Week 5: Exercises

1. Closest Points

Write a program that reads a series of points, one per line. Each point will consist of N floating-point coordinates separated by spaces, for some N ≥ 2. It is guaranteed that all points will have the same number of coordinates. Determine which two points are closest to each other. Write those points, along with the distance rounded to 1 decimal point. For example, if the input is

0.0 0.0
4.0 3.0
20.0 20.0

then the output will be

Points (0.0, 0.0) and (4.0, 3.0) are closest, with distance 5.0

2. Letter Histogram

Write a program that reads a series of input lines and determines how many times each letter A-Z appears in the input. You should ignore case, considering 'a' and 'A' to be the same letter. The input text is guaranteed to contain at least one letter, and will not contain any accented characters such as 'ř'.

The program should print the most frequent letter with a count of its occurrences. It should also print a histogram showing how many times each letter occurred in the input. If a letter occurs 1-3 times, print a single *. If it occurs 4-6 times, print two asterisks (**), and so on.

Sample input:

The quick fox jumped over the lazy dog.
Then the dog got up and jumped over the fox.

Sample output:

Most frequent letter: e (9)

a: *
b: 
c: *
d: **
e: ***
f: *
g: *
h: **

…

3. Column with Largest Number

Write a program that reads a square matrix of integers. The program should print the largest value in the matrix and the column number that contains it.

Input:

2 8 3
9 6 7
0 3 -1

Output:

Column 1 contains 9.

4. Symmetric Matrix

A matrix M is symmetric if M_ij = M_ji for all i and j. For example, here is a symmetric matrix:

1 2 3
2 5 4
3 4 6

Write a function that takes a square matrix M represented as a list of lists, and returns True if the matrix is symmetric.

5. Identity Matrix

The identity matrix of size N x N contains ones along its main diagonal, and zeroes everywhere else. For example, here is the identity matrix of size 4 x 4:

Write a function identity_matrix(n) that returns the identity matrix of size n x n, represented as a list of lists.

6. Largest Row or Column Sum

Write a program that reads a square matrix of integers. The program should print the largest sum of any row or column in the matrix.

Input:

Output: