A. Contest Proposal
brute force; greedy; two pointers
A contest contains \(n\) problems and the difficulty of the \(i\)-th problem is expected to be at most \(b_i\). There are already \(n\) problem proposals and the difficulty of the \(i\)-th problem is \(a_i\). Initially, both \(a_1, a_2, \ldots, a_n\) and \(b_1, b_2, \ldots, b_n\) are sorted in non-decreasing order.Some of the problems may be more difficult than expected, so the writers must propose more problems. When a new problem with difficulty \(w\) is proposed, the most difficult problem will be deleted from the contest, and the problems will be sorted in a way that the difficulties are non-decreasing.In other words, in each operation, you choose an integer \(w\), insert it into the array \(a\), sort array \(a\) in non-decreasing order, and remove the last element from it.Find the minimum number of new problems to make \(a_i\le b_i\) for all \(i\).
Each test contains multiple test cases. The first line contains the number of test cases \(t\) (\(1\le t\le 100\)). The description of the test cases follows.The first line of each test case contains only one positive integer \(n\) (\(1 \leq n \leq 100\)), representing the number of problems.The second line of each test case contains an array \(a\) of length \(n\) (\(1\le a_1\le a_2\le\cdots\le a_n\le 10^9\)).The third line of each test case contains an array \(b\) of length \(n\) (\(1\le b_1\le b_2\le\cdots\le b_n\le 10^9\)).
For each test case, print an integer as your answer in a new line.
In the first test case: Propose a problem with difficulty \(w=800\) and \(a\) becomes \([800,1000,1400,2000,2000,2200]\). Propose a problem with difficulty \(w=1800\) and \(a\) becomes \([800,1000,1400,1800,2000,2000]\). It can be proved that it's impossible to reach the goal by proposing fewer new problems.In the second test case: Propose a problem with difficulty \(w=1\) and \(a\) becomes \([1,4,5,6,7,8]\). Propose a problem with difficulty \(w=2\) and \(a\) becomes \([1,2,4,5,6,7]\). Propose a problem with difficulty \(w=3\) and \(a\) becomes \([1,2,3,4,5,6]\). It can be proved that it's impossible to reach the goal by proposing fewer new problems.