AMR11A  Magic Grid
Thanks a lot for helping Harry Potter in finding the Sorcerer's Stone of Immortality in October. Did we not tell you that it was just an online game ? uhhh! now here is the real onsite task for Harry. You are given a magrid S ( a magic grid ) having R rows and C columns. Each cell in this magrid has either a Hungarian horntail dragon that our intrepid hero has to defeat, or a flask of magic potion that his teacher Snape has left for him. A dragon at a cell (i,j) takes away S[i][j] strength points from him, and a potion at a cell (i,j) increases Harry's strength by S[i][j]. If his strength drops to 0 or less at any point during his journey, Harry dies, and no magical stone can revive him.
Harry starts from the topleft corner cell (1,1) and the Sorcerer's Stone is in the bottomright corner cell (R,C). From a cell (i,j), Harry can only move either one cell down or right i.e., to cell (i+1,j) or cell (i,j+1) and he can not move outside the magrid. Harry has used magic before starting his journey to determine which cell contains what, but lacks the basic simple mathematical skill to determine what minimum strength he needs to start with to collect the Sorcerer's Stone. Please help him once again.
Input (STDIN):
The first line contains the number of test cases T. T cases follow. Each test case consists of R C in the first line followed by the description of the grid in R lines, each containing C integers. Rows are numbered 1 to R from top to bottom and columns are numbered 1 to C from left to right. Cells with S[i][j] < 0 contain dragons, others contain magic potions.
Output (STDOUT):
Output T lines, one for each case containing the minimum strength Harry should start with from the cell (1,1) to have a positive strength through out his journey to the cell (R,C).
Constraints:
1 ≤ T ≤ 5
2 ≤ R, C ≤ 500
10^3 ≤ S[i][j] ≤ 10^3
S[1][1] = S[R][C] = 0
Sample Input:
3
2 3
0 1 3
1 2 0
2 2
0 1
2 0
3 4
0 2 3 1
1 4 0 2
1 2 3 0
Sample Output:
2
1
2
Explanation:
Case 1 : If Harry starts with strength = 1 at cell (1,1), he cannot maintain a positive strength in any possible path. He needs at least strength = 2 initially.
Case 2 : Note that to start from (1,1) he needs at least strength = 1.
hide comments
i_am_looser:
20150608 22:08:07
Good question ..... try to solve it using binary search also 

!(loGic):
20150601 07:04:13
Test Cases are weak. for


novice_dhunnu:
20150305 07:39:19
Last edit: 20150308 11:14:33 

Ankit Sultana:
20150202 09:02:05
Phew! Great Question!!


S:
20150101 07:40:37
T*N^2log(10^6) TLE .. TLE .. TLE frustrate 

swordfish12:
20141230 12:40:54
dp never ceases to amaze me :) 

Aditya Joshi:
20140929 14:48:47
Tricky 

ayush:
20140717 17:34:19
Alcatraz is right 

RAMSDEN:
20140418 09:40:37
100th AC :) 

AlcatraZ:
20140403 07:14:04
VERY Tricky.. The DP state is different from what you are thinking.. ;) 
Added by:  Varun Jalan 
Date:  20111215 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Anil Kishore  ICPC Asia regionals, Amritapuri 2011 