BYTESM2  Philosophers Stone
One of the secret chambers in Hogwarts is full of philosopher’s stones. The floor of the chamber is covered by h × w square tiles, where there are h rows of tiles from front (first row) to back (last row) and w columns of tiles from left to right. Each tile has 1 to 100 stones on it. Harry has to grab as many philosopher’s stones as possible, subject to the following restrictions:
 He starts by choosing any tile in the first row, and collects the philosopher’s stones on that tile. Then, he moves to a tile in the next row, collects the philosopher’s stones on the tile, and so on until he reaches the last row.
 When he moves from one tile to a tile in the next row, he can only move to the tile just below it or diagonally to the left or right.
Input
The first line consists of a single integer T, the number of test cases. In each of the test cases, the first line has two integers. The first integer h (1 <= h <= 100) is the number of rows of tiles on the floor. The second integer w (1 <= w <= 100) is the number of columns of tiles on the floor. Next, there are h lines of inputs. The ith line of these, specifies the number of philosopher’s stones in each tile of the ith row from the front. Each line has w integers, where each integer m (0 <= m <= 100) is the number of philosopher’s stones on that tile. The integers are separated by a space character.
Output
The output should consist of T lines, (1 <= T <= 100), one for each test case. Each line consists of a single integer, which is the maximum possible number of philosopher’s stones Harry can grab, in one single trip from the first row to the last row for the corresponding test case.
Example
Input: 1 6 5 3 1 7 4 2 2 1 3 1 1 1 2 2 1 8 2 2 1 5 3 2 1 4 4 4 5 2 7 5 1 Output: 32 //7+1+8+5+4+7=32
hide comments
candyzack:
20181004 14:32:46
What is the complexity of the DP? 

mayank_75:
20180903 12:27:43
can somebody help me with the logic, I am new to dynamic programming. Just tell me the pattern, I am not able to figure out the pattern.


identity_1x:
20180831 22:11:26
Input are malformed. Tried everything in java to accept inputs got RTE. Same logic got accepted in CPP. 

nobody550:
20180823 16:10:04
AC in one go!!!! Good question for beginner, try edit distance..... 

ayusofayush:
20180723 21:21:46
Gotcha!!


castor21:
20180701 07:18:28
AC IN SUMMER . THANDI HAWA. 

r210397:
20180629 12:05:07
don't try the question on python the input is malformed


mag1x_:
20180627 10:21:51
first ever DP :3 

thisistia:
20180626 11:52:39
This really helped me grasp DP concept better. Quite same as edit distance problem, but bottomup approach.


mr_robot_rb01:
20180612 14:02:47
AC in one go ...10 min 
Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  ADA95 ASM32 BASH BF C CSHARP CPP C99 CLPS LISP sbcl LISP clisp D FORTRAN HASK ICON ICK JAVA LUA NEM NICE OCAML PASGPC PASFPC PERL PHP PIKE PRLGswi PYTHON RUBY SCM qobi SCM guile ST TEXT WHITESPACE 