考虑对于确定的排列$\{p_{i}\}$,如何求出其(交换后)会得到的排列-- 令$cnt_{x}$为在$i$之前比$x$大的元素个数(其中$p_{i}=x$),显然排列合法当且仅当$cnt_{i}\le k$ 注意到每一次交换至多只有初始靠后的元素$cnt_{i}$减小1,因此交换次数至少为$\sum_{i=1}^{n}\max(cnt_{i}-k,0)$ (这里可以简单分析一下交换对$cnt_{i}$的影响,方便理解) 另一方面,取$x=\min_{cnt_{i}>k}i$和$p_{i}=x…

What is Branch Prediction? Consider a railroad junction: Image by Mecanismo, via Wikimedia Commons. Used under the CC-By-SA 3.0 license. Now for the sake of argument, suppose this is back in the 1800s - before long distance or radio communication. Yo…

Given two sorted integer arrays nums1 and nums2, merge nums2 into nums1 as one sorted array. Note:You may assume that nums1 has enough space (size that is greater or equal to m + n) to hold additional elements from nums2. The number of elements initi…

The last post is mainly about the unsorted set,in this post I will show you the sorted set playing an important role in Redis.There are many command added after the version 2.8.9.OK,let's see the below picture firstly.There are 24 commands to handle…

问题: There are two sorted arrays nums1 and nums2 of size m and n respectively.Find the median of the two sorted arrays. The overall run time complexity should be O(log (m+n)). Example1:nums1 = [1, 3]nums2 = [2]The median is 2.0Example2:nums1 = [1, 2]n…

Sept. 22, 2015 学一道算法题, 经常回顾一下. 第二次重温, 决定增加一些图片, 帮助自己记忆. 在网上找他人的资料, 不如自己动手. 把从底向上树的算法搞通俗一些. 先做一个例子: 9/22/2015 Go over one example to build some muscle memory about this bottom up, O(1) solution to find the root node in subtree function. Sorted List: 1…

Given a n x n matrix where each of the rows and columns are sorted in ascending order, find the kth smallest element in the matrix. Note that it is the kth smallest element in the sorted order, not the kth distinct element. Example: matrix = [ [ 1, 5…

Given an array of integers that is already sorted in ascending order, find two numbers such that they add up to a specific target number.The function twoSum should return indices of the two numbers such that they add up to the target, where index1 mu…

Follow up for "Find Minimum in Rotated Sorted Array":What if duplicates are allowed? Would this affect the run-time complexity? How and why? Suppose a sorted array is rotated at some pivot unknown to you beforehand. (i.e., 0 1 2 4 5 6 7 might be…

Suppose a sorted array is rotated at some pivot unknown to you beforehand. (i.e., 0 1 2 4 5 6 7 might become 4 5 6 7 0 1 2). Find the minimum element. You may assume no duplicate exists in the array. 这道寻找旋转有序数组的最小值肯定不能通过直接遍历整个数组来寻找,这个方法过于简单粗暴,这样的话,旋不…