hello-algo/en/docs/chapter_introduction/algorithms_are_everywhere.md

Algorithms are everywhere

When we hear the word "algorithm," we naturally think of mathematics. However, many algorithms do not involve complex mathematics but rely more on basic logic, which can be seen everywhere in our daily lives.

Before formally discussing algorithms, there's an interesting fact worth sharing: you have already unconsciously learned many algorithms and have become accustomed to applying them in your daily life. Here, I will give a few specific examples to prove this point.

Example 1: Looking Up a Dictionary. In an English dictionary, words are listed alphabetically. Suppose we're searching for a word that starts with the letter r. This is typically done in the following way:

1. Open the dictionary to about halfway and check the first letter on the page, let's say the letter is m.
2. Since r comes after m in the alphabet, we can ignore the first half of the dictionary and focus on the latter half.
3. Repeat steps 1. and 2. until you find the page where the word starts with r.

=== "<1>"

=== "<2>"

=== "<3>"

=== "<4>"

=== "<5>"

Looking up a dictionary, a must-have skill for primary school students, is actually the famous "binary search" algorithm. From the perspective of data structure, we can regard the dictionary as a sorted "array"; from the perspective of algorithm, we can regard the above series of dictionary lookup operations as "binary search."

Example 2: Organizing Playing Cards. When playing cards, we need to arrange the cards in our hand in ascending order, as shown in the following process.

1. Divide the playing cards into "ordered" and "unordered" sections, assuming initially the leftmost card is already in order.
2. Take out a card from the unordered section and insert it into the correct position in the ordered section; after this, the leftmost two cards are in order.
3. Repeat step 2 until all cards are in order.

The above method of organizing playing cards is essentially the "Insertion Sort" algorithm, which is very efficient for small datasets. Insertion sort is included in the sorting functions of many programming languages.

Example 3: Making Change. Suppose we buy goods worth 69 yuan at a supermarket and give the cashier 100 yuan, then the cashier needs to give us 31 yuan in change. They would naturally complete the thought process as shown in the figure below.

1. The options are currencies smaller than 31, including 1, 5, 10, and 20.
2. Take out the largest 20 from the options, leaving 31 - 20 = 11.
3. Take out the largest 10 from the remaining options, leaving 11 - 10 = 1.
4. Take out the largest 1 from the remaining options, leaving 1 - 1 = 0.
5. Complete the change-making, with the solution being 20 + 10 + 1 = 31.

In the above steps, we make the best choice at each step (using the largest denomination possible), ultimately resulting in a feasible change-making plan. From the perspective of data structures and algorithms, this method is essentially a "Greedy" algorithm.

From cooking a meal to interstellar travel, almost all problem-solving involves algorithms. The advent of computers allows us to store data structures in memory and write code to call the CPU and GPU to execute algorithms. In this way, we can transfer real-life problems to computers and solve various complex issues in a more efficient way.

!!! tip

If concepts such as data structures, algorithms, arrays, and binary search still seem somewhat obscure, I encourage you to read on. This book will guide you step by step into the world of data structures and algorithms.