Algorithm Complexity Chart
Visual comparison of algorithm time complexities with growth rates.
📊 Complexity Growth Visualization
📈 Growth Rate Examples (n = 1000)
Understanding Algorithm Complexity Charts
Algorithm complexity charts visualize how different time complexities scale with input size. This visual representation makes it easier to understand why O(log n) is vastly more efficient than O(n²) for large inputs.
The chart above shows relative growth rates from the most efficient O(1) constant time to the least efficient O(n!) factorial time. Understanding these differences is crucial for algorithmic problem solving.
Reading the Chart
Bar length represents relative computational cost. Constant time O(1) is always minimal. Logarithmic O(log n) grows slowly. Linear O(n) scales directly with input. Quadratic O(n²) and above become impractical for large inputs.
Practical Implications
An O(n²) algorithm processing 1 million items requires 1 trillion operations. An O(n log n) algorithm needs only about 20 million. This difference can mean seconds versus hours of processing time.
Optimization Target
Always aim for the lowest complexity possible. Many problems have optimal solutions. Binary search (O(log n)) replaces linear search (O(n)). Merge sort (O(n log n)) replaces bubble sort (O(n²)).