🧩 How Algorithms Solve Computational Problems
1. Problem Understanding
- An algorithm starts by clearly defining the problem and the desired output.
- Example: Sorting a list of numbers in ascending order.
2. Input and Output
- Algorithms take some input data.
- They produce an output that solves the problem.
Example:
Input: [5, 3, 8, 1]
Output: [1, 3, 5, 8] (sorted list)
3. Step-by-Step Instructions
- Algorithms break the problem down into finite, clear, and ordered steps.
- Each step describes an operation (like comparing two numbers, swapping elements).
4. Effectiveness
- Steps must be simple enough to be performed exactly and in a finite amount of time.
- The algorithm must terminate after a finite number of steps.
5. Efficiency
- Algorithms aim to solve problems using as few resources as possible:
- Time complexity: How fast the algorithm runs (speed).
- Space complexity: How much memory it uses.
6. Correctness
- A good algorithm produces the correct output for all valid inputs.
- It handles edge cases and invalid inputs gracefully.
7. Types of Algorithms
- Sorting algorithms (e.g., QuickSort, MergeSort)
- Searching algorithms (e.g., Binary Search)
- Graph algorithms (e.g., Dijkstra’s shortest path)
- Dynamic programming for optimization problems
- Divide and conquer, greedy algorithms, etc.
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