Mathematical AlgorithmsBeginner

Pascal's Triangle

Triangular array of binomial coefficients where each number is the sum of the two numbers directly above it. Named after Blaise Pascal (1623-1662), though known to mathematicians centuries earlier. Demonstrates beautiful mathematical patterns including binomial expansion, combinatorics, and connections to Fibonacci numbers.

#mathematical#combinatorics#binomial-coefficients#dynamic-programming

Complexity Analysis

Time (Average)

O(n²)

Expected case performance

Space

O(n²)

Memory requirements

Time (Best)

O(n²)

Best case performance

Time (Worst)

O(n²)

Worst case performance

Number of Rows: 8

Step: 1 / 0

Animation Speed500ms

SlowFast

Keyboard Shortcuts

Space Play/Pause← → StepR Reset1-4 Speed

Real-time Statistics

Algorithm Performance Metrics

Progress0%

Comparisons

Swaps

Array Accesses

Steps

1/ 0

Algorithm Visualization

Step 1 of 0

Initialize array to begin

Default

Comparing

Swapped

Sorted

Code Execution

Currently executing

Previously executed

Implementation

Related Algorithms

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Sieve of Eratosthenes

Beginner

Find all prime numbers up to n by iteratively marking composites. Named after Eratosthenes of Cyrene (c. 276-194 BC).

O(n log log n)

O(n)

mathematicalprime-numbers

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Euclidean Algorithm (GCD)

Beginner

Ancient algorithm from around 300 BC that efficiently computes the greatest common divisor of two integers. Based on the principle that GCD(a, b) = GCD(b, a mod b). One of the oldest algorithms in continuous use, forming the foundation of number theory, cryptography, and fraction simplification.

O(log min(a, b))

O(1)

mathematicalnumber-theory

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Extended Euclidean Algorithm

Intermediate

Extends the Euclidean algorithm to find integers x and y satisfying Bézout's identity: ax + by = GCD(a, b). Not only computes GCD but also finds the coefficients of linear combinations. Fundamental to modular arithmetic, RSA cryptography, and solving linear Diophantine equations.

O(log min(a, b))

O(1)

mathematicalnumber-theory

Start Learning

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