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.
Given the values of h and w, and the number of philosopher’s stones on each tile, write a program to compute the maximum possible number of philosopher’s stones Harry can grab in one single trip from the first row to the last row.

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 i-th line of these, specifies the number of philosopher’s stones in each tile of the i-th 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
Akshay Aradhya: 2015-07-18 22:28:48

Ahh.. DFS+DP :) Beautiful Problem

Akshay Aradhya: 2015-07-18 22:28:09

Got WA because of noob problems statement.One part of the problem says :
"Each tile has 1 to 100 stones on it"

The other part says :
"m (0<=m<=100) is the number of philosopher’s stones on that tile"

I saw 1 to 100 and got WA.
Please Update Problem Statement.

Obliterator: 2015-07-17 18:57:42

This question is for educational purposes only. In fact, there was only one philosophers stone which was destroyed by Dumbledore to stop Voldemort from achieving immortality.

ankit kumar: 2015-07-04 06:10:38

@hareen your k value goes beyond testcases in printing answer
PS: check scope for each test case

Amit Doshi: 2015-07-03 11:46:34

Problem Setter, please correct the input format. I wasted half an hour over it inspite of getting correct solution. Its still not corrected. Cant even use Scanner class in Java. I did it btw.

Last edit: 2015-07-03 11:47:45
hareesh: 2015-07-02 06:37:56

can someone say me what is wrong with my code
http://ideone.com/zUHpG9

ani_991: 2015-06-28 17:06:20

Can't feel any better than this, my first DP ! :D

r0bo_dart: 2015-06-26 11:18:03

same as MISERMAN... after that try WPC4F ... By the way AC at a go :D

vasayashwanth: 2015-06-23 06:27:28

recursion causes TLE......just use memoization

Marcin: 2015-06-10 18:47:27

"""The integers are separated by a space character""" -- it's not true. There are 1+ space characters between integers in the test cases.


Added by:Paritosh Aggarwal
Date:2009-02-21
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 PAS-GPC PAS-FPC PERL PHP PIKE PRLG-swi PYTHON RUBY SCM qobi SCM guile ST TEXT WHITESPACE