FINDMAX - Finding Maximum
One way of finding the maximum element in an array is to initialize a variable to the first element in the array, iterate through the remaining array, and update the variable whenever a value strictly greater than it is found. Assuming that the array contains N elements each in the range 1..K, how many such arrays exist such that the above algorithm performs exactly P updates? Initialization of the variable is not counted as an update.
For example,the possible arrays for N = 4, K = 3 and P = 2 are:
The first line contains T the number of test cases. There follow T lines, containing 3 space seperated integers N, K and P.
Output T lines, one for each test case. On each line, output the answer as asked above. Since the answers can get very big, output the answer modulo 1000000007.
Sample Input: 3 4 3 2 2 3 1 3 4 1 Sample Output: 6 3 30
1 <= T <= 100
1 <= n <= 100
1 <= K <= 300
0 <= P < n
For those scratching their head , just think about finding the number of arrays of length n , and given k and p, assuming you already know the number of arrays of length <= n
how to approach the recurrence relation?
optimization tips here:
Not per test case, but per input :)
Is O(n*K*P) per test case sufficient?