Decrease-and-Conquer

Continually reduces the problem into a smaller sub-problem, until a ‘base problem’, i.e. a trivial problem is reached. Then solves this base problem and starts ‘adding the sub-problems back’. Most recursive algorithms use the decreases and conquer approach.

• Depth First Search Algorithm: Starts by reducing the graph into a subgraph of just the start node and it’s neighbours. Then it builds on this subgraph
• Breadth First Search Algorithm: Same idea as DFS
• Recursive Factorial Algorithm: $n!$ is reduced to $(n-1)!\to (n-2)!$ until the problem becomes $(n-n)!=0!=1$

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• Binary Search Algorithm
• Breadth First Search Algorithm
• Depth First Search Algorithm
• Insertion Sort
• Selection Sort

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