题意 给出一个\(n*m\)的\(0,1\)矩阵,若一个矩阵中的所有元素都相同,则这个矩阵的代价为\(0\),如果不是则选择一种将它分成两个子矩阵的方案,代价为所有方案中(两个子矩阵的代价的较大值+\(1\))的最小值. \(n,m \leq 185\) 传送门 思路 \(dp[ i ][ j ][ k ][ l ]\) 表示左上角是 $( i , j ) $ .右下角是 $ ( k , l ) $的矩阵的最小代价,四维扛不住. 因为如果每次从中间分,\(log(n)+log(m)\)次就变成\…

收录一些比较冷门的 DP 优化方法. 1. 树上依赖性背包 树上依赖性背包形如在树上选出若干个物品做背包问题,满足这些物品连通.由于 01 背包,多重背包和完全背包均可以在 \(\mathcal{O}(V)\) 的时间内加入一个物品,\(\mathcal{O}(V ^ 2)\) 的时间内合并两个背包,所以不妨设背包类型为多重背包. 先考虑一个弱化版问题.给定一棵有根树,若一个节点被选,则它的父亲必须被选. 显然存在一个 \(\mathcal{O}(nV ^ 2)\) 的树形 DP 做法,它能求出…

Instant Complexity Time Limit: 1000MS Memory Limit: 10000K Description Analyzing the run-time complexity of algorithms is an important tool for designing efficient programs that solve a problem. An algorithm that runs in linear time is usually much f…

Runtime Complexity of .NET Generic Collection   I had to implement some data structures for my computational geometry class. Deciding whether to implement the data structures myself or using the build-in classes turned out to be a hard decision, as t…

O(1):constant - the operation doesn't depend on the size of its input, e.g. adding a node to the tail of a linked list where we always maintain a pointer to the tail node.int i=0;i++;++i;i+=6; O(n):linear - the run time complexity is proportionate to…

这一章比较短! 空间复杂度(space complexity)和辅助空间(auxiliary space)经常混用,下面是正确的辅助空间和空间复杂度的定义 辅助空间:算法需要用到的额外或者暂时的存储空间. 空间复杂度:是指算法所需要的所有存储空间,这是跟输入数据的大小决定的.空间复杂度包括辅助空间和保存输入的存储空间. 如果我们想比较几个标准的排序算法所需要的空间,那么用辅助空间来分析会比空间复杂度好.归并排序用了O(n)的辅助空间.而插入排序和堆排序用的O(1)的辅助空间.但是他们这些算法的空…

Instant Complexity Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 20000/10000K (Java/Other) Total Submission(s) : 8   Accepted Submission(s) : 7 Problem Description Analyzing the run-time complexity of algorithms is an important tool for desi…

THE ARCHITECTURE OF COMPLEXITY HERBERT A. SIMON* Professor of Administration, Carnegie Institute of Technology (Read April 26, 1962)…

T(n)=aT(n/b)+f(n); where we can interpret n/b to mean either floor(b/n) or ceil(b/n), Then T (n) has the following asymptotic bounds: 1. If f (n)= O(nlogb a-c) for some constant c> 0, then T (n)=Θ(nlogb a)2.If f (n)= Θ(nlogb a), then T (n)=Θ(nlogb a…

The Brain vs Deep Learning Part I: Computational Complexity — Or Why the Singularity Is Nowhere Near July 27, 2015July 27, 2015 Tim Dettmers Deep Learning, NeuroscienceDeep Learning, dendritic spikes, high performance computing, neuroscience, singula…