SQRBR - Square Brackets
You are given:
- a positive integer n,
- an integer k, 1<=k<=n,
- an increasing sequence of k integers 0 < s1 < s2 < ... < sk <= 2n.
What is the number of proper bracket expressions of length 2n with opening brackets appearing in positions s1, s2,...,sk?
Several proper bracket expressions:
An improper bracket expression:
There is exactly one proper expression of length 8 with opening brackets in positions 2, 5 and 7.
Write a program which for each data set from a sequence of several data sets:
- reads integers n, k and an increasing sequence of k integers from input,
- computes the number of proper bracket expressions of length 2n with opening brackets appearing at positions s1,s2,...,sk,
- writes the result to output.
The first line of the input file contains one integer d, 1 <= d <= 10, which is the number of data sets. The data sets follow. Each data set occupies two lines of the input file. The first line contains two integers n and k separated by single space, 1 <= n <= 19, 1 <= k <= n. The second line contains an increasing sequence of k integers from the interval [1;2n] separated by single spaces.
The i-th line of output should contain one integer - the number of proper bracket expressions of length 2n with opening brackets appearing at positions s1, s2,...,sk.
Sample input: 5 1 1 1 1 1 2 2 1 1 3 1 2 4 2 5 7 Sample output: 1 0 2 3 2
solved and Motivated :)
Try iterative DP, you will definitely enjoy.
easy recursion :)
recursion with mem... nice one..
nice problem :)
good problem :)
Nice DP problem .. .enjoyed solving it...some good thinking is required :D
nice problem :)