Algorithms form the core of computer science and software engineering. An algorithm is a step‑by‑step procedure for solving a specific problem or performing a computation.
What Is an Algorithm?
An algorithm can be expressed in natural language, pseudocode, flowcharts, or a programming language. The essential characteristics are:
- Finite: It must terminate after a limited number of steps.
- Definitive: Each step is precisely defined.
- Input: It may have zero or more inputs.
- Output: It produces at least one output.
- Effectiveness: Each operation is basic enough to be performed exactly.
Why Study Algorithms?
Understanding algorithms enables you to:
- Design efficient solutions that scale.
- Predict performance and resource consumption.
- Choose the right data structures for a given problem.
- Communicate solutions clearly to other engineers.
Algorithm Classification
Algorithms can be grouped by the problems they solve or the techniques they use. Below is a high‑level classification:
| Category | Typical Problems | Representative Algorithms |
|---|---|---|
| Sorting | Arrange items in order | QuickSort, MergeSort, HeapSort |
| Searching | Find items in a collection | Binary Search, Depth‑First Search |
| Graph | Traverse or optimize networks | Dijkstra, Bellman‑Ford, A* |
| Dynamic Programming | Optimization with overlapping subproblems | Knapsack, Floyd‑Warshall |
| Greedy | Make locally optimal choices | Prim’s MST, Huffman Coding |
Complexity Analysis
The efficiency of an algorithm is measured using asymptotic notation. The two most common measures are:
- Time Complexity: How the running time grows with input size.
Common notations: O(1), O(log n), O(n), O(n log n), O(n²). - Space Complexity: How the memory usage grows with input size.
Example: Analyzing Insertion Sort
Insertion sort has the following characteristics:
- Best case (already sorted):
O(n) - Average and worst case:
O(n²) - Space:
O(1)(in‑place)
Pseudocode
function insertionSort(A)
for i ← 1 to length(A) - 1
key ← A[i]
j ← i - 1
while j ≥ 0 and A[j] > key
A[j + 1] ← A[j]
j ← j - 1
A[j + 1] ← keyImplementation in Python
def insertion_sort(arr):
for i in range(1, len(arr)):
key = arr[i]
j = i - 1
while j >= 0 and arr[j] > key:
arr[j + 1] = arr[j]
j -= 1
arr[j + 1] = key
return arrImplementation in Java
public static void insertionSort(int[] arr) {
for (int i = 1; i < arr.length; i++) {
int key = arr[i];
int j = i - 1;
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
j--;
}
arr[j + 1] = key;
}
}Implementation in C++
void insertionSort(vector<int>& arr) {
for (size_t i = 1; i < arr.size(); ++i) {
int key = arr[i];
int j = i - 1;
while (j >= 0 && arr[j] > key) {
arr[j + 1] = arr[j];
--j;
}
arr[j + 1] = key;
}
}Common Algorithmic Paradigms
Divide and Conquer
The problem is divided into sub‑problems, each solved recursively, and the solutions are combined. Example: MergeSort.
Dynamic Programming
Builds up solutions to larger sub‑problems from previously solved smaller sub‑problems, storing intermediate results to avoid recomputation.
Greedy Algorithms
Makes the locally optimal choice at each step with the hope of finding a global optimum. Example: Huffman coding.
Backtracking
Explores all possible configurations by building a solution incrementally and abandoning a partial solution (“backtrack”) as soon as it is determined that it cannot lead to a valid complete solution. Example: N‑Queens problem.
“The most important property of an algorithm is its correctness; efficiency comes next.” – Robert Sedgewick
Practical Tips for Algorithm Design
- Start by clearly defining the input, output, and constraints.
- Choose the appropriate data structure before designing the algorithm.
- Write pseudocode first to capture the logic without language syntax.
- Analyze both time and space complexity early in the design process.
- Test with edge cases such as empty inputs, maximum size, and duplicate values.
Further Reading & Resources
- Cormen, Thomas H., et al. Introduction to Algorithms, 4th Edition.
- Sedgewick, Robert & Wayne, Kevin. Algorithms, 4th Edition.
- Khan Academy – Algorithms playlist.
🎥 Video
Q: What is the difference between an algorithm and a program?
A: An algorithm is a language‑independent, abstract procedure for solving a problem, while a program is a concrete implementation of one or more algorithms in a specific programming language.
Q: Why is Big‑O notation important?
A: Big‑O provides a high‑level, machine‑independent way to compare the scalability of algorithms, helping engineers choose solutions that perform well as data grows.
Q: Can I use a slower algorithm if my data set is small?
A: Yes. For small inputs, constant factors dominate, so a simpler O(n²) algorithm may be easier to implement and maintain than a more complex O(n log n) solution.
Q. What is the worst‑case time complexity of quicksort when the pivot is always the smallest element?
- O(n log n)
- O(n²)
- O(n)
- O(log n)
Answer: O(n²)
Choosing the smallest element as pivot leads to highly unbalanced partitions, resulting in quadratic behavior.
Q. Which algorithmic paradigm is used by Dijkstra’s shortest‑path algorithm?
- Greedy
- Dynamic Programming
- Divide and Conquer
- Backtracking
Answer: Greedy
Dijkstra repeatedly selects the vertex with the smallest tentative distance, a classic greedy choice.