【cf100506】Pachinko

2014年10月18日1,0180

Pachinko is a Japanese game played for amusement and prizes, and is similar to pinball.
The game is very simple: you shoot small metal balls into the machine and they fall down,
bouncing off the obstacles until they fall into a gate. The gate into which your ball falls
determines the winnings.
Since you can more or less determine the column into which the ball is dropped (by setting
its initial speed and direction), you can influence your win chances. You are to calculate
your expected winnings.
We model the pachinko machine as follows: you can drop the ball in any column and it
falls down until it either reaches the bottom of the machine (which results in no wins), a
gate (indicated by a number 1 to 9, which results in that win) or an obstacle (indicated by
a asterisk). If a ball hits an obstacle it proceeds falling in the column to the left or to the
right of the obstacle, with 50/50 probability. No two obstacles or gates are adjacent, not
even diagonally, and none ara located in the leftmost or rightmost column.
Input
On the first line an integer t (1 ≤ t ≤ 100): the number of test cases. Then for each test
case:
• One line with two integers h and w (1 ≤ h, w ≤ 100): the width and height of the
pachinko machine.
• h lines with w characters describing the pachinko machine. A ‘.’ denotes an empty
space, ‘*’ an obstacle and ‘1’. . . ‘9’ the winning gates.
Output
For each testcase:
• One line with the maximal expected winnings with either an absolute or a relative
error of at most 10−6

Sample in- and output

3
7 5
…..
.1…
…2.
.*…
…..
…..
..5..
8 8
…1….
……..
..*…*.
….*…
.1……
…*.*..
……..
..9.7.7.
10 10
.*.*.*.*..
……….
..*.*.*.*.
……….
.*.*.*.*..
……….
..*.*.*.*.
……….
.*.*.*.*..
….9…..

Output

5.000000
7.500000
3.375000

题解

一行一行dp就能轻松转移了吧。。