Data structure and algorithm analysis (C language description) Exercise 2.7

Problem Description: Suppose you need to generate a random permutation of the first n natural numbers. For example, {4,1,2,5,2} and {3,1,4,2,5} are legal permutations, but {5,4,1,2,1} is not, because the number 1 appears twice and the number 3 is missing. This program is often used to simulate some algorithms. We assume that there is a random number generator Randint (i, j), which generates an integer between I and J at the same probability. Here are three algorithms:

1. Fill in an array of a[0] to a[n-1], fill in a[i], generate a random number until it differs from the a[0],a[1], ..., a[i-1], and then populate it with A[i].

2. Same as algorithm 1, but to save an additional array, called used (used) array. When a random number Ran was initially put into array A, the used[ran]=1 was placed. This means that when a random number is filled in with a[i], one step can be used to test whether the random number has been used, rather than the I test, as in the first algorithm (possibly).

3. Fill in the array to make the a[i]=i+1. And then:

 for 1; i < N; i++    Swap (&a[i], &a[randint (0, i)]);

Write the program to execute each algorithm 10 times, to obtain a good average. For n=250,500,1 000,2 000 Run Program 1, to n=2500,5 000,10 000,20 000,40 000,80 000 Run program 2; to N=1 0000,2 0000,4 0000,8 0000,160 000,320 000, 640 000 Run program 3.

Realize:

1 //returns a random number in [I, J]2 intRandint (intIintj)3 {4     if(J-i = =0)5         returni;6     Else if(J-i <0)7         return 0;8     Else9         returnRand ()% (j-i) +i;Ten } One  A //Algorithm 1 - intFillArray1 (intA[],intN) - { the     intCount, ran, K; -  -Count =0; -      while(Count <N) +     { -ran = Randint (0, n); +          for(k =0; K < count; k++) A         { at             if(A[k] = =ran) -                  Break; -         } -         if(k = =count) -         { -A[count] =ran; incount++; -         } to     } +     return 1; - } the  * //Algorithm 2 $ intFillArray2 (intA[],intN)Panax Notoginseng { -     int*used, count, ran; the  +Used = (int*)calloc(N,sizeof(int)); A     if(used = =NULL) the         return 0; +  -Count =0; $      while(Count <N) $     { -ran = Randint (0, n); -         if(Used[ran] = =0) the         { -A[count] =ran;WuyiUsed[ran] =1; thecount++; -         } Wu     } -      Free(used); About     return 1; $ } -  - Static voidSwapintBint*b) - { A     inttemp = *A; +*a = *b; the*b =temp; - } $  the //Algorithm 3 the intFillArray3 (intA[],intN) the { the     inti; -      in      for(i =0; I < n; i++) theA[i] = i +1; the      for(i =0; I < n; i++) AboutSwap (&a[i], &a[randint (0, i)]); the}

The above algorithms have two main problems:

1). Dynamic array problem: limited available memory

In algorithm 2, it is required to do array subscript "used[ran]=1" with random numbers, which means that we must use a variable-length array used array with the largest number of random elements. vs2013 compiler does not support this feature, I chose the dynamic Memory allocation malloc () to implement the used array. This is limited by the amount of available memory.

2). C Random Number problem: limited range of random numbers

C generates pseudo-random numbers using Srand () and Rand (). We know that they can only produce a value between [0, Rand_max]. A maximum of (rand_max+1) non-repeating random numbers can be generated. When n > rand_max+1, the algorithm keeps trying to get new random numbers that are not duplicated and into a dead loop.

If you have a better algorithm, welcome to the communication.

Data structure and algorithm analysis (C language description) Exercise 2.7