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
kushalanand:
20160906 23:54:54
must practice for beginners like me.


lalywr:
20160903 08:20:13
that \n after every answer caused me a wa :( no recursion just memoisation ;D ad yeah , BOTTOM up Approach :) Last edit: 20160903 09:07:51 

Shravan Murali:
20160901 18:12:56
Recursive Top down approach kept giving me wrong answer , although bottom up worked :/ 

testing java:
20160822 14:26:27
Input format is bad and author should feel bad. Use Scanner instead of BufferedReader in java to avoid problems with wrong line formatting 

lalit_nit:
20160712 20:24:32
1st DP with 2D array...NO HELP...Confidence booster....Easy but still 2 hours for me...Worth solving :) 

pulkitgulati:
20160703 10:25:37
try WPC4F before this. 

madhavgaba:
20160701 21:20:01
Debut with DP....AC in one go;) 

baadshah_:
20160622 22:37:11
AC in 1 Go!Had solved similar type problem in CodeChef 

chakkriii:
20160609 09:05:27
AC in 1st go,


get_right_jr:
20160604 19:58:43
Bottomup in 0.08 in Java :)

Added by:  Paritosh Aggarwal 
Date:  20090221 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
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