coursera algorithms

Algorithms-Meanings of mathematical terms and mathematical terms in discrete mathematics, and answers to discrete mathematics and Algorithms Here we will introduce two important functions in discrete mathematics: The base function and the top function. Make x a real number. The base function rounds x to an integer smaller than or equal to x and closest to x, while the top function rounds x to an integer gr

Quick sorting (Quick sort)Start by selecting one of the data (usually the first number of the array) as the key data, and then putting all the smaller numbers in front of it, all the larger numbers are placed behind it, this process is called a quick sort.The array is split into two arrays and then the remaining two arrays are sorted, so the loop is done until one element is left.Import Time,randomimport copydef Cal_time (func): #该装饰器用来测量函数运行的时间 def wrapper (*args,**kwargs): T1 = Tim E.time () r

15 is:27-15=12 (15>12) 15-12=3 (12>3)12-3=9 (9>3) 9-3=6 (6>3)6-3=3 (3==3)Therefore, 3 is the greatest common divisor#include ⑶ Poor Lifting methodThere are two integers a and B:①i=1② If a, B can be divisible by I at the same time, then t=i③i++④ If I ⑤ If i > A (or b), then T is greatest common divisor, endingImproved:①i= A (or b)② If a, B can be divisible by I at the same time, then I is greatest common divisor,End③i--, go back and run ②.There are two integers a and B:①i=1② If a, B can be divis

System;Namespace Shellsorter{public class Shellsorter{public void Sort (int [] list){INT Inc;For (inc=1;incfor (; inc>0;inc/=3){for (int i=inc+1;i{int t=list[i-1];int j=i;while ((J>inc) (list[j-inc-1]>t)){LIST[J-1]=LIST[J-INC-1];J-=inc;}list[j-1]=t;}}}}public class MainClass{public static void Main (){Int[] Iarrary=new int[]{1,5,13,6,10,55,99,2,87,12,34,75,33,47};Shellsorter sh=new Shellsorter ();Sh. Sort (iarrary);for (int m=0;mConsole.Write ("{0}", Iarrary[m]);Console.WriteLine ();}}}Classic

;3)12-3=9 (9>3) 9-3=6 (6>3)6-3=3 (3==3)Therefore, 3 is the greatest common divisor#include ⑶ Poor Lifting methodThere are two integers a and B:①i=1② If a, B can be divisible by I at the same time, then t=i③i++④ If I ⑤ If i > A (or b), then T is greatest common divisor, endingImproved:①i= A (or b)② If a, B can be divisible by I at the same time, then I is greatest common divisor,End③i--, go back and run ②.There are two integers a and B:①i=1② If a, B can be divisible by I at the same time, then t=

Method One: Incremental construction methodUnderstanding recursion has to understand what a function does.#include { printf ("{"); for (int i=0;i, A[i]); printf ("}\n"); int mi=cur?a[cur-1]+1:0; Use dictionary order to avoid duplicate printing for (int i=mi;i { a[cur]= }}int main () {int n; int a[ 10]={}; scanf ("%d",N); Print_subset (n,a,0);//initially a subset of 0 elements is stored in a, starting to recursively print return 0;} Method Two: Bit vector methodEnumer

Liu zitao Here we mainly introduce a method to prove that the greedy algorithm is the best: Exchange Argument (I do not know how to translate it to Chinese and Exchange parameters? It sounds awkward, not like the name of a method ~ O (Clerk □clerk) o) The main idea of Exchange Argument is to assume that an optimal algorithm is the closest to our greedy algorithm, and then Exchange one step (or element) of the two algorithms ), A new optimal algorithm

When I was in elementary school, I learned the ball's volume formula V = (4/3) π R weight. At that time, I thought it was amazing, is it possible for someone who has obtained this formula to melt an iron into molten metal and put it in a rectangular container? It wasn't until I went to school that I realized that I had used points for calculation. Of course, the calculus may hate more than love for many students, including me, however, it is undeniable that points play an irreplaceable role in a

trees in the forest, figure 6.22 (d) There is only one tree in the forest, and this tree is the husky tree. I may ask whether the length of the weighted path is unique in the Heman tree composed of N leaves? It is unique. Is the tree unique? Not unique. This is because when we merge the two sub-trees with the minimum and minimum weights in the forest, it is not strictly limited to the left sub-tree and the right sub-tree. The practice in Figure 6.22 is to treat the left subtree with a smaller w

Basic sorting (5): Summary of basic sorting algorithms and summary of sorting algorithmsBasic sorting If a basic sorting algorithm is slower than data processing, such as reading and reading data, there is no need to find a faster algorithm. If the sorted files are suitable for storing in memory, the sorting method is called"Internal sorting"; Sorting files from a disk is called"External sorting".DifferencesInternal sorting can easily access any el

SymmetricAlgorithmUsed in combination with asymmetric algorithms, such: The sender has a public key and the receiver has a private key. 1. Sender: First, the sender generates a random symmetric key, encrypts the data with the symmetric key, and puts it in a digital envelope. Then, the sender uses the public key to package the random symmetric key, put it in a digital envelope, and finally transmits the digital envelope to the receiver. 2 "receiv

Chapter 2-Introduction to Algorithms Summary: This chapter describes the examples of insertion sorting and algorithm analysis, proof of non-variant loops, combined sorting (divide and conquer), and algorithm analysis. 1. Insert sorting Similar to the playing card insertion process, set a [1... j-1] is an array of sorted order, insert a [J] into a [1... in J-1], making a [J] an array of sorted orders, j Algorithm Analysis: In the best case, the ent

behind socks. 2,Theorem:Directed Graph G has no loop. If the directed graph G does not have a reverse edge. 3. Theorem: the topological-sort (g) algorithm can generate topological sorting for directed acyclic graph G. 5. Strongly Connected branches 1. In a directed graph, if any two different points are reachable, the directed graph is strongly connected. A strongly connected subgraph of a directed graph is calledStrongly Connected branches. 2. Many algor