variable l for e. We are then taking that expression and replacing e in all the constraints with this expression we got by solving the equation corresponding to l. Since each of these algebraic operations are valid, the result of the sequence of them is also algebraically equivalent to the original.

Next, we'll see that the objective functions are equal. We decrease each by, which is to say that we replace the non-basic variable we are making basic with the expression we got it was equal to once we made it basic.

Since the slack form returned by PIVOT, has the same feasible region and an equal objective function, it is equivalent to the original slack form passed in.

4.Suppose we convert a linear program (A, b, c) in standard form to slack form. Show that the basic solution is feasible if and only if for .

5.Solve the following linear program using SIMPLEX:

6.Solve the following linear program using SIMPLEX:

$\begin{array}{lrcrcrl} \text{maximize} & 5x_1 & - & 3x_2 \\ \text{subject to} & \\ & x_1 & - & x_2 & \le & 1 \\ & 2x_1 & + & x_2 & \le & 2 \\ & & x_1, x_2 & & \ge & 0 & . \end{array}$

very nonbasic variable now has negative coefficient in the objective function, so we take the basic solution . The objective value this achieves is 5.

7.Solve the following linear program using SIMPLEX:

8.In the proof of Lemma 29.5, we argued that there are at most ways to choose a set B of basic variables. Give an example of a linear program in which there are strictly fewer than ways to choose the set B.

29.4 Duality

1.Formulate the dual of the linear program given in Exercise 29.3-5.

By just transposing A, swapping b and c, and switching the maximization to a minimization, we want to minimize subject to the constrain

2.Suppose that we have a linear program that is not in standard form. We could produce the dual by first converting it to standard form, and then taking the dual. It would be more convenient, however, to be able to produce the dual directly. Explain how we can directly take the dual of an arbitrary linear program.

By working through each aspect of putting a general linear program into standard form, as outlined on page 852, we can show how to deal with transforming each into the dual individually. If the problem is a minimization instead of a maximization, replace by in (29.84). If there is a lack of nonnegativity constraint on we duplicate the jth column of A, which corresponds to duplicating the jth row of . If there is an equality constraint for , we convert it to two inequalities by duplicating then negating the iith column of , duplicating then negating the ith entry of b, and adding an extra variable. We handle the greater-than-or-equal-to sign by negating iith column of and negating . Then we solve the dual problem of minimizing subject to and y≥0.

3.Write down the dual of the maximum-flow linear program, as given in lines (29.47)–(29.50) on page 860. Explain how to interpret this formulation as a minimum-cut problem.

4.Write down the dual of the minimum-cost-flow linear program, as given in lines(29.51)(29.52) on page 862. Explain how to interpret this problem in terms of graphs and flows.

5.Show that the dual of the dual of a linear program is the primal linear program.

6.Which result from Chapter 26 can be interpreted as weak duality for the maximum-flow problem?

Corollary 26.5 from Chapter 26 can be interpreted as weak duality.

29.5 The initial basic feasible solution

1.Give detailed pseudocode to implement lines 5 and 14 of INITIALIZE-SIMPLEX.

2.Show that when the main loop of SIMPLEX is run by INITIALIZE-SIMPLEX, it can never return "unbounded."

In order to enter line 10 of INITIALIZE-SIMPLEX and begin iterating the main loop of SIMPLEX, we must have recovered a basic solution which is feasible for $L_{aux}$ . Since and the objective function is , the objective value associated to this solution (or any solution) must be negative. Since the goal is to aximize, we have an upper bound of 0 on the objective value. By Lemma 29.2,SIMPLEX correctly determines whether or not the input linear program is unbounded. Since $L_{aux}$ is not unbounded, this can never be returned by SIMPLEX.

3.Suppose that we are given a linear program L in standard form, and suppose that for both L and the dual of L, the basic solutions associated with the initial slack forms are feasible. Show that the optimal objective value of L is =0.

Since it is in standard form, the objective function has no constant term, it is entirely given by , which is going to be zero for any basic solution. The same thing goes for its dual. Since there is some solution which has the objective function achieve the same value both for the dual and the primal, by the corollary to the weak duality theorem, that common value must be the optimal value of the objective function.

