Arya and the Grid of Stars

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Arya is planning to go back to Winterfell. In order to reach there and survive, she must collect maximum stars from a maze. The maze is in the form of a grid of size $m \times n$. Each cell is either blank, has a star or has a stone. She starts from $(1,1)$ to reach $(m, n)$ using right and bottom moves and then she returns to $(1, 1)$ using top and left moves. The only constraint is that if she visits some cells in a particular row in the whole journey (forward and backward), then maximum distance between any pair of visited cells (forward and backward) for every row is $x$, where $x$ is given in the input. Distance between $(i, j)$ and $(i, k)$ is $k  j$. **Also note that she cannot go into the cells with a stone.** Tell the maximum stars that can be collected by Arya. ###Input:  First line will contain three integers: $m$, number of rows, $n$, number of columns and $x$, the distance constraint.  Next $m$ lines contain the grid. Each line contains '.', '*' or '#' denoting empty cell, star or stone. The cells $(1, 1)$ or $(m, n)$ can have stones. ###Output: Print the maximum number of stars that can be collected by Arya. If it is not possible to reach $(m, n)$ from $(1, 1)$, then print 1. ###Constraints  $1 \leq m, n \leq 1000$  $0 \leq x \leq 5$ ###Sample Input: 3 3 0 .*. *.* .*. ###Sample Output: 1 ###EXPLANATION: If x = 0, then it is not possible to reach 3,3 as we cannot move left in any row.. ###Sample Input: 3 3 1 .*. *.* .*. ###Sample Output: 3 ###EXPLANATION: If x = 1, then we can at most visit 2 consecutive cells in any row. Thus (0,0) => (0,1) => (1,1) => (1,2) => (2,2) => (2,1) => (1,1) => (0,1) => (0,0) OR (0,0) => (1,0) => (1,1) => (2,1) => (2,2) => (2,1) => (1,1) => (0,1) => (0,0) Note that in this case, we cannot go to (1, 2) while returning as it will lead to maximum distance of 3 between (1,0) and (1,2). ###Sample Input: 3 3 2 .*. *.* .*. ###Sample Output: 4 ###EXPLANATION: (0,0) => (0,1) => (0,2) => (1,2) => (2,2) => (2,1) => (2,0) => (1,0) => (0,0)Author:  aashu_k 
Tags  aashu_k 
Date Added:  25032019 
Time Limit:  1 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, R, COB, FS 
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