12 Examples of Algorithm

Computers use Algorithms to do things like find the biggest piece of pizza to share (Euclid’s GCD), organize large lists (quicksort), and understand the sounds in music (discrete Fourier transforms).

image showing Examples of Algorithm

They also help companies make more money (simplex optimization), speed up computer calculations (Strassen’s method), and make sure things work properly (Gaussian elimination, numerical integration, minimum spanning trees, Dijkstra, SHA-256).

Examples of Algorithm

Here are 10 examples of algorithms in math:

1. Euclid’s Algorithm

One example of an algorithm is Euclid’s GCD, which is a way of finding the largest number that divides two other numbers. Euclid’s algorithm finds the greatest common factor of two numbers. It works by repeatedly dividing larger numbers by smaller ones until finding the highest factor they share.

2. Quicksort Algorithm

Another example of an algorithm is Quicksort. The quicksort algorithm sorts data sets by dividing them into smaller partitions. It picks a pivot value then orders other elements by being higher or lower than the pivot.

3. Integer Factorization

Integer factorization finds the prime numbers that multiply together to get a target composite integer. This aids breaking large numbers into simpler factors.

4. Discrete Fourier Transform

This algorithm converts data between time and frequency domains. It identifies frequency components present in patterns across time intervals.

5. Simplex Algorithm

The simplex algorithm solves constrained optimization problems efficiently. It provides the most favorable solution fitting preset requirements.

6. Strassen Matrix Multiplication

Strassen’s method multiplies large matrices faster than normal methods. It divides matrices into smaller pieces, computes products in chunks then sums them up efficiently.

7. Newton-Raphson Root Finding

The Newton-Raphson algorithm approximates real roots and zeroes of mathematical functions. It uses tangent lines and derivative values to estimate points where curves hit the x-axis.

8. Gaussian Elimination

This technique solves systems of linear equations which model real problems. It eliminates variables through successive substitution to reduce equations to trivial forms with simpler variables.

9. Newton-Cotes Integration

Newton-Cotes formulas estimate the area under curves to numerically define integrals. Using point intervals and fitted assumptions, they approximate integrands with areas of known geometric shapes.

Financial analysts apply numerical integration to forecast movements from changing indicators and data trends. Estimating risk, returns and changing liabilities involves statistically integrating unpredictable variables.

10. Minimum Spanning Tree

This determines the shortest pathway route connecting multiple points on a plane using graph theory. It saves infrastructure costs in applications.

11. Dijkstra’s Shortest Path Algorithm

Dijkstra finds the minimum path length between two graph nodes evaluating one node at a time to its neighbors. It incrementally builds shortest routes.

12. SHA-256 Cryptographic Hash

The SHA algorithm generates a hash identifier string from any digital input. Hashes uniquely identify files and messages to protect authenticity and check tampering.

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