All Tracks Algorithms Graphs Min-cut Problem

Edge Destruction
Tag(s):

Algorithms, Graph Theory, Medium

Problem
Editorial
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Given a graph having $$N$$ vertices and $$M$$ bidirectional edges, with each edge having some length and some destruction cost. You have to increase the length of the shortest path between vertex $$1$$ and vertex $$N$$, for that you can destroy some edges. Find the minimum cost of doing it.

Input Format:
First line consists of two space separated integers denoting $$N$$ and $$M$$.
Following $$M$$ lines consists of four space separated integers $$X \; Y \; D \; C$$ denoting that there is an edge between vertex $$X$$ and $$Y$$ having length $$D$$ and destruction cost $$C$$.

Output Format:
Print the required answer.

Constraints:
$$2 \le N \le 1000$$
$$1 \le M \le 4 \times 10^5$$
$$1 \le X, Y \le N$$
$$1 \le D, C \le 1000000$$

SAMPLE INPUT
4 6
1 2 4 1
1 3 8 6
1 4 1 8
2 3 8 8
2 4 5 7
3 4 7 5
SAMPLE OUTPUT
8
Explanation

Currently the shortest path between $$1$$ and $$4$$ is of length $$1$$, so we delete this vertex at a cost of $$8$$, so that the length of shortest path increases to $$9$$.

Time Limit: 1.0 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: C, C++, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Scala 2.11.8, Swift, Visual Basic

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This Problem was Asked in

HackerEarth

Challenge Name

HackerEarth Collegiate Cup - Mirror Round

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