Introduction to the algorithm calls random (0,1) to implement the random (A, b) process

An implementation of the procedure describing the random (A, b), which only calls random (0,1). As A and B functions, what is the expected run time of your program? (RANDOM (0,1) with equal probability output 0 or 1,random (A, a, b) output the number of [A, b] between equal probability (integer))

to the probability of random (A, b) output the number between [A, a], as long as the probability of getting [0,b-a] a number between. Since it is possible to get 1 or 0 by random (0,1), it is possible to divide the [0,b-a] interval into smaller intervals, assuming that when the 1 o'clock interval is reduced to [(B-A)/2,b-a],0 It is [0, (B-A)/2]. So recursion, finally get only an integer interval if [x,x], at this time a+x is the final result.

The above idea seems very good, but there is a pretty deadly problem not to consider, that is [0,b-a] in the b-a+1 must be 2^x (power of 2) to ensure equal probability. For a chestnut, [0,2] has 3 numbers {0,1,2} and the probability of getting 2 is significantly greater than 0 and 1. The solution here is that the number of integers in the extended interval guarantee interval is a power of 2. When the resulting integer is larger than b-a, it is re-executed. So

1 //Random.cpp: Defines the entry point of the console application. 2 //3 4#include"stdafx.h"5#include"windows.h"6#include"stdio.h"7#include"math.h"8#include"time.h"9 Ten /* One implementing the random (0,1) function A */ -  - intEitherrand () the { -     returnRAND ()%2; - } - /* + perform recursion - */ + LongRandint*arr,intBegintend) A { at     if(Beg = =end) -     { -         returnBeg; -     } -     Else -     { in         returnEitherrand () = =0? rand (Arr,beg, (beg+end)/2): Rand (arr, (beg+end)/2+1, end);  -     } to } + intMain () - {     the     intA=2; *     intb=7; $     intdif=b-a+1;Panax Notoginseng     Longrs =1; -     intExp =0;  the      while(rs<dif) +     { Ars = rs*2; theExp + +; +     } -     int*arr = (int*) malloc (rs*sizeof(Long)); $     //random seed, set it all the time. Duplicate settings produce the same value $Srand ((unsigned) time (0)); -     intRdnum = rand (arr,0, rs-1); -      while(rdnum>dif) the     { -Rdnum = rand (arr,0, rs-1);Wuyi     } theprintf"%d", rdnum+a); -System"Pause"); Wu     return 0; -}

Introduction to the algorithm calls random (0,1) to implement the random (A, b) process