An algorithm is a set of step-by-step procedures, or a set of rules to follow, for completing a specific task or solving a particular problem. Algorithms are all around us. The recipe for baking a cake, the method we use to solve a long division problem, and the process of doing laundry are all examples of an algorithm. Here’s what baking a cake might look like, written out as a list of instructions, just like an algorithm:
1. Preheat the oven
2. Gather the ingredients
3. Measure out the ingredients
4. Mix together the ingredients to make the batter
5. Grease a pan
6. Pour the batter into the pan
7. Put the pan in the oven
8. Set a timer
9. When the timer goes off, take the pan out of the oven
10. Enjoy!
Algorithmic programming
is all about writing a set of rules that instruct the computer how to perform a
task. A computer program is essentially an algorithm that tells the computer
what specific steps to execute, in what specific order, in order to carry out a
specific task. Algorithms are written using particular syntax, depending on the
programming language being used.
Types of Algorithms
Algorithms are
classified based on the concepts that they use to accomplish a task. While
there are many types of algorithms, the most fundamental types of computer science
algorithms are:
1. Divide and conquer algorithms – divide the problem into smaller
subproblems of the same type; solve those smaller problems, and combine those
solutions to solve the original problem.
2. Brute force algorithms – try all possible solutions until a
satisfactory solution is found.
3. Randomized algorithms – use a random number at least once during
the computation to find a solution to the problem.
4. Greedy algorithms – find an optimal solution at the local level
with the intent of finding an optimal solution for the whole problem.
5. Recursive algorithms – solve the lowest and simplest version of a
problem to then solve increasingly larger versions of the problem until the
solution to the original problem is found.
6. Backtracking algorithms – divide the problem into subproblems,
each which can be attempted to be solved; however, if the desired solution is
not reached, move backwards in the problem until a path is found that moves it
forward.
7. Dynamic programming algorithms – break a complex problem into a
collection of simpler subproblems, then solve each of those subproblems only
once, storing their solution for future use instead of re-computing their
solutions.
Example of an Algorithm
There are a number of
different algorithms, from simple to very complicated, that exist for solving a
Rubik’s cube. Below is just one simple algorithm. First, let’s specify a
notation to use (similar to picking a programming language).
Each of the six faces of
a Rubik’s cube can be represented by the first letter of their name:
·
U - up
·
D - down
·
L - left
·
R - right
·
F - front
·
B - back
Each face can be turned
in three different ways/directions. Using U as an example, these are
represented as:
·
U - clockwise
quarter-turn of the upper face
·
U' - counter-clockwise
quarter-turn of the upper face
·
U2 - half turn in either
direction of the upper face
Now, let’s go through
the steps in the algorithm to solve a Rubik’s Cube. Feel free to grab one of
your own and follow along!
Step 1: The Cross
1. First, flip some edges so that there is a white cross on the upper
face.
2. Apply the following turns: F, R’, D’, R, F2, R’, U, R, U’, R’, R2,
L2, U2, R2, L2.
3. The cross is now solved.
Step 2: The White Corners
1. The edges on the white face are now complete, but the corners
remain.
2. Depending on where the white-orange-green corner is in the puzzle,
apply one of the following series of turns:
1. Bottom: R’, D’, R, D (repeat until the corner moves to its correct
place)
2. Top: R’, D’, R, D (this moves the corner to the bottom; then,
follow the above instructions)
Step 3: Middle Layer Edges
1. Flip the cube so that the white is on the bottom.
2. Look for an edge that is on the top face and doesn’t have yellow
on it.
3. Perform a U-turn so that the color on the front face of the edge
matches with the center.
4. Depending on the direction that the edge could go, apply one of
the following series of turns:
1. Left: U’, L’, U, L, U, F, U’, F’
2. Right: U, R, U’, R’, U’, F’, U, F)
Step 4: Yellow Cross
1. Apply the following turns, until a yellow cross on the face
appears with the yellow center: F, R, U, R’, U’, F’.
2. If there is an “L” shape, where the two yellow pieces showing are
adjacent to each other, apply the following turns: F, U, R, U’, R’, F’.
3. If there is a “Line” shape, which is horizontal, apply the
following turns: F, R, U, R’, U’, F’.
Step 5: Sune and Antisune
1. Look at the face with the yellow center.
2. Depending on the below contingencies, apply one of the following
series of turns:
1. If there is only one oriented corner: R, U, R’, U, R, U2, R’
(repeat until the desired position is attained)
2. There is one oriented corner and one right-facing corner: U2, R, U2,
R’, U’, R, U’, R’
Step 6: Finishing the puzzle
1. Look for sets of “headlights” (two stickers of the same color in
the same row, separated by a sticker of a different color).
2. Depending on how many there are, apply one of the following series
of turns:
1. If there are a set of headlights on each side: R, U’, R, U, R, U,
R, U’, R’, U’, R2
2. Otherwise: R’, F, R’, B2, R, F’, R’, B2, R2
Sorting Algorithms
A sorting algorithm is
an algorithm that puts elements of a list in a certain order, usually in
numerical or lexicographical order. Sorting is often an important first step in
algorithms that solves more complex problems. There are a large number of sorting
algorithms, each with their own benefits and costs. Below, we will focus on
some of the more famous sorting algorithms.
1. Linear sort: Find the smallest element in the list to be sorted,
add it to a new list, and remove it from the original list. Repeat this until
the original list is empty.
2. Bubble sort: Compare the first two elements in the list, and if
the first is greater than the second, swap them. Repeat this with every pair of
adjacent elements in the list. Then, repeat this process until the list is fully
sorted.
3. Insertion sort: Compare each element in the list to all the prior
elements until a smaller element is found. Swap these two elements. Repeat this
process until the list is fully sorted.
Where Algorithms are Used in Computer Science?
Algorithms are used in
every part of computer science. They form the field's backbone. In computer
science, an algorithm gives the computer a specific set of instructions, which
allows the computer to do everything, be it running a calculator or running a
rocket. Computer programs are, at their core, algorithms written in programming
languages that the computer can understand. Computer algorithms play a big role
in how social media works: which posts show up, which ads are seen, and so on.
These decisions are all made by algorithms. Google’s programmers use algorithms
to optimize searches, predict what users are going to type, and more. In
problem-solving, a big part of computer programming is knowing how to formulate
an algorithm.
Why are Algorithms Important to Understand?
Algorithmic thinking, or
the ability to define clear steps to solve a problem, is crucial in many
different fields. Even if we’re not conscious of it, we use algorithms and
algorithmic thinking all the time. Algorithmic thinking allows students to
break down problems and conceptualize solutions in terms of discrete steps.
Being able to understand and implement an algorithm requires students to
practice structured thinking and reasoning abilities.
This article originally appeared on junilearning.com
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