Straightest path
Tag(s):

## Algorithms, Dijkstra's algorithm, Easy-Medium, Graph, Shortest path problem

Problem
Editorial
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You are playing a game on a grid of size $N \times M$. The game has the following rules:

• The grid contains cells that the player can move to. These are denoted by a period (.)
• The grid contains cells that the player cannot move to. These are denoted by an asterisk (*)
• The player starts on the cell marked with a V.
• The player has to reach the cell marked with an H.

Write a program to find the path which has the minimum number of changes in direction. Print the number of times that the player needs to turn on the path

Input format

• First line: N and M
• Next N lines: M characters (denoting the cells of the grid)

Output format

Print the minimum number of times that the player needs to turn on the required path. If no path exists, print -1.

Constraints

$1 ≤ N, M ≤ 10^{3}$

SAMPLE INPUT
5 4
V...
***.
....
.***
.H.*

SAMPLE OUTPUT
4
Explanation

For the given sample case, Wizard will take first turn at cell $(1, 4)$ , second turn at cell $(3, 4)$ ,third turn at cell $(3, 1)$, and fourth turn at cell $(5, 1)$.

Time Limit: 4,0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: Bash, C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Swift-4.1, TypeScript, Visual Basic

## CODE EDITOR

Initializing Code Editor...

## This Problem was Asked in Challenge Name

August Circuits '17

OTHER PROBLEMS OF THIS CHALLENGE
• Basic Programming > Implementation
• Algorithms > Dynamic Programming
• Math > Combinatorics