Modern computers are like biological organisms in that they are emergent systems. They are built from small parts, yet no one part is very important. The overall structure somehow make up the entity of the object. In this way, transistors can make up the computational power of a computer (even if you don’t believe it). But programers certainly do not deal with transistors when creating programs. They deal in a higher level of software, the level below the user interface that so many use. Here are a few commonly used algorithms/methods behind the basic functions on your computer
This one is self explanatory, but there are many ways to search for something. Some of them are complex, some of them are simple, but this is one of the more important algorithms. The ability to quickly find something is very useful.
The ability to sort objects into an orderly list can be useful two ways. The first way is that it makes search a lot easier (imagine trying to find a word in a dictionary that had arbitrary placement of words). The second is that the sorted list can be used for other algorithms
Finding the shortest path/best path between two objects. What do you think your GPS does?