Similar to <dfn>breadth-first search</dfn>, here we will learn about another graph traversal algorithm called <dfn>depth-first search</dfn>.
Whereas the breadth-first search searches incremental edge lengths away from the source node, <dfn>depth-first search</dfn> first goes down a path of edges as far as it can.
Once it reaches one end of a path, the search will backtrack to the last node with an un-visited edge path and continue searching.
Visually, this is what the algorithm is doing where the top node is the starting point of the search.
A simple output of this algorithm is a list of nodes which are reachable from a given node. So when implementing this algorithm, you'll need to keep track of the nodes you visit.
</section>
## Instructions
<sectionid='instructions'>
Write a function <code>dfs()</code> that takes an undirected, adjacency matrix <code>graph</code> and a node label <code>root</code> as parameters. The node label will just be the numeric value of the node between <code>0</code> and <code>n - 1</code>, where <code>n</code> is the total number of nodes in the graph.
Your function should output an array of all nodes reachable from <code>root</code>.
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>1</code> should return an array with <code>0</code>, <code>1</code>, <code>2</code>, and <code>3</code>.
testString: assert.sameMembers((function() { var graph = [[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0]]; return dfs(graph, 1);})(), [0, 1, 2, 3], 'The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>1</code> should return an array with <code>0</code>, <code>1</code>, <code>2</code>, and <code>3</code>.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>1</code> should return an array with four elements.
testString: assert((function() { var graph = [[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0]]; return dfs(graph, 1);})().length === 4, 'The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>1</code> should return an array with four elements.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0]]</code> with a start node of <code>3</code> should return an array with <code>3</code>.
testString: assert.sameMembers((function() { var graph = [[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0]]; return dfs(graph, 3);})(), [3], 'The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0]]</code> with a start node of <code>3</code> should return an array with <code>3</code>.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0]]</code> with a start node of <code>3</code> should return an array with one element.
testString: assert((function() { var graph = [[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0]]; return dfs(graph, 3);})().length === 1, 'The input graph <code>[[0, 1, 0, 0], [1, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 0]]</code> with a start node of <code>3</code> should return an array with one element.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>3</code> should return an array with <code>2</code> and <code>3</code>.
testString: assert.sameMembers((function() { var graph = [[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]; return dfs(graph, 3);})(), [2, 3], 'The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>3</code> should return an array with <code>2</code> and <code>3</code>.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>3</code> should return an array with two elements.
testString: assert((function() { var graph = [[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]; return dfs(graph, 3);})().length === 2, 'The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>3</code> should return an array with two elements.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>0</code> should return an array with <code>0</code> and <code>1</code>.
testString: assert.sameMembers((function() { var graph = [[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]; return dfs(graph, 0);})(), [0, 1], 'The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>0</code> should return an array with <code>0</code> and <code>1</code>.');
- text: The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>0</code> should return an array with two elements.
testString: assert((function() { var graph = [[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]; return dfs(graph, 0);})().length === 2, 'The input graph <code>[[0, 1, 0, 0], [1, 0, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]</code> with a start node of <code>0</code> should return an array with two elements.');