4.Suppose that we allow strict inequalities in a linear program. Show that in this case, the fundamental theorem of linear programming does not hold.

Consider the linear program in which we wish to maximize subject to the constraint and . This has no optimal solution, but it is clearly bounded and has feasible solutions. Thus, the Fundamental theorem of linear programming does not hold in the case of strict inequalities.

5.Solve the following linear program using SIMPLEX:

6.Solve the following linear program using SIMPLEX:

7.Solve the following linear program using SIMPLEX:

8.Solve the linear program given in (29.6)–(29.10).

9.Consider the following 1-variable linear program, which we call P:

One option is that r = 0,s≥0 and t≤0. Suppose that r>0, then, if we have that s is non-negative and tt is non-positive, it will be as we want.
We will split into two cases based on r. If r = 0, then this is exactly when tt is non-positive and s is non-negative. The other possible case is that r is negative, and t is positive. In which case, because r is negative, we can always get rx as small as we want so s doesn't matter, however, we can never make rx positive so it can never be ≥t.
Again, we split into two possible cases for r. If r=0, then it is when t is nonnegative and s is non-positive. The other possible case is that r is positive, and s is negative. Since r is positive, rx will always be non-negative, so it cannot be ≤s. But since r is positive, we have that we can always make rx as big as we want, in particular, greater than tt.
If we have that r=0 and t is positive and s is negative. If r is nonzero, then we can always either make rx really big or really small depending on the sign of r, meaning that either the primal or the dual would be feasable.

