# Algorithm: largest of the four

## Main Question or Discussion Point

Write an algorithm to find the largest of the four numbers A, B, C, D.

1: See if A is greater than the three of the rest, if YES, then go to Step 5
2: See if B is greater than the two of the rest, if YES, then go to Step 5
3: See if C is greater than the last one, if YES, then go to Step 5
4: The last one is the largest, proceed to Step 5 to end the algorithm
5: END

Do you find the above algorithm correct? Please let me know.

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Mark44
Mentor
That's much more complicated than it needs to be. I would pick the larger of A and B, and then the larger of C and D. Finally, I would compare the two winners. That would be the largest of all four numbers.

rcgldr
Homework Helper
I assume this takes 3 compares no matter how you do it.

Code:
lntext = "A"
ln = A
if (B > ln){
lntext = "B"
ln = B}
if (C > ln){
lntext = "C"
ln = C}
if (D > ln){
lntext = "D"
ln = D}
ouput "largest number is ", lntext

Borek
Mentor
max(max(a,b),max(c,d));

AlephZero
Homework Helper
max(max(max(a,b),c),d)

Borek's is neater for 4 variables, but this is easier to generalize to N variables.

I assume this takes 3 compares no matter how you do it.
The minimum number of compares is 3, for the same reason that in a knockout tennis tournament between n players, the number of matches played must be n-1 however you organize the competition. with "seeded players" or whatever.

Of course you can use more than the minimum number of compares - see the OP for an example!

I assume this takes 3 compares no matter how you do it.

Code:
lntext = "A"
ln = A
if (B > ln){
lntext = "B"
ln = B}
if (C > ln){
lntext = "C"
ln = C}
if (D > ln){
lntext = "D"
ln = D}
ouput "largest number is ", lntext
Thanks a lot, everyone, Mark, RCG, Borek, Aleph. Things would have been a lot difficult without your help.

I think the algorithms, which are precise and to the point, are more suited to programming-related problems. I wanted an algorithm which could also be written in the form of a simple flowchart. The simple example would be: http://upload.wikimedia.org/wikipedia/commons/9/91/LampFlowchart.svg

RCG: Could you please explain your algorithm? I don't get what these "intext", "In", etc., are. Please guide me. Thanks.

rcgldr
Homework Helper
RCG: Could you please explain your algorithm? I don't get what these "intext", "In", etc., are. Please guide me. Thanks.
ln = largest number (the value)
lntext = largest number text, to display which number was largest (A, B, C, or D)

I assume this takes 3 compares no matter how you do it.

Code:
[B][COLOR="Red"]lntext = "A"
ln = A
if (B > ln){
lntext = "B"
ln = B}[/COLOR][/B]
if (C > ln){
lntext = "C"
ln = C}
if (D > ln){
lntext = "D"
ln = D}
ouput "largest number is ", lntext
Thank you for the explanation.

This is how I interpret your first step (is it first?):
largest number text is "A" and "A" is the largest number if: B is greater than the largest number which is "A"??? Obviously as you can see this is misinterpretation. So, please help.

rcgldr
Homework Helper
This is how I interpret your first step (is it first?):
largest number text is "A" and "A" is the largest number
Correct.

if B is greater than the largest number which is "A"?
if B is greater than largest number (which is currently A), then set the largest number to the value of B and set lntext to the letter "B".

I assume this takes 3 compares no matter how you do it.

Code:
lntext = "A"
ln = A
if (B > ln){
lntext = "B"
ln = B}
Thanks. I get it now. Perhaps, there is a reason the way you have written the algorithm. I would have written it somewhat like this:
lntext = "A"
ln = A
if (B > ln){lntext = "B", ln = B}.

Is my way also correct?

Is it okay to use the shortened form "algo" for the full form "algorithm"?

Please guide me. And thanks a lot for being there to help me most of the time.

jtbell
Mentor
Code:
lntext = "A"
ln = A
if (B > ln){
lntext = "B"
ln = B}
if (C > ln){
lntext = "C"
ln = C}
if (D > ln){
lntext = "D"
ln = D}
ouput "largest number is ", lntext

Why use both text and number variables, when the original problem mentions only numbers?

