前者是长为 nn 的Fk2F2k 向量序列秩为 kk 的方案数,行秩等于列秩所以转置一下就是 kk 个Fn2F2n 两两线性无关的方案数,是 ∏k−1i=0(2n−2i)∏i=0k−1(2n−2i)。后者就是 ∏ki=12ai−(i−1)∏i=1k2ai−(i−1)。 先把常数 ∏k−1i=0(2n−2i)2−(k2)∏i=0k...
「ARC 139F」Many Xor Optimization Problems 对于一个长为nn的序列aa,我们记f(a)f(a)表示从aa中选取若干数,可以得到的最大异或值。 现在给定n,mn,m,你需要对于所有长为nn,且0≤ai<2m0≤ai<2m的序列,计算f(a)f(a)的和。 1≤n,m≤2500001≤n,m≤250000。 PS:本题解的做法可以做到n=109,m=107...
Sometimes people sprinkle “asserts” in their code because they think something is true, and they want to get data about whether it really is or not. Maybe they’re considering some change to enforce it via contract, or maybe they want to make an optimization based...
Sometimes people sprinkle “asserts” in their code because they think something is true, and they want to get data about whether it really is or not. Maybe they’re considering some change to enforce it via contract, or maybe they want to make an optimization based...
引理. 长为nn 的Fk2F2k 向量序列生成的线性空间即为 Fk2F2k 的方案数为 ∏k−1i=0(2n−2i)∏i=0k−1(2n−2i)。 转置一下即为长为 kk 的Fn2F2n 向量序列线性无关的方案数。 所以枚举线性子空间的秩 kk,为了求出最大元素我们还需要枚举主元,设其从低到高分别为 a1,⋯,aka1,⋯,ak...
2.1. Many-Objective Optimization Multi-objective optimization [20,21,22,23] falls into the field of multiple criteria decision-making. It optimizes all goals at the same time to get the optimal solution. Therefore, multi-objective optimization problems (MOPs) get a set of solutions. Generally,...