Problems

1.Linear-inequality feasibility

2.Complementary slackness

3.Integer linear programming

4.Farkas'ss lemma

5.Minimum-cost circulation

max_element()和min_element()函数及用法介绍藕粉和藕片数据结构 c++
头文件：algorithminta[]={1,4,7,2,8,9,3,5};1.max_element（first,last）作用：返回数组区间[first，last）中最大元素的位置用法：intt=max_element(a,a+8)-a;//注意要减去a本身的地址cout<
CSE101 C++ Introduction to Data Structures and Algorithms zhuyu0206girl c++开发语言
CSE101IntroductiontoDataStructuresandAlgorithmsProgrammingAssignment5Inthisprojectyouwillcreateanew,andsomewhatdifferentintegerListADT,thistimeinC++.YouwillusethisListtoperformshufflingoperations,andd
后量子签名：Hash-and-Sign（上篇）山登绝顶我为峰 3(^v^)3 #后量子密码学哈希算法算法密码学机器学习零知识证明
参考文献：[CT65]CooleyJW,TukeyJW.AnalgorithmforthemachinecalculationofcomplexFourierseries[J].Mathematicsofcomputation,1965,19(90):297-301[Babai86]BabaiL.OnLovász’latticereductionandthenearestlatticepointp
0101插入排序-算法基础-算法导论第三版 gaog2zh 数据结构和算法插入排序算法基础算法导论第三版
文章目录一插入排序二循环不变式与插入排序的正确性三伪代码中的一些约定四Java代码实现插入排序结语一插入排序输入：nnn个数订单一个序列(a1,a2,⋯ ,an)(a_1,a_2,\cdots,a_n)(a1,a2,⋯,an).**输出：**输入序列的一个排列(a1′,a2′,⋯ ,an′)(a^{'}_1,a^{'}_2,\cdots,a^{'}_n)(a1′,a2′,⋯,an′),满足a1′≤
【C++】贪心算法 Z_shsf c++c++贪心算法开发语言
贪心算法（GreedyAlgorithm）是一种基于贪心策略的算法，它在每一步选择中都采取当前状态下最优的选择，以希望最终得到全局最优解。贪心算法通常适用于满足最优子结构性质的问题，即问题的最优解可以通过其子问题的最优解来构造。贪心算法的基本思路是：定义问题的目标函数，即要最大化或最小化的目标。将问题分解为若干个子问题。对每个子问题进行求解，选择当前最优解。将每个子问题的最优解合并成原问题的解。贪
LTE Network Quality Analysis Method Based on MR Data and XGBoost Algorithm YZRuin 网络机器学习人工智能
原文链接：LTENetworkQualityAnalysisMethodBasedonMRDataandXGBoostAlgorithm|IEEEConferencePublication|IEEEXploreBasicInformation:Title:LTENetworkQualityAnalysisMethodBasedonMRDataandXGBoostAlgorithm(基于MR数据和X
vector--erase()安全删除指定元素八月的雨季最後的冰吻 stl 算法 c++stl
如何使用erase方法删除指定元素？algorithm头文件remove()和erase()一起使用代码：1remove方法介绍vectorvi={1,2,2,4};remove(vi.begin(),vi.end(),2);for(auto&i:vi)coutvi={1,2,2,4};vi.erase(remove(vi.begin(),vi.end(),2),vi.end());for(aut
【改进算法】【IHAOAVOA】天鹰优化算法和非洲秃鹫混合优化算法科研工作站智能算法算法智能算法天鹰优化算法非洲秃鹫算法
目录1主要内容IHAOAVOA流程图主要创新点2部分代码3程序结果4下载链接1主要内容该程序复现《IHAOAVOA:AnimprovedhybridaquilaoptimizerandAfricanvulturesoptimizationalgorithmforglobaloptimizationproblems》，天鹰优化算法（AO）和非洲秃鹫算法（AVOA）各有优势：AO具有强大的全局勘探能力
不错链接整理 xushuanglu_csdn 提升学习开源
不错链接整理算法https://github.com/MisterBooo/LeetCodeAnimation手把手撕LeetCode题目，扒各种算法套路的裤子https://github.com/labuladong/fucking-algorithm算法学习笔记https://github.com/nonstriater/Learn-Algorithms常用数据结构及其算法的Java实现，包括
学算法要读《算法导论》吗？方圆想当图灵算法
大家好，我是方圆。这篇文章是我学习算法的心得，希望它能够给一些将要学习算法且准备要读大部头算法书籍的朋友一些参考，节省一些时间，也为了给经典的“黑皮书”祛魅，我觉得这些书籍在大部分互联网从业者心中已经不再是进步的阶梯，而是恐惧的阴影了，因为当一些学习路线中列出这些书目时，评论区多是调侃少是交流和讨论。在这之前我也这些书抱有读起来很困难的看法，但是在我参考过《算法导论》之后，我觉得它更像是一杯“鸡尾
蛙跳算法例子依然风yrlf 算法 python
蛙跳算法（JumpingFrogAlgorithm，简称JFA）是一种仿生优化算法，模拟了青蛙在搜索食物时的跳跃行为。该算法通过模拟青蛙的跳跃过程来寻找最优解，适用于连续优化、离散优化和多目标优化等问题。下面是一个详细的蛙跳算法示例，用于解决一维连续优化问题：importnumpyasnp#定义目标函数defobjective_function(x):return(x-2)**2-1#定义蛙跳算法
贪心算法的介绍依然风yrlf 贪心算法算法
贪婪算法（GreedyAlgorithm）是一种基于贪心策略的优化算法，通常用于在组合优化问题中找到最优解。贪婪算法的基本思想是在每一步选择中都采取当前状态下最优的选择，希望通过局部最优解的积累来达到全局最优解。尽管贪婪算法不能保证总是找到最优解，但它通常能够在很短的时间内找到一个接近最优解的解决方案。贪婪算法的详细介绍和讲解：基本思想：贪婪算法的基本思想是通过每一步的局部最优选择来构建问题的解决
【机器学习】多元线性回归 Mount256 #机器学习机器学习线性回归人工智能
文章目录多元线性回归模型（multipleregressionmodel）损失/代价函数（costfunction）——均方误差（meansquarederror）批量梯度下降算法（batchgradientdescentalgorithm）特征工程（featureengineering）特征缩放（featurescaling）正则化线性回归（regularizationlinearregress
Leo赠书活动-16期名校毕业生教材 LeoToJavaer CSDN送书活动送书福利
Leo赠书活动-16期名校毕业生教材✅作者简介：大家好，我是Leo，热爱Java后端开发者，一个想要与大家共同进步的男人个人主页：Leo的博客当前专栏：赠书活动专栏✨特色专栏：MySQL学习本文内容：Leo赠书活动-16期名校毕业生教材个人知识库：Leo知识库，欢迎大家访问目录Leo赠书活动-16期名校毕业生教材1.《深入理解计算机系统》2.《算法导论》3.《计算机程序的构造和解释》4.《数据库系
ConcurrentHashMap多线程下比HashTable效率更高 z.jiaminf java 开发语言
HashTable使用一把锁处理并发问题，当有多个线程访问时，需要多个线程竞争一把锁，导致阻塞ConcurrentHashMap则使用分段，相当于把一个HashMap分成多个，然后每个部分分配一把锁，这样就可以支持多线程访问术语定义术语英文解释哈希算法hashalgorithm是一种将任意内容的输入转换成相同长度输出的加密方式，其输出被称为哈希值。哈希表hashtable根据设定的哈希函数H(ke
10 中科院1区期刊优化算法|基于开普勒优化-卷积-双向长短期记忆网络-注意力时序预测Matlab程序KOA-CNN-BiLSTM-Attention 机器不会学习CSJ 时间序列预测算法网络 matlab cnn lstm 深度学习
文章目录一、开普勒优化算法二、CNN卷积神经网络三、BiLSTM双向长短期记忆网络四、注意力机制五、KOA-CNN-BiLSTM-Attention时间序列数据预测模型六、获取方式一、开普勒优化算法基于物理学定律的启发，开普勒优化算法（KeplerOptimizationAlgorithm，KOA）是一种元启发式算法，灵感来源于开普勒的行星运动规律。该算法模拟行星在不同时间的位置和速度，每个行星代
06基于WOA-CNN-BiLSTM-Attention鲸鱼优化-卷积-双向长短时记忆-注意力机制的数据分类算法机器不会学习CSJ 数据分类专栏 cnn 分类深度学习 lstm matlab 启发式算法数据分析
基于WOA-CNN-BiLSTM-Attention鲸鱼优化-卷积-双向长短时记忆-注意力机制的数据分类算法鲸鱼智能优化基本原理鲸鱼智能优化算法（WhaleOptimizationAlgorithm，WOA）是一种基于自然界中的鲸鱼群体行为而提出的全局优化算法。该算法由莫扬（SeyedaliMirjalili）于2016年提出，其灵感来源于鲸鱼群体的捕猎行为和社交行为。在WOA算法中，每个解都被看
07基于WOA-CNN-BiLSTM-Attention鲸鱼优化-卷积-双向长短时记忆-注意力机制的时间序列预测算法机器不会学习CSJ 时间序列预测 cnn 算法人工智能
文章目录鲸鱼优化算法CNN卷积神经网络BiLSTM双向长短期记忆网络Attention注意力机制WOA-CNN-BiLSTM-Attention鲸鱼优化-卷积-双向长短时记忆-注意力机制数据展示代码程序实验结果获取方式鲸鱼优化算法鲸鱼优化算法（WhaleOptimizationAlgorithm，WOA）是一种启发式优化算法，灵感来源于座头鲸的捕食行为。该算法最早由SeyedaliMirjalil
基于WOA优化CNN-LSTM-Attention的回归或时序算法，包含多种CNN-LSTM算法进行对比|Matlab 机器不会学习CSJ 算法深度学习
01基于WOA优化CNN-LSTM-Attention的回归或时序算法，包含多种CNN-LSTM算法进行对比|Matlab基础知识：基于WOA-CNN-LSTM-Attention的数据回归算法是一种利用深度学习技术来进行数据回归分析的方法。它结合了WOA（WhaleOptimizationAlgorithm）、CNN（ConvolutionalNeuralNetwork）、LSTM（LongSh
算法——图论——最短路径——Floyd / 传递闭包戏拈秃笔数据结构与算法（java版）算法
目录Floyd-Warshall（弗洛伊德）算法传递闭包一、试题算法训练盾神与离散老师2Floyd-Warshall（弗洛伊德）算法求所有顶点到所有顶点的最短路径问题弗洛伊德算法（Floyd-Warshallalgorithm）是一种用于寻找图中所有顶点对之间最短路径的动态规划算法。该算法可以处理带有负权边但不含负权环的加权有向图或无向图。弗洛伊德算法的核心思想是利用三重循环遍历所有顶点，逐步更新
查看文件的md5值 chen_znn Linux系统 linux macos windows md5
MD5的定义MD5（MessageDigestAlgorithm5）是一种常用的哈希函数算法，用于生成数据的唯一标识。它接受任意长度的输入数据，并将其转换为固定长度的哈希值（通常为128位），该哈希值被称为MD5值。MD5算法经常用于验证数据的完整性和一致性。当两个文件的MD5值相同时，可以非常高的概率认为这两个文件是相同的。即使文件只有微小的改动，其生成的MD5值也会有较大的差异。查看文件的MD
让vscode使用Pipenv工作环境 yeshan333 Python
1、查看Pipenv的位置#先激活Pipenv环境pipenvshell#获取当前虚拟环境的位置pipenv--venv2、打开setting.json配置文件Ctrl+Shift+P，输入settings，选择OpenSettings(JSon)将之前得到的Pipenv环境路径添加进去“python.venvPath”:“C:\Users\Algorithm\.virtualenvs”3、重启v
龟兔赛跑算法码农一指 ACWING每日一题算法
一、题目给定一个长度为n+1的数组nums，数组中所有的数均在1∼n1的范围内，其中n≥1。请找出数组中任意一个重复的数。样例给定nums=[2,3,5,4,3,2,6,7]。返回2或3。二、解析解决这个问题的一种有效方法是使用快慢指针，也称为龟兔赛跑算法（Floyd'sCycleDetectionAlgorithm）。该算法的基本思想是在一个循环链表中，快指针和慢指针分别以不同的速度移动，如果存
Point.java spencer_tseng java java
Point.javapackagealgorithm_graphics_2;/**Copyright(c)1995,2008,Oracleand/oritsaffiliates.Allrightsreserved.*ORACLEPROPRIETARY/CONFIDENTIAL.Useissubjecttolicenseterms.*********************///packagejav
《STL源码剖析》---stl_iterator.h阅读笔记 KangRoger STL stl c++迭代器 iterator
STL设计的中心思想是将容器（container）和算法（algorithm）分开，迭代器是容器（container）和算法（algorithm）之间的桥梁。迭代器可以如下定义：提供一种方法，能够依序寻访某个容器内的所有元素，而又无需暴露该容器的内部表达方式。在阅读代码之前，要先了解一个新概念：Traits编程技法templatestructMyIter{typedefTvalue_type//内
Programming Abstractions in C阅读笔记：p283-p292 c
《ProgrammingAbstractionsinC》学习第72天，p283-p292总结，总计10页。一、技术总结1、anylasisofalgorithms算法分析——即判断程序的效率(efficiency)。2、mathematicalinduction(数学归纳法)3、Big-Onotation(大O标记法)4、constanttime(常量时间)5、lineartime(线性时间)p2
react的different算法光影少年 react.js 前端前端框架
React中的差异算法，也称为协调算法（ReconciliationAlgorithm），是用于比较新旧虚拟DOM树并确定最小更新集合的一种策略。React的协调算法基于两个主要原则：1.**相同类型的组件生成相似的树形结构：**如果两个组件类型相同，则它们产生相似的树形结构。React会假设相同类型的组件在不同渲染周期中生成的虚拟DOM结构是类似的。2.**不同类型的组件会生成不同的树形结构：*
算法竞赛常用的库函数 lijiachang030718 算法算法
目录引言万能头文件一、iostream二、algorithm1.sort2.next_permutation2.unique三、string1.substr2.stoi四、cmath1.log类2.取整五、climits、cfloat六、cctype七、numeric1.accmulate引言这个竞赛中的一些库还是非常的好用，可以节省代码量和时间，而且在项目和工作面试中知道一些常用的算法还是比较有
