TOURIST - Tourist

A lazy tourist wants to visit as many interesting locations in a city as possible without going one step further than necessary. Starting from his hotel, located in the north-west corner of city, he intends to take a walk to the south-east corner of the city and then walk back. When walking to the south-east corner, he will only walk east or south, and when walking back to the north-west corner, he will only walk north or west. After studying the city map he realizes that the task is not so simple because some areas are blocked. Therefore he has kindly asked you to write a program to solve his problem.

Given the city map (a 2D grid) where the interesting locations and blocked areas are marked, determine the maximum number of interesting locations he can visit. Locations visited twice are only counted once.


The first line in the input contains the number of test cases (at most 20). Then follow the cases. Each case starts with a line containing two integers, W and H (2 ≤ W , H ≤ 100), the width and the height of the city map. Then follow H lines, each containing a string with W characters with the following meaning:

. Walkable area
* Interesting location (also walkable area)
# Blocked area

You may assume that the upper-left corner (start and end point) and lower-right corner (turning point) are walkable, and that a walkable path of length H + W − 2 exists between them.


For each test case, output a line containing a single integer: the maximum number of interesting locations the lazy tourist can visit.


9 7
5 5


hide comments
blackrise: 2020-04-21 11:36:10

This question is such a beauty... Worth spending time on

hetp111: 2019-11-19 20:18:01

getting 10,8 for example tc.. idk why.

shubham: 2018-06-23 01:07:15

A very interesting problem, kudos to the setter.

smso: 2018-06-14 07:45:29

use dp[x1][y1][x2] and dp==-1 => unmarked, dp==-INF => blocked

chetan4060: 2018-02-02 12:15:22

very good question:)

danish4200: 2017-09-29 11:22:40

Nice problem.Learnt something new.

hunter17: 2017-03-04 08:59:36

Can anyone explain how the answer to following test case could be 4????
Please really need help

3 6

Last edit: 2017-03-04 09:00:06
weramajstor: 2016-10-04 02:33:08

Very interesting problem,huge upgrade on the problem in which you just have to go from the top-left to the bottom-right corner.

Shubham Gupta: 2016-07-05 10:59:23

Solving this problem was totally worth it! :D
Hints: Optimally going down and then optimally coming back up will NOT fetch you the correct answer!
O(n^4) might not pass.

Annu Purohit: 2016-06-10 18:58:35

Accepted after trying a whole day!
This case should be included in the test cases!
5 5
The answer should be 4! :)

Last edit: 2016-06-11 12:59:07

Added by:Daniel Gómez Didier
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:2007 PUJ - Circuito de Maratones ACIS / REDIS