In this section, we will explore practical applications of ALGOL through detailed case studies and projects. This will help you understand how to apply the concepts you've learned in real-world scenarios. Each case study will include a problem statement, a step-by-step solution, and a discussion of the results. Additionally, we will provide project ideas for you to work on independently.
Case Study 1: Sorting Algorithms
Problem Statement
Implement and compare the performance of different sorting algorithms (e.g., Bubble Sort, Quick Sort, and Merge Sort) in ALGOL.
Step-by-Step Solution
Bubble Sort
begin
integer array[1:10];
integer i, j, temp;
for i := 1 step 1 until 10 do
read(array[i]);
for i := 1 step 1 until 9 do
for j := 1 step 1 until 10 - i do
if array[j] > array[j + 1] then
temp := array[j];
array[j] := array[j + 1];
array[j + 1] := temp;
end if;
end for;
end for;
for i := 1 step 1 until 10 do
write(array[i]);
end for;
end;Explanation:
- The program reads 10 integers into an array.
- It then uses nested loops to compare and swap adjacent elements if they are in the wrong order.
- Finally, it prints the sorted array.
Quick Sort
procedure quicksort(array, low, high);
integer array[], low, high;
begin
integer pivot, i, j, temp;
if low < high then
pivot := array[low];
i := low;
j := high;
while i < j do
while array[i] <= pivot and i < high do
i := i + 1;
end while;
while array[j] > pivot do
j := j - 1;
end while;
if i < j then
temp := array[i];
array[i] := array[j];
array[j] := temp;
end if;
end while;
array[low] := array[j];
array[j] := pivot;
quicksort(array, low, j - 1);
quicksort(array, j + 1, high);
end if;
end;
end;
begin
integer array[1:10];
integer i;
for i := 1 step 1 until 10 do
read(array[i]);
end for;
quicksort(array, 1, 10);
for i := 1 step 1 until 10 do
write(array[i]);
end for;
end;Explanation:
- The
quicksortprocedure is defined to sort the array using the Quick Sort algorithm. - The main program reads 10 integers into an array, calls the
quicksortprocedure, and then prints the sorted array.
Merge Sort
procedure mergesort(array, low, high);
integer array[], low, high;
procedure merge(array, low, mid, high);
integer array[], low, mid, high;
integer i, j, k, temp[1:10];
begin
i := low;
j := mid + 1;
k := low;
while i <= mid and j <= high do
if array[i] <= array[j] then
temp[k] := array[i];
i := i + 1;
else
temp[k] := array[j];
j := j + 1;
end if;
k := k + 1;
end while;
while i <= mid do
temp[k] := array[i];
i := i + 1;
k := k + 1;
end while;
while j <= high do
temp[k] := array[j];
j := j + 1;
k := k + 1;
end while;
for i := low step 1 until high do
array[i] := temp[i];
end for;
end;
end;
begin
if low < high then
integer mid;
mid := (low + high) div 2;
mergesort(array, low, mid);
mergesort(array, mid + 1, high);
merge(array, low, mid, high);
end if;
end;
end;
begin
integer array[1:10];
integer i;
for i := 1 step 1 until 10 do
read(array[i]);
end for;
mergesort(array, 1, 10);
for i := 1 step 1 until 10 do
write(array[i]);
end for;
end;Explanation:
- The
mergesortprocedure is defined to sort the array using the Merge Sort algorithm. - The
mergeprocedure is used to merge two sorted halves of the array. - The main program reads 10 integers into an array, calls the
mergesortprocedure, and then prints the sorted array.
Discussion
- Bubble Sort is simple but inefficient for large datasets.
- Quick Sort is efficient but has a worst-case time complexity of O(n^2).
- Merge Sort is efficient and has a consistent time complexity of O(n log n), but it requires additional memory for the temporary array.
Case Study 2: Matrix Multiplication
Problem Statement
Implement matrix multiplication in ALGOL.
Step-by-Step Solution
begin
integer A[1:3, 1:3], B[1:3, 1:3], C[1:3, 1:3];
integer i, j, k;
for i := 1 step 1 until 3 do
for j := 1 step 1 until 3 do
read(A[i, j]);
end for;
end for;
for i := 1 step 1 until 3 do
for j := 1 step 1 until 3 do
read(B[i, j]);
end for;
end for;
for i := 1 step 1 until 3 do
for j := 1 step 1 until 3 do
C[i, j] := 0;
for k := 1 step 1 until 3 do
C[i, j] := C[i, j] + A[i, k] * B[k, j];
end for;
end for;
end for;
for i := 1 step 1 until 3 do
for j := 1 step 1 until 3 do
write(C[i, j]);
end for;
end for;
end;Explanation:
- The program reads two 3x3 matrices, A and B.
- It then multiplies these matrices to produce matrix C.
- Finally, it prints the resulting matrix C.
Discussion
- Matrix multiplication is a fundamental operation in many scientific and engineering applications.
- This example demonstrates nested loops and array manipulation in ALGOL.
Project Ideas
Project 1: Simple Database Management System
- Objective: Create a simple database management system that can store, retrieve, update, and delete records.
- Key Concepts: File handling, data structures (records), and user interface.
Project 2: Text Editor
- Objective: Develop a basic text editor with functionalities like opening, editing, saving, and searching text files.
- Key Concepts: File handling, string manipulation, and user interface.
Project 3: Scientific Calculator
- Objective: Implement a scientific calculator that can perform advanced mathematical operations like trigonometry, logarithms, and exponentiation.
- Key Concepts: Functions, user input/output, and mathematical operations.
Project 4: Game Development
- Objective: Create a simple game (e.g., Tic-Tac-Toe or Snake) using ALGOL.
- Key Concepts: Control structures, arrays, and user interface.
Conclusion
In this section, we explored practical applications of ALGOL through case studies and project ideas. By implementing sorting algorithms and matrix multiplication, you gained hands-on experience with ALGOL's capabilities. The project ideas provided will help you further apply your knowledge and develop more complex applications. Continue practicing and experimenting with ALGOL to enhance your programming skills.