深度学习-图解反向传播算法 AI_王布斯深度学习算法神经网络深度学习
什么是正向传播网络？前一层的输出作为后一层的输入的逻辑结构，每一层神经元仅与下一层的神经元全连接，通过增加神经网络的层数虽然可为其提供更大的灵活性，让网络具有更强的表征能力，也就是说，能解决的问题更多，但随之而来的数量庞大的网络参数的训练，一直是制约多层神经网络发展的一个重要瓶颈。什么是反向传播？反向传播（Backpropagationalgorithm）全称“误差反向传播”，是在深度神经网络中，
世界顶级名校计算机专业，都在用哪些书当教材？(文末送书) 小尘要自信 java 开发语言数据库算法赠书计算机组成
目录01《深入理解计算机系统》02《算法导论》03《计算机程序的构造和解释》04《数据库系统概念》05《计算机组成与设计：硬件/软件接口》06《离散数学及其应用》07《组合数学》08《斯坦福算法博弈论二十讲》参与规则清华、北大、MIT、CMU、斯坦福的学霸们在新学期里要学什么？今天我们来盘点一下那些世界名校计算机专业采用的教材。01《深入理解计算机系统》原书第3版）作者：兰德尔E.布莱恩特大卫R.
jQuery 跨域访问的三种方式 No 'Access-Control-Allow-Origin' header is present on the reque qiaolevip 每天进步一点点学习永无止境跨域众观千象
XMLHttpRequest cannot load http://v.xxx.com. No 'Access-Control-Allow-Origin' header is present on the requested resource. Origin 'http://localhost:63342' is therefore not allowed access. test.html:1
mysql 分区查询优化 annan211 java 分区优化 mysql
分区查询优化引入分区可以给查询带来一定的优势，但同时也会引入一些bug. 分区最大的优点就是优化器可以根据分区函数来过滤掉一些分区，通过分区过滤可以让查询扫描更少的数据。所以，对于访问分区表来说，很重要的一点是要在where 条件中带入分区，让优化器过滤掉无需访问的分区。可以通过查看explain执行计划，是否携带 partitions
MYSQL存储过程中使用游标 chicony Mysql存储过程
DELIMITER $$ DROP PROCEDURE IF EXISTS getUserInfo $$ CREATE PROCEDURE getUserInfo(in date_day datetime)-- -- 实例-- 存储过程名为：getUserInfo-- 参数为：date_day日期格式:2008-03-08-- BEGINdecla
mysql 和 sqlite 区别 Array_06 sqlite
转载： http://www.cnblogs.com/ygm900/p/3460663.html mysql 和 sqlite 区别 SQLITE是单机数据库。功能简约，小型化，追求最大磁盘效率 MYSQL是完善的服务器数据库。功能全面，综合化，追求最大并发效率 MYSQL、Sybase、Oracle等这些都是试用于服务器数据量大功能多需要安装，例如网站访问量比较大的。而sq
pinyin4j使用 oloz pinyin4j
首先需要pinyin4j的jar包支持；jar包已上传至附件内方法一:把汉字转换为拼音；例如：编程转换后则为biancheng /** * 将汉字转换为全拼 * @param src 你的需要转换的汉字 * @param isUPPERCASE 是否转换为大写的拼音； true:转换为大写；fal
微博发送私信随意而生微博
在前面文章中说了如和获取登陆时候所需要的cookie，现在只要拿到最后登陆所需要的cookie，然后抓包分析一下微博私信发送界面 http://weibo.com/message/history?uid=****&name=**** 可以发现其发送提交的Post请求和其中的数据，让后用程序模拟发送POST请求中的数据，带着cookie发送到私信的接入口，就可以实现发私信的功能了。
jsp 香水浓 jsp
JSP初始化容器载入JSP文件后，它会在为请求提供任何服务前调用jspInit()方法。如果您需要执行自定义的JSP初始化任务，复写jspInit()方法就行了 JSP执行这一阶段描述了JSP生命周期中一切与请求相关的交互行为，直到被销毁。当JSP网页完成初始化后
在 Windows 上安装 SVN Subversion 服务端 AdyZhang SVN
在 Windows 上安装 SVN Subversion 服务端2009-09-16高宏伟哈尔滨市道里区通达街291号最佳阅读效果请访问原地址：http://blog.donews.com/dukejoe/archive/2009/09/16/1560917.aspx 现在的Subversion已经足够稳定，而且已经进入了它的黄金时段。我们看到大量的项目都在使
android开发中如何使用 alertDialog从listView中删除数据？ aijuans android
