DWITE Online Computer Programming Contest

LEGO Ladder

January 2012
Problem 4

Little Alice and Little Bob are playing with their favourite toys, LEGO blocks. They have N blocks of various heights, arranged in a row. They decide to play a game with their blocks.

Alice and Bob take turns removing one LEGO block from the row, with Alice going first. At the beginning of a player’s turn, if the blocks form a ladder – a sequence of either non-increasing or non-decreasing heights – that player loses. Given the heights of the initial row of blocks, determine who has the winning strategy, if they play optimally.

The input file DATA4.txt will contain 5 test cases, and each test case describes 3 games. The first line of each game contains a number N (1 ≤ N ≤ 15), the number of blocks in that game. The next line contains N space-separated integers representing the heights of the blocks, which will be integers from 0 to 100 inclusive.

The output file OUT4.txt will contain 5 lines, each being a string of 3 characters. The ith character of the jth line should represent the result of the ith game of the jth test case: “A” if Little Alice wins or “B” if Little Bob wins.

Sample Input (only one case shown):
2 3
0 2 2
1 2 4 3
Sample Output: