Alternating PermutationsProblem code: SNCK03 |
All submissions for this problem are available.
[Problem Idea : Varun Jalan]
You are given K indices, A[1], A[2], ... , A[K].
A[1] < A[2] < ... < A[K].
A[1] = 1 and A[K] = N.
A permutation of the numbers between 1 and N is called valid if :
The numbers in the permutation between indices A[1] and A[2] (inclusive) form an increasing sequence, the numbers in the permutation between indices A[2] and A[3] (inclusive) form a decreasing sequence, those between A[3] and A[4] (inclusive) form an increasing sequence and so on.
Count the number of valid permutations.
Input:
There will be multiple test cases. The first line contains the number of test cases T. There follow 2*T lines, 2 lines for each test case. The first line for each test case contains the numbers N and K. The second line contains K space seperated numbers, ie. A[1] to A[K].
Output:
Output T lines, one for each test case. All answers should be output modulo 1000000007.
Constraints :
T <= 111
2 <= N <= 20000
2 <= K <= 22
K <= N
A[1] < A[2] < ... < A[K].
A[1] = 1 and A[K] = N.
Time Limit : 20 seconds.
Sample Input :
3 3 3 1 2 3 4 3 1 3 4 10 6 1 2 5 7 8 10
Sample Output :
2 3 6166
Note :
For the first test case,
(1 3 2) and (2 3 1) are the valid permutations.
For the second test case,
(1 2 4 3), (1 3 4 2) and (2 3 4 1) are the valid permutations.
| Date: | 2009-11-13 |
| Time limit: | 20s |
| Source limit: | 50000 |
| Languages: | C C99 strict C++ 4.0.0-8 C++ 4.3.2 PAS gpc PAS fpc JAVA NICE JAR C# C#2 NEM ST ASM D FORT ADA BASH PERL PYTH RUBY LUA ICON PIKE PHP SCM guile SCM qobi LISP sbcl LISP clisp SCALA HASK ERL CAML CLPS PRLG WSPC BF ICK JS |
Comments
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I am not able to sign in from
in second test case 'k' no.
6166 permutations for 6
6166 permutations for 6 numbers? only 720 permutations are possible...
@ Shitij You need to sign in
@ Shitij
You need to sign in from your team account.
The second test case is
The second test case is correct.
There are K=3 indices given and the line following it contains the indices values.
For k=2,shouldn't the 2nd
For k=2,shouldn't the 2nd permutation be (1 4 3 2) instead of (1 3 4 2) ??
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the max indice A[K]=N
the max indice A[K]=N possible is 20,000...does that mean that the max length of the permutation is 20,000 !
@ BBDNITM You have to output
@ BBDNITM
You have to output your answer modulo 1000000007
For k=2,shouldn't the 2nd
For k=2,shouldn't the 2nd permutation be (1 4 3 2) instead of (1 3 4 2) ??
what is meant by modulo
what is meant by modulo 1000000007
@arun garg : divide the count
@arun garg : divide the count by 1000000007 and take the remainder. thats the answer.
@ random : are you refering
@ random : are you refering to the 2nd test case ?
yup....for 2nd case
yup....for 2nd case 1(increase)->4 (decrease)-> 3
instead of what is given 1(increase)->3(increase)->4..
@ random I think the given
@ random
I think the given sample output is correct for the second case you mentioned.
(1 3 4 2) makes sense as 1, 3, 4 is an increasing subsequence in indices [1..3]
and 4, 2 is a decreasing subsequence in indices [3..4]
Can someone change our
Can someone change our display name from my email address to our actual team name, "Audrey Horne"?
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Thanks,
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Can someone change our
Can someone change our display name from my email address to our actual team name, "Audrey Horne"?
I can't do it with "Edit Profile".
Thanks,
Frank
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