# Homework 16 February, 2022

## Focus on previous days' unsolved problems first.

1. **Rectangle Mania:**
You are given an input array of Cartesian coordinates(i.e. (x, y)). Write a program that outputs the number of rectangles formed by these coordinates.

A rectangle must have its four corners amongst the input coordinates in order to be counted. We only care about rectangles parallel to the x/y axes, meaning you won't have to worry about 20/30/45 deg rotated rectangles etc.

**Input and Output:**

1.

    [
        [0, 0],
        [0, 1],
        [1, 1],
        [1, 0],
        [2, 1],
        [2, 0]
    ]

    3

2.

    [
        [0, 0],
        [0, 1],
        [1, 1],
        [1, 0],
        [2, 1],
        [2, 0],
        [3, 1],
        [3, 0],
        [1, 3],
        [3, 3],
        [0, -4],
        [3, -4],
        [1, -3],
        [3, -3],
        [-1, 0],
        [-10, 0],
        [-1, -1],
        [2, -2],
        [0, -1],
        [1, -4],
        [-10, -4]
    ]

    23

3.

    [
        [0, 0],
        [0, 1],
        [1, 0],
        [2, 1],
        [1, 3],
        [3, 3],
        [0, -4],
        [3, -5],
        [1, -3],
        [3, -2],
        [-1, 0],
        [-10, 0],
        [-1, -1],
        [2, -2]
    ]

    0

2. **Generating DOT (gv) Files from graph/tree**:
Consult the wiki and documentation for learning about syntax. For a DOT file named `graph_of_dfs.gv`, running the command

    dot -Tpng -o image_of_graph.png graph_of_dfs.gv

will create a png image file named `image_of_graph.png`.

Try to modify your previous codes (related to graph) to also output gv files. Some examples:

- Adjacency List Input Array from **Cycle In Graph** problem.
- DFS tree from your recursive DFS function in **Cycle In Graph** problem. May also try to color back edge to highlight it.
- Family Tree from **Youngest Common Ancestor** problem. May also try to color `descendantOne` and `descendantTwo` to highlight them.