Divide and Conquer

Divide the problems into sub problems
Conquer sub problems recursively
Combine solutions

It is an algorithm design technique.

Examples

Merge sort

Binary search

Find x in sorted array
Only have one sub problem

X to the power of n

Fibonacci numbers

Bottom up algorithm: Compute F0, F1, …Fn O(n)
Recursive squaring
- Matrix squaring O(lgn)

Exponential time is bad, Polynomial time is good

Matrix multiplication

Naive implementation: O(n^3), 8 times matrix multiplication
Strassen algorithm: O(n^2.81), 7 times matrix multiplication