10183: How many Fibs?[First Java Code Accepted]

>> রবিবার, ১ নভেম্বর, ২০০৯

The most relevant definition for this problem is 2a: An integer g>1 is said to be prime if and only if its only positive divisors are itself and one (otherwise it is said to be composite). For example, the number 21 is composite; the number 23 is prime. Note that the decompositon of a positive number g into its prime factors, i.e., is unique if we assert that fi > 1 for all i and for i
One interesting class of prime numbers are the so-called Mersenne primes which are of the form 2p- 1. Euler proved that 231 - 1 is prime in 1772 -- all without the aid of a computer.



Input
The input will consist of a sequence of numbers. Each line of input will contain one number g in the range -231 < g <231, but different of -1 and 1. The end of input will be indicated by an input line having a value of zero.


Output 
For each line of input, your program should print a line of output consisting of the input number and its prime factors. For an input number , where each fi is a prime number greater than unity (with  for i<j), the format of the output line should be

When g < 0, if , the format of the output line should be




-190
-191
-192
-193
-194
195
196
197
198
199
200
0
-190 = -1 x 2 x 5 x 19
-191 = -1 x 191
-192 = -1 x 2 x 2 x 2 x 2 x 2 x 2 x 3
-193 = -1 x 193
-194 = -1 x 2 x 97
195 = 3 x 5 x 13
196 = 2 x 2 x 7 x 7
197 = 197
198 = 2 x 3 x 3 x 11
199 = 199
200 = 2 x 2 x 2 x 5 x 5

Discussion

Algorithm:
  1. Generate prime number in a array.

  2. Divide the given number by the array element until arr[ele]<=sqrt(input). print arr[ele].

  3. Print output carefully.
How we generate prime number:
Let: p[]={1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}; ie p[ele]=1 means ele is a prime.
Take i=2 which is prime, Now p[2]=0,p[4]=0,p[6]=0,p[8]=0,p[10]=0;p[12]=0;p[14]=0;
So now p[]={1,1,1,1,0,0,1,0,1,0,1,0,1,0,1}
Take i=3 which is prime, Now p[6]=0,p[9]=0;p[12]=0;p[15]=0;
So now p[]={1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0}
For i=4 , i<=sqrt(16) false so end
P[0]=1 ;p[1]=1,p[2]=1;p[3]=1;p[5]=1,p[7]=1;p[11]=1;p[13]=1;
Move a[0]=0,a[1]=1;a[2]=2;a[3]=3;a[4]=5;a[5]=7;a[6]=11;a[7]=13



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