programming algorithms book

the backtracking condition of a state point of the "backtracking point."--------------------------------------------------------------------------------------------------Branch gauge : Similar to backtracking, it is also an algorithm for searching problem solution on the solution space tree T of problem. However, under normal circumstances, the branch-bound method and the backtracking method are different in solving the target. The goal of backtracking is to find out all the solutions that sati

Series Address: Introduction to Algorithms (CLRS) reference answers and matching programming questions1.1 Algorithm1.1-1 such as undergraduate semester statistics sorting to assign scholarships and so on.1.1-2 such as the memory needed to solve the problem, and so on.1.1-3 Sequential table, the advantage of support random lookup, you can find elements in \ (O (1) \) , the disadvantage is to add/remove eleme

Series Address: Introduction to Algorithms (CLRS) reference answers and matching programming questions2.1 Insert SortExercise 2.1-1 originally titled \ (a= , each time after the order changes as follows:To demonstrate the effect, all values are reduced uniformly (10\). The following is a demonstration of the sort procedure for \ (a= :practice 2.1-2 Rewrite to a non-ascending sort result as follows:Click to

"(2) If the first and last elements of X are not the same, then F "I,j" =max (f "i+1,j", F "i,j-1")2, construct a land-return solutionF "I,j" =f "I+1,j-1" when X[i] =x "J"F "I, J" =max (F[i+1,j],f[i,j-1]) when X "I"! = X "J"3, calculate the optimal solution#include #includestring.h>using namespacestd;//finding the longest palindrome subsequenceintLspChar*a,intN) { intDp[n][n]; inttem; inti,j; Memset (DP,0,sizeof(DP));//assigning initial values to all DP elements 0 for(i=0; i) Dp[i][i]=1;

The subscript in the introduction to algorithms starts from 1, but in order to be consistent with the c ++ STL design idea, all functions are implemented in a unified left-closed and right-open interval. It has been modified many times in the middle, because the subscript modification is not easy to get rid of, you need to always maintain the cycle unchanged, a slight step error will make the results some errors. # Include # Include # Include # Includ

//use recursion to solve the problem although concise, but not high efficiency, to dynamic planning better functionRECURFIB (n) {//Fibonacci Sequence--recursion if(N ) { return1; } Else { returnRECURFIB (n-1) + RECURFIB (n-2); } } functionDYNFIB (n) {//Fibonacci Sequence--Dynamic programming varval = []; if(n = = 1 | | n = = 2) { return1; } Else{val[1] = 1; val[2] = 2; for(vari = 3; I i) {Val[i]

]) *double (Dy[i])#Sqx = double (Dx[i]) **2Sumxy= VDOT (Dx,dy)#returns the point multiplication of two vectors multiplySQX = SUM (Power (dx,2))#Square of the vector: (x-meanx) ^2#calculate slope and interceptA = sumxy/SQXB= meany-a*MeanxPrintA, b#Draw a graphicPlotscatter (XMAT,YMAT,A,B,PLT)7.1.4 Normal Equation Group methodCode implementation of 7.1.5 normal equation set#data Matrix, category labelsXarr,yarr = Loaddataset ("Regdataset.txt")#Importing Data Filesm= Len (Xarr)#generate x-coordinat

); returnlist; } PrivateListintStartintend) {ListNewArraylist(); if(Start >end) {List.add (NULL); returnlist; } for(inti = start; I ) {List); List, end); for(intj = 0; J ) { for(intk = 0; K ) {TreeNode node=NewTreeNode (i); Node.left=Left.get (j); Node.right=Right.get (k); List.add (node); } } } returnlist; }I understand that: for example, n nodes, it is divided into n-1, the same as the Cattleya number above, and then we constr

mathematical sense. Main functions:functools.partialis to fix some parameters of a function (that is, to set a default value) and return a new function, which is simpler to call the new function. For example, int () is the default conversion of a string to a decimal integer, so what if I want to convert to binary by default?To create a new function directly using the following code int2 :>>> import functools>>> int2 = functools.partial(int, base=2)>>> int2(‘1000000‘)64>>> int2(‘1010101‘)85Final

