UCI2009B - Binomial Coefficients
We all got too excited when we learned (A + B)^2 = A^2 + 2AB + B^2. After solving this problem, maybe you could get even more excited because you will have to calculate (A + B)^N, where (0 <= N <= 1000).
Follow the rules below when giving the answer:
- Consecutive terms must be separated by a '+' character.
- At the i-th term, A must be raised to N - i and B must be raised to i (0<=i<=N).
- Binomial coefficients must not be printed, print their prime factorization instead.
- Use '^' for exponentiation and 'x' for multiplication in step 3.
- Avoid the use of number 1 when possible.
See sample output for clarification.
Input
Input starts with an integer T, representing the number of test cases (1<=T<=15). T lines follow, each one consisting of an integer N, (0<=N<=1000).
Output
For each test case, print (A + B)^N, on a single line.
Example
Input:
6
0
1
2
3
4
5
Output:
1
A+B
A^2+2xAB+B^2
A^3+3xA^2B+3xAB^2+B^3
A^4+2^2xA^3B+2x3xA^2B^2+2^2xAB^3+B^4
A^5+5xA^4B+2x5xA^3B^2+2x5xA^2B^3+5xAB^4+B^5
Warning: Large output. Be careful with certain languages.
hide comments
nadstratosfer:
2019-11-26 06:35:55
Output for (A+B)^1000 is 340+KB. How about, instead of advising "being careful", set the TL appropriately? In fact, I only got an elegant PyPy solution accepted because I took advantage of certain undefined behaviour. No amount of care will make up for unreasonable TL. |
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Parul Yadav:
2015-08-11 07:39:02
my 100th |
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Bharath Reddy:
2013-06-13 12:50:22
Not so hard... |
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saket diwakar:
2013-01-27 21:55:08
very painful to code it..bt never mind...:) Last edit: 2013-01-30 21:50:14 |
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Ajey Golsangi:
2011-12-06 05:58:32
Painful to code the solution. |
Added by: | Yandry Perez |
Date: | 2009-06-23 |
Time limit: | 1s |
Source limit: | 50000B |
Memory limit: | 1536MB |
Cluster: | Cube (Intel G860) |
Languages: | All except: ERL JS-RHINO |