A directed acyclic graph (DAG) is a graph which doesn’t contain a cycle and has directed edges. We are given a DAG, we need to clone it, i.e., create another graph that has copy of its vertices and edges connecting them.
Input : 0 - - - > 1 - - - -> 4 | / \ ^ | / \ | | / \ | | / \ | | / \ | | / \ | v v v | 2 - - - - - - - - -> 3 Output : Printing the output of the cloned graph gives: 0-1 1-2 2-3 3-4 1-3 1-4 0-2
To clone a DAG without storing the graph itself within a hash (or dictionary in Python). To clone, it we basically do a depth-first traversal of the nodes, taking original node’s value and initializing new neighboring nodes with the same value, recursively doing, till the original graph is fully traversed. Below is the recursive approach to cloning a DAG (in Python). We make use of dynamic lists in Python, append operation to this list happens in constant time, hence, fast and efficient initialization of the graph.
Graph Before Cloning:- edge 0x7fa03dd43878-0x7fa03dd43908:0-1 edge 0x7fa03dd43908-0x7fa03dd43950:1-2 edge 0x7fa03dd43950-0x7fa03dd43998:2-3 edge 0x7fa03dd43998-0x7fa03dd439e0:3-4 edge 0x7fa03dd43908-0x7fa03dd43998:1-3 edge 0x7fa03dd43908-0x7fa03dd439e0:1-4 edge 0x7fa03dd43878-0x7fa03dd43950:0-2 Cloning Process Starts Cloning Process Completes. Graph After Cloning:- edge 0x7fa03dd43a28-0x7fa03dd43a70:0-1 edge 0x7fa03dd43a70-0x7fa03dd43ab8:1-2 edge 0x7fa03dd43ab8-0x7fa03dd43b00:2-3 edge 0x7fa03dd43b00-0x7fa03dd43b48:3-4 edge 0x7fa03dd43a70-0x7fa03dd43b90:1-3 edge 0x7fa03dd43a70-0x7fa03dd43bd8:1-4 edge 0x7fa03dd43a28-0x7fa03dd43c20:0-2
Creating the DAG by appending adjacent edges to the vertex happens in O(1) time. Cloning of the graph takes O(E+V) time.
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- Euler Circuit in a Directed Graph
- Detect Cycle in a Directed Graph
- Find if there is a path between two vertices in a directed graph