. 7.5 910.5 . 13.5]]# n Powers of each element of the matrix: n=2mymatrix1 = Mat ([[[1,2,3],[4,5,6],[7,8,9]])print power (mymatrix1,2 1 4 9] [[49 6481]]# matrix multiplied by matrix mymatrix1 = Mat ([[1,2,3],[4,5,6],[7,8,9 = Mat ([[[1],[2],[3]])print mymatrix1*mymatrix2 output: [[[][+][50]]# Transpose of the matrix mymatrix1 = Mat ([[[1,2,3],[4,5,6],[7,8,9]])print mymatrix1. The transpose of the # Matrix to the transpose of the T # Matrix print mymatrix1 output results as follow

the basis of all n-2 envelopes, the letters in the last two envelopes (n envelopes and any one of the 1 to n-1 envelopes, a total of n-1 options) are exchanged and the number of ways in which all envelopes are incorrectly loaded. In summary, f[n] = (n-1) * f[n-1] + (n-1) * f[n-2]. This is the wrong row formula.The specific code is as follows:#include LongLongf[ +];//long long for larger valuesintMain () {f[1] =0; f[2] =1;//Initial value 　　 for(inti =3; I -; i + +) F[i]= (I-1) * F[i-1] + (I-1)

in a previous article on the greedy algorithm to solve the problem of active selection ("Introduction to the algorithm" Greedy algorithm activity selection problem ), found that there is a practice 16.1-1 is to use dynamic programming to solve the problem of active selection. In fact, the matrix chain is similar to the previous multiplication, but also consider the partition of the activity is which, and two-dimensional data to record Sij---the maximu

line. The line contains an integer that indicates the minimum number of times the cut is made, so that the resulting substring is a palindrome. Sample input 3abaaccaabcdabcba Sample output 130 Tips for the first set of samples, Ford cut at least 1 times, the original string was cut to "ABA" and "ACCA" two palindrome substring. For the second set of samples, Ford cut at least 3 ti

(First chapter above)1.2.5 Linalg Linear Algebra LibraryBased on the basic operation of matrices, the Linalg Library of NumPy can satisfy most linear algebra operations.. determinant of matrices. Inverse of the Matrix. Symmetry of matrices. The rank of the matrix. The reversible matrix solves the linear equation1. Determinant of matrices from Import * in[#N-order matrix determinant operation in [6]: A = Mat ([[[1,2,3],[4,5,6],[7,8,9]]) in [print]det (A):"6.66133814775e-162. Inverse of the Matrix

, stored in m[i][j], and the corresponding k stored in the s[i][j], we have the desired results.According to the above analysis, it is not difficult to give the code of the process, note here is also the use of the bottom-up method, see "Pipe cutting":The ranks of the AI matrix are p[i-1] and p[i],1after the above code, we have obtained the minimum multiplication times and corresponding best division S[I][J] for each combination of I and J.third, the optimal structure of the output division:Afte

Steps for dynamic planning problems1. Describe the structure of the optimal solution2, recursive definition of the value of the optimal solution3. Calculate the value of the optimal solution from the bottom up4, the optimal solution is constructed by the result of calculation.In general, the 3rd step is to record some additional information,There is another way to calculate the bottom-up step, which can be calculated from the top of the memo.15.1 assembly line Scheduling15.2 matrix chain Multipl

Programming algorithms-food chain and code query (C)Code for checking the food chain (C) Question: There are N animals numbered 1, 2 ,..., n. all animals belong to one of A, B, and C. it is known that A eats B, B eats C, and C eats. Two types of information are provided in order. First, x and y belong to the same class. Type 2: x eat y. There may be errors and contradictions between the information, and t

How many possibilities are there for a Shooting athlete to target a total of 10 rings and even a dozen or 90 rings? Use Recursive Algorithms for programming ., Targeting Recursion # Include Using namespace std;Int sum;Int store [10];Void OutPut (){For (int I = 9; I> = 0; I --){Cout }Cout Sum ++;}Void Cumput (int score, int num) // score indicates the total score (90n). num indicates the number of times (0

Longest ascending sub-sequence problem code (C)This address: Http://blog.csdn.net/caroline_wendyTitle: There is a series A that is long n. Request the length of the longest ascending subsequence in this sequence. The number of the longest ascending subsequence can be spaced.That is, the longest ascending subsequence (LIS, longest increasing subsequence), such as: N=5, a={4,2,3,1,5}, Result=3 (2,3,5).Use dynamic solver (DP).Method 1: The longest ascending subsequence before each number is calcula

[i][j-1]+dp[i+1][j]-dp[i+1][j-1];11137-ingenuous Cubrency Fully Backpack10201-adventures in Moving-part IV？ 10154-weights and Measures10453-make palindrome Minimum number of changes on the side palindrome + output palindrome？ 10029-edit Step Ladders10313-pay The price backpack variantDP[I][J] The scheme number of I denominations with a J-coin dp[i][j] + = Dp[i-w][j-1] W is a certain denomination of the current enumeration of coins10401-injured Queen problem Dp[i][j] Represents (i, j) the number