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math misc

Combinatorics

Combinatorics deals with counting and enumerating arrangements of objects. Key formulas include nCk (binomial coefficient) for combinations and Pascal's triangle for efficient computation. These techniques are essential for probability, optimization, and enumeration problems.

Use Cases

  • •Calculating probabilities in games and simulations
  • •Generating subsets and permutations for brute-force searches
  • •Dynamic programming solutions that require counting arrangements

Complexity Analysis

MetricBestAverageWorst
TimeO(n)O(n*k)O(n*k)
SpaceO(n)

Visualization

C(n, k) = C(n-1, k-1) + C(n-1, k)
Speed:1x
Build Pascal's triangle, rows 0 through 5Step 1 / 12

Implementation

Output

Click "Run Code" to see output...