problem↵
////////////////////////////////////////////////////↵
Expected Xor↵
↵
Given a random variable X↵
, and another integer N, this random variable X can take any value between 1 and N↵
↵
with equal probability.↵
↵
Now, we define a function F(X)↵
↵
:↵
↵
F(X)↵
: The bitwise exclusive OR of all the digits of X. For example, for X=34536,F(X)=3⊕4⊕5⊕3⊕6=7↵
↵
.↵
↵
Considering X↵
can take any value between 1 and N with equal probability, you are to find expected value of F(X)↵
↵
. Can you do it ?↵
↵
The answer equals to P/Q↵
where P/Q is an irreducible fraction, i.e, P and Q↵
↵
are co-prime to each other.↵
↵
You can read more about expected value of a random variable here.↵
↵
Input:↵
↵
The first line of the input contains T↵
↵
, denoting the number of test cases.↵
↵
The next T↵
lines contain a single positive integer N↵
↵
.↵
↵
Output:↵
↵
For each test-case, print the answer in a separate line in the form of P/Q↵
where P/Q is an irreducible fraction i.e. P and Q↵
↵
are co-prime to each other.↵
↵
Constraints:↵
↵
1≤T≤105↵
↵
1≤N≤1018↵
↵
Sample Input↵
(Plaintext Link)↵
↵
4↵
1↵
3↵
5↵
10↵
↵
Sample Output↵
(Plaintext Link)↵
↵
1/1↵
2/1↵
3/1↵
23/5↵
↵
Explanation↵
↵
For N=1↵
, there is only one possible value X can take which is 1. Hence expected value of X=1↵
↵
.↵
↵
For N=3↵
, there are three possible values of X ,i.e, 1,2 and 3. Hence, expected value of X=1/3∗1+1/3∗2+1/3∗3=2↵
↵
.↵
↵
For N=10↵
, X can take all the values from 1 to 9 where X will be equal to 1 for both 1 and 10. Hence, X=2/10∗1+1/10∗(2+3+4+5+6+7+8+9)=23/5↵
↵
.↵
my code↵
↵
http://ideone.com/SRbjnv↵
↵
please anyone great guy tell me where this code is going on wrong thanx in advance↵
And explain how I can solve this↵
////////////////////////////////////////////////////↵
Expected Xor↵
↵
Given a random variable X↵
, and another integer N, this random variable X can take any value between 1 and N↵
↵
with equal probability.↵
↵
Now, we define a function F(X)↵
↵
:↵
↵
F(X)↵
: The bitwise exclusive OR of all the digits of X. For example, for X=34536,F(X)=3⊕4⊕5⊕3⊕6=7↵
↵
.↵
↵
Considering X↵
can take any value between 1 and N with equal probability, you are to find expected value of F(X)↵
↵
. Can you do it ?↵
↵
The answer equals to P/Q↵
where P/Q is an irreducible fraction, i.e, P and Q↵
↵
are co-prime to each other.↵
↵
You can read more about expected value of a random variable here.↵
↵
Input:↵
↵
The first line of the input contains T↵
↵
, denoting the number of test cases.↵
↵
The next T↵
lines contain a single positive integer N↵
↵
.↵
↵
Output:↵
↵
For each test-case, print the answer in a separate line in the form of P/Q↵
where P/Q is an irreducible fraction i.e. P and Q↵
↵
are co-prime to each other.↵
↵
Constraints:↵
↵
1≤T≤105↵
↵
1≤N≤1018↵
↵
Sample Input↵
(Plaintext Link)↵
↵
4↵
1↵
3↵
5↵
10↵
↵
Sample Output↵
(Plaintext Link)↵
↵
1/1↵
2/1↵
3/1↵
23/5↵
↵
Explanation↵
↵
For N=1↵
, there is only one possible value X can take which is 1. Hence expected value of X=1↵
↵
.↵
↵
For N=3↵
, there are three possible values of X ,i.e, 1,2 and 3. Hence, expected value of X=1/3∗1+1/3∗2+1/3∗3=2↵
↵
.↵
↵
For N=10↵
, X can take all the values from 1 to 9 where X will be equal to 1 for both 1 and 10. Hence, X=2/10∗1+1/10∗(2+3+4+5+6+7+8+9)=23/5↵
↵
.↵
my code↵
↵
http://ideone.com/SRbjnv↵
↵
please anyone great guy tell me where this code is going on wrong thanx in advance↵
And explain how I can solve this↵
