Problem $3.$

Let $G=(V,E)$ be a graph such that each edge of $E$ is colored either blue or red. When calculating the length of a path, we count a blue edge as two edges $($a red edge is counted as I one edge, just like in a graph with no edge colors$).$ For example, a path consisting of three blue edges and three red edges has length $3*1+3*2=9.$

Describe an algorithm that receives a vertex $s$ from $V$ and finds a shortest paths tree from $s.$ This is similar to the BFS tree, except that the length of an edge is not always one. The running time should be $O(|V|+|E|).$

Hint: Use the BFS algorithm without changing it$.$ Instead, change the graph.