The P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every problem whose solution can be quickly verified can also be quickly solved.

P vs. NP 是一个遗留未解决的计算机科学的重要问题，也是算法领域的重要问题。 下面分成几个部分为大家介绍这个问题： 什么是算法？ 算法就是一系列描述好的计算过程。 比如曹冲称象： 有了计算机后，算法本质没有变化，我们将计算步骤编码，变成了计算机程序执行的序列。 算法构成了计算机解决问题的基本单元，每个算法的执行都需要时间和空间。 通常的，输入规模越大，往往需要的时间和空间越多。 比如要统计一个电商网站的流量，数据量越大，需要的时间越多。 考 …

2024年10月2日 · NP类问题是指那些 可以在多项式时间内验证解是否正确，但我们不确定是否能在多项式时间内找到解的问题。 换句话说， NP问题 的一个解可以在多项式时间内验证，但不一定能在多项式时间内找到该解。 旅行商问题（TSP）：给定一组城市和它们之间的距离，找到一条经过每个城市一次的最短路径。 对于这个问题，找到最优解非常困难且耗时，但如果给出一个候选解（路径），可以在多项式时间内验证它是否是最短路径。 子集和问题：给定一个整数集合， …

算法：P=NP或理论上等效，例如NP的快速概率算法(fast Probilistic algorithm) 启发式：NP问题在最坏的情况下很难求解，但平均来说还是可以得到求解的

The importance of the P vs NP question stems from the successful theories of NP-completeness and complexity-based cryptography, as well as the potentially stunning practical consequences of a constructive proof of P = NP.

2023年5月4日 · p与np的定义. 由此我们引出了 \(p\) 问题的定义，所有能用多项式时间算法计算得到结果的问题，称为多项式问题。 而 \(np\) 的定义，如果你只是如字面上看起来那样去理解，指不能用多项式时间算法计算得到结果的问题，那就大错特错了

If \(\mathbf{P}=\mathbf{NP}\) then we can solve all \(\mathbf{NP}\) search and optimization problems in polynomial time. But can we do more? It turns out that the answer is that Yes we can! An \(\mathbf{NP}\) decision problem can be thought of as the task of deciding, given some string \(x\in \{0,1\}^*\) the truth of a statement of the form

2023年3月2日 · We proposed a method to settle the P vs. NP problem by solving an np-complete problem, namely the maximum independent set problem. Our technique transforms any graph into a perfect graph such that the source graph maximum independent set is either twice in size the maximum independent set of the transformed graph or twice in size the second ...

The P vs NP problem is the most famous open problem in Computer Science (specifically in ComputationalComplexityTheory), and one of the most famous outstanding problems in mathematics in general.

NP could radically change their relative power, and so any resolutions of the P vs. NP question (with either outcome!) must involve techniques that were sensitive to such changes. The major signi cance of the observation was that diagonalization, a technique that had been used to great