ds-algo-study/DS-n-Algos/Graphs/graphs.md

Just experimenting with publishing a package

# Example Graph

### Visual Aid

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## ![picture alt](https://s3-us-west-1.amazonaws.com/appacademy-open-assets/data_structures_algorithms/graphs/images/graphs.png)

---

### Example Code

---

```js
class GraphNode {
  constructor(val) {
    this.val = val;
    this.neighbors = [];
  }
}

let a = new GraphNode("a");
let b = new GraphNode("b");
let c = new GraphNode("c");
let d = new GraphNode("d");
let e = new GraphNode("e");
let f = new GraphNode("f");
a.neighbors = [b, c, e];
c.neighbors = [b, d];
e.neighbors = [a];
f.neighbors = [e];
```

---

---

# Basics

- A graph is **any** collection of nodes and edges.
  - Much more relaxed in structure than a tree.
- It doesn't have to have a root node (so not every node can be accessed from a single node)
- It could have cycles (a group of nodes whose paths begin and end at the same node)
- Any number of edges may leave a node

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# Ways To Reference a Graph Data Structure

## Visual Reference

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## ![picture alt](https://s3-us-west-1.amazonaws.com/appacademy-open-assets/data_structures_algorithms/graphs/images/adj_matrix_graph.png)

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## Adjacency Matrix

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The row index will corespond to the source of an edge and the column index will correspond to the edges destination.

- When the edges have a direction, `matrix[i][j]` may not be the same as `matrix[j][i]`
- It is common to say that a node is adjacent to itself so matrix[x][x] is true for any node
- Will be O(n^2) space complexity

---

### A 2D Array as the method of storing the location of Nodes

let matrix = [

|       | **A**   | **B**  | **C**  | **D**  | **E**  | **F**  |
| ----- | ------- | ------ | ------ | ------ | ------ | ------ |
| **A** | [True,  | True,  | True,  | False, | True,  | False] |
| **B** | [False, | True,  | False, | False, | False, | False] |
| **C** | [False, | True,  | True,  | True,  | False, | False] |
| **D** | [False, | False, | False, | True,  | False, | False] |
| **E** | [True,  | False, | False, | False, | True,  | False] |
| **F** | [False, | False, | False, | False, | True,  | True]  |

];

---

## Adjacency List

---

Seeks to solve the shortcomings of the matrix implementation. It uses an object where keys represent node labels and values associated with that key are the adjacent nodes.

---

```js
let graph = {
  a: ["b", "c", "e"],
  b: [],
  c: ["b", "d"],
  d: [],
  e: ["a"],
  f: ["e"],
};
```

---

# Graph Traversal

## Depth First

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### With a Node Class

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#### Node Class Example

- There may not always be a suitable root-like starting point. But in this example all the nodes can be traversed to in some way from the "f" node

```js
class GraphNode {
  constructor(val) {
    this.val = val;
    this.neighbors = [];
  }
}

let a = new GraphNode("a");
let b = new GraphNode("b");
let c = new GraphNode("c");
let d = new GraphNode("d");
let e = new GraphNode("e");
let f = new GraphNode("f");
a.neighbors = [e, c, b];
c.neighbors = [b, d];
e.neighbors = [a];
f.neighbors = [e];
```

---

---

#### Recursive Traversal

```js
function depthFirstRecur(node, visited = new Set()) {
  if (visited.has(node.val)) return;

  console.log(node.val);
  visited.add(node.val);

  node.neighbors.forEach((neighbor) => {
    depthFirstRecur(neighbor, visited);
  });
}

depthFirstRecur(f); // starting with f as it is a node that can reach all other nodes
```

#### Iterative Traversal

```js
function depthFirstIter(node) {
  let visited = new Set();
  let stack = [node];

  while (stack.length) {
    let node = stack.pop();

    if (visited.has(node.val)) continue;

    console.log(node.val);
    visited.add(node.val);

    stack.push(...node.neighbors);
  }
}

depthFirstIter(f);
```

---

---

### With an Adjacency List

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#### Adjacency List Example

Remember that the nodes are stored as strings in an array in an object.

```js
let graph = {
  a: ["b", "c", "e"],
  b: [],
  c: ["b", "d"],
  d: [],
  e: ["a"],
  f: ["e"],
};
```

---

---

#### Recursive Example

```js
function depthFirstRecur(node, graph, visited = new Set()) {
  if (visited.has(node)) return;

  console.log(node);
  visited.add(node);

  graph[node].forEach((neighbor) => {
    depthFirstRecur(neighbor, graph, visited);
  });
}

depthFirstRecur("f", graph);
```

---

#### Dynamic Recursive Example

```js
function depthFirst(graph) {
  let visited = new Set();

  for (let node in graph) {
    _depthFirstRecur(node, graph, visited);
  }
}

function _depthFirstRecur(node, graph, visited) {
  if (visited.has(node)) return;

  console.log(node);
  visited.add(node);

  graph[node].forEach((neighbor) => {
    _depthFirstRecur(neighbor, graph, visited);
  });
}

depthFirst(graph);
```