> For the complete documentation index, see [llms.txt](https://jenhsuan.gitbook.io/algorithm/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://jenhsuan.gitbook.io/algorithm/algorithms-in-a-nutshell/performance-and-complexity.md).

# Performance and Complexity

Performance的三個要素是時間, 空間, 網路; Complexity是用來衡量Performance的指標

## 1. Performance

* Consuming more of one resource can help consume less of another
* Measure of performance
  * Time
    * The mount of processing or number of operations code has to perform to accomplish it's objective
  * Space
    * This is both memory needed by code to store information at runtime as well as disk space needed by code for persistent storage
  * Network
    * The bandwidth code uses to pass information to client or other machines
  * Efficient code uses fewer resource along all these axes
* The amount of resource used determines code's performance

## **2. Complexity**

* Focus here is on space and time complexity
* Complexity is a measure of how resource requirement change as the size of the problem gets larger
  * 當input size 變大時, complexity很重要
  * We also focus on the worst case performance
  * What is the maximum number of basic operations that might have to be performed on the input
* The higher the complexity of a problem the lower the performance