我现在使用listView展示了很多的配置信息，我现在想在点击其中一条的时候填出 alertDialog,点击确认后就删除该条数据，（ ArrayAdapter ，ArrayList，listView 全部删除），我知道在下面的onItemLongClick 方法中参数 arg2 是选中的序号，但是我不知道如何继续处理下去 1 2 3
jdk-6u26-linux-x64.bin 安装 baalwolf linux
1.上传安装文件(jdk-6u26-linux-x64.bin) 2.修改权限 [root@localhost ~]# ls -l /usr/local/jdk-6u26-linux-x64.bin 3.执行安装文件 [root@localhost ~]# cd /usr/local [root@localhost local]# ./jdk-6u26-linux-x64.bin&nbs
MongoDB经典面试题集锦 BigBird2012 mongodb
1.什么是NoSQL数据库？NoSQL和RDBMS有什么区别？在哪些情况下使用和不使用NoSQL数据库？ NoSQL是非关系型数据库，NoSQL = Not Only SQL。关系型数据库采用的结构化的数据，NoSQL采用的是键值对的方式存储数据。在处理非结构化/半结构化的大数据时；在水平方向上进行扩展时；随时应对动态增加的数据项时可以优先考虑使用NoSQL数据库。在考虑数据库的成熟
JavaScript异步编程Promise模式的6个特性 bijian1013 JavaScript Promise
Promise是一个非常有价值的构造器，能够帮助你避免使用镶套匿名方法，而使用更具有可读性的方式组装异步代码。这里我们将介绍6个最简单的特性。在我们开始正式介绍之前，我们想看看Javascript Promise的样子： var p = new Promise(function(r
[Zookeeper学习笔记之八]Zookeeper源代码分析之Zookeeper.ZKWatchManager bit1129 zookeeper
ClientWatchManager接口 //接口的唯一方法materialize用于确定那些Watcher需要被通知 //确定Watcher需要三方面的因素1.事件状态 2.事件类型 3.znode的path public interface ClientWatchManager { /** * Return a set of watchers that should
【Scala十五】Scala核心九：隐式转换之二 bit1129 scala
隐式转换存在的必要性，在Java Swing中，按钮点击事件的处理，转换为Scala的的写法如下： val button = new JButton button.addActionListener( new ActionListener { def actionPerformed(event: ActionEvent) {
Android JSON数据的解析与封装小Demo ronin47
转自：http://www.open-open.com/lib/view/open1420529336406.html package com.example.jsondemo; import org.json.JSONArray; import org.json.JSONException; import org.json.JSONObject; impor
[设计]字体创意设计方法谈 brotherlamp UI ui自学 ui视频 ui教程 ui资料
从古至今，文字在我们的生活中是必不可少的事物，我们不能想象没有文字的世界将会是怎样。在平面设计中，UI设计师在文字上所花的心思和功夫最多，因为文字能直观地表达UI设计师所的意念。在文字上的创造设计，直接反映出平面作品的主题。如设计一幅戴尔笔记本电脑的广告海报，假设海报上没有出现“戴尔”两个文字，即使放上所有戴尔笔记本电脑的图片都不能让人们得知这些电脑是什么品牌。只要写上“戴尔笔
单调队列-用一个长度为k的窗在整数数列上移动，求窗里面所包含的数的最大值 bylijinnan java 算法面试题
import java.util.LinkedList; /* 单调队列滑动窗口单调队列是这样的一个队列：队列里面的元素是有序的，是递增或者递减题目：给定一个长度为N的整数数列a(i),i=0,1,...,N-1和窗长度k. 要求：f(i) = max{a(i-k+1),a(i-k+2),..., a(i)},i = 0,1,...,N-1 问题的另一种描述就
struts2处理一个form多个submit chiangfai struts2
web应用中，为完成不同工作，一个jsp的form标签可能有多个submit。如下代码： <s:form action="submit" method="post" namespace="/my"> <s:textfield name="msg" label="叙述：">
shell查找上个月，陷阱及野路子 chenchao051 shell
date -d "-1 month" +%F 以上这段代码，假如在2012/10/31执行，结果并不会出现你预计的9月份，而是会出现八月份，原因是10月份有31天，9月份30天，所以-1 month在10月份看来要减去31天，所以直接到了8月31日这天，这不靠谱。野路子解决：假设当天日期大于15号
mysql导出数据中文乱码问题 daizj mysql 中文乱码导数据
