best book for permutation and combination

Algorithm: C ++ permutation and combination Question: give 1-N numbers and arrange and combine them. Solution: recursion. The first number has n options, the second number has n-1 options, and the output is recursively arranged. Use an array to represent n numbers, and set the number used to 0. Implementation language: C ++ # Include Using namespace std; /*************************************** * **

=0; i ) { if(Flag[i] = =false)//The bit has not been taken {Flag[i]=true; Result[level++] =a[i];//Remove the modified marker bit Pailie (A, N, K, level);//choose one of the unused insidelevel--;//re-fetch another bit flag[i]=false; } }}combinations: Combinations and permutations are different: not in order. We can assume that we have always been back to the previous selection, then the first number as the beginning, then we can not start again. For example: A,b,c,d. When I first se

This article mainly introduces the php method of adding numbers from 1 to 9 equal to 20 by means of arrangement and combination. The example analyzes the related skills of php arrangement and combination mathematical operation, which has some reference value, for more information, see This article mainly introduces the php method of adding numbers from 1 to 9 equal to 20 by means of arrangement and

First, using the binary state method to find the permutation combination, this method is easy to understand, but the operation efficiency is not high, small data permutation combination can be used Copy Code code as follows: Import Java.util.Arrays; Using binary algorithm to arrange allcount1:170187count

multiplication into a linear operation of summation, that is, the upper formula has greatly simplified the computational complexity, but can be further optimized. From the above, it is easy to see that the 3 items on the right are necessarily duplicates. Now let's split the first item on the right into two parts:In this way, the first item on the right side of the top can be offset, thus getting:The above method directly reduces the 2m logarithm calculation and the summation operation. But this

An arrangement and combination algorithm has been learned in middle school. nbsp; arrangement and combination nbsp; 1 nbsp; 2 nbsp; 3 nbsp; 4 nbsp; 5 nbsp; 6. you can construct 720 different strings. here we write a rough implementation method nbsp; for example, nbsp; 1- nbsp; 6. Which of the following experts can you advise; question about a permutation

of the I item, which has (p-1) * s (p-1, K) method.Second Class Stirling Number S (P, K)A combination of S (P, K) is the number of methods used to divide P objects into k non-empty unidentifiable (which can be understood as a box without serial numbers) sets.K! S (P, K) is the number of methods for dividing P individuals into k different rooms (for example, rooms marked with room numbers) (no room available.The recursive formula of s (P, K) is: s (P,

Next Permutation Think of the entire arrangement as a number, sort by number size, and find the next Arrangement // ① Locate the first non-incrementing position from right to left // ② locate the first position greater than * increment from right to left change // ③ switch * between and * Change // ④ reverse all the elements on the right of the listener // @ algorithm http: //? Sherlei.blogspot.com/2012/12/leetcode-next-permutation.html // @ author

the permutation combination: The result is C (n,k) *a (n,k), that is, from n rows to choose K Line to put the car, and then this k row to be assigned column is from the N column to choose the arrangement of K column.1#include 2#include 3 using namespacestd;4 Long Longc[ to][ to];5 intMain () {6 for(intI=0; i to; ++i) c[i][0]=1;7 for(intI=1; i to; ++i) {8 for(intj=1; j1][j-1]+c[i-1][j];9

of the label.Obviously, the tree and Prufer series one by one correspond.That is, there is only one prufer sequence for a tree.For a prufer sequence, only one tree can be restored.Some propertiesEach prufer sequence has n-2 entries (n is the number of nodes)For a node with a degree of x, it appears x-1 times in the Prufer sequenceThe prufer sequence that satisfies both of these conditions (of course each number cannot exceed N) must be able to form a valid tree　With this idea, you can begin to

to get only its remainder modulo 9 + 7. Help him! InputThe first line contains the integers, n and k (0≤ k n ≤105). The second line contains a string consisting of n digits.OutputPrint the answer to the problem modulo 9 + 7. Sample Test (s) inputC + + 12 3 1 108 OutputC + + 1 27 InputC + + 12 3 2 108 OutputC + + 1 9 NoteIn the first sample the result equals (1 +

moves the world". is a discussion of whether or not an element is to be categorized, and this element is often the last. At this point, the problem can often be divided into two sub-naturalization.The above two examples are actually discussed for an element, but they divide the problem much, so the outer layer has loops to traverse. Here is an example of a two-part recursive naturalization.Gives an array with an int number that is not duplicated. The combin