解决mysql导入导出数据乱码问题方法：１、进入mysql，通过如下命令查看数据库编码方式： mysql> show variables like 'character_set_%'; +--------------------------+----------------------------------------+ | Variable_name&nbs
SAE部署Smarty出现：Uncaught exception 'SmartyException' with message 'unable to write dcj3sjt126com PHP smarty sae
对于SAE出现的问题：Uncaught exception 'SmartyException' with message 'unable to write file...。官方给出了详细的FAQ：http://sae.sina.com.cn/?m=faqs&catId=11#show_213 解决方案为： 01 $path
《教父》系列台词 dcj3sjt126com
Your love is also your weak point. 你的所爱同时也是你的弱点。 If anything in this life is certain, if history has taught us anything, it is that you can kill anyone. 不顾家的人永远不可能成为一个真正的男人。 &
mongodb安装与使用 dyy_gusi mongo
一.MongoDB安装和启动,widndows和linux基本相同 1.下载数据库, linux:mongodb-linux-x86_64-ubuntu1404-3.0.3.tgz 2.解压文件,并且放置到合适的位置 tar -vxf mongodb-linux-x86_64-ubun
Git排除目录 geeksun git
在Git的版本控制中，可能有些文件是不需要加入控制的，那我们在提交代码时就需要忽略这些文件，下面讲讲应该怎么给Git配置一些忽略规则。有三种方法可以忽略掉这些文件，这三种方法都能达到目的，只不过适用情景不一样。 1. 针对单一工程排除文件这种方式会让这个工程的所有修改者在克隆代码的同时，也能克隆到过滤规则，而不用自己再写一份，这就能保证所有修改者应用的都是同一
Ubuntu 创建开机自启动脚本的方法 hongtoushizi ubuntu
转载自： http://rongjih.blog.163.com/blog/static/33574461201111504843245/ Ubuntu 创建开机自启动脚本的步骤如下： 1) 将你的启动脚本复制到 /etc/init.d目录下以下假设你的脚本文件名为 test。 2) 设置脚本文件的权限 $ sudo chmod 755
第八章流量复制/AB测试/协程 jinnianshilongnian nginx lua coroutine
流量复制在实际开发中经常涉及到项目的升级，而该升级不能简单的上线就完事了，需要验证该升级是否兼容老的上线，因此可能需要并行运行两个项目一段时间进行数据比对和校验，待没问题后再进行上线。这其实就需要进行流量复制，把流量复制到其他服务器上，一种方式是使用如tcpcopy引流；另外我们还可以使用nginx的HttpLuaModule模块中的ngx.location.capture_multi进行并发
电商系统商品表设计 lkl
DROP TABLE IF EXISTS `category`; -- 类目表 /*!40101 SET @saved_cs_client = @@character_set_client */; /*!40101 SET character_set_client = utf8 */; CREATE TABLE `category` ( `id` int(11) NOT NUL
修改phpMyAdmin导入SQL文件的大小限制 pda158 sql mysql
　用phpMyAdmin导入mysql数据库时，我的10M的数据库不能导入，提示mysql数据库最大只能导入2M。　　 phpMyAdmin数据库导入出错：　　You probably tried to upload too large file. Please refer to documentation for ways to workaround this limit.
Tomcat性能调优方案 Sobfist apache jvm tomcat 应用服务器
一、操作系统调优对于操作系统优化来说，是尽可能的增大可使用的内存容量、提高CPU的频率，保证文件系统的读写速率等。经过压力测试验证，在并发连接很多的情况下，CPU的处理能力越强，系统运行速度越快。。【适用场景】任何项目。二、Java虚拟机调优应该选择SUN的JVM，在满足项目需要的前提下，尽量选用版本较高的JVM，一般来说高版本产品在速度和效率上比低版本会有改进。 J
SQLServer学习笔记 vipbooks 数据结构 xml
1、create database school 创建数据库school 2、drop database school 删除数据库school 3、use school 连接到school数据库，使其成为当前数据库 4、create table class(classID int primary key identity not null) 创建一个名为class的表，其有一

算法导论第三版 第29章习题答案