Code:
input A, B, C, D;
largest = A;
if (B > largest)
{
largest = B;
}
if (C > largest)
{
largest = C;
}
if (D > largest)
{
largest = D;
}
print largest;

jtbell
Mentor
Perhaps, there is a reason the way you have written the algorithm. I would have written it somewhat like this:
lntext = "A"
ln = A
if (B > ln){lntext = "B", ln = B}.
When writing an algorithm, either version is OK. It's not intended to be compiled directly into an actual executable program, so the rules for writing out an algorithm aren't as strict as when writing it in an actual programming language. We often call this "pseudocode."

Most people probably write pseudocode that looks somewhat like whichever programming language they usually use, but doesn't have all the details that would be necessary to make a complete program in C or C++ or Java or whatever.

Is it okay to use the shortened form "algo" for the full form "algorithm"?
It's a matter of taste. I prefer to use the complete word, but you often see the short version in slangy colloquial writing. I'm old-fashioned.

When writing an algorithm, either version is OK. It's not intended to be compiled directly into an actual executable program, so the rules for writing out an algorithm aren't as strict as when writing it in an actual programming language. We often call this "pseudocode."

Most people probably write pseudocode that looks somewhat like whichever programming language they usually use, but doesn't have all the details that would be necessary to make a complete program in C or C++ or Java or whatever.

It's a matter of taste. I prefer to use the complete word, but you often see the short version in slangy colloquial writing. I'm old-fashioned.
Thanks a lot, JT. You have also helped me a lot in the past. Thanks for all the help and I hope you would continue to help me as much as you can.

Please remember that I'm neither a student of science or computer science.

"compiled" - Don't they write "0's" and "1's" when writing a program?

"...pseudocode..." - You mean that they use a kind of generic format which could easily be converted to some specific format for some particular programming language?

Thanks.

jtbell
Mentor
"compiled" - Don't they write "0's" and "1's" when writing a program?
A program called a compiler does that for you. It translates the C or C++ or Fortran (or whatever) code that you write, into strings of 0s and 1s that are the actual "machine language" that you find in a .exe file.

"...pseudocode..." - You mean that they use a kind of generic format which could easily be converted to some specific format for some particular programming language?
Yes. To take your example, if I were starting from scratch with pseudocode, I might write this:

Code:
Get A, B, C, D from user;
largest = A;
if B > largest then
Largest = B;
if C > largest then
Largest = C;
if D > largest then
largest = D;
Print largest.
This is something that I could almost read out loud and it would be understandable. It just describes the logical sequence of what I want to do. Here's a complete C++ program for it, with all the extra details and "scaffolding" that C++ requires, and in the style that I usually use for formatting the code:

Code:
#include <iostream>

using namespace std;

int main ()
{
cout << "Enter four integers: ";
int A, B, C, D;
cin >> A >> B >> C >> D;

int largest = A;

if (B > largest)
{
largest = B;
}

if (C > largest)
{
largest = C;
}

if (D > largest)
{
largest = D;
}

cout << "The largest one is: " << largest << "." << endl;

return 0;
}
I put this in a file named largest.cpp. Here's what I see when I compile and run it, using the Unix command line in a Terminal window on my Mac:

Code:
Jons-Mac-Pro:c++ jtbell$g++ largest.cpp -o largest Jons-Mac-Pro:c++ jtbell$ ./largest
Enter four integers: 4 25 12 20
The largest one is: 25.
Jons-Mac-Pro:c++ jtbell$ On each line, the stuff up to and including the$ is my system's command prompt. "g++" is the name of my C++ compiler.

Last edited:
Why use both text and number variables, when the original problem mentions only numbers?

Code:
input A, B, C, D;
largest = A;
if (B > largest)
{
largest = B;
}
if (C > largest)
{
largest = C;
}
if (D > largest)
{
largest = D;
}
[B][COLOR="Red"]print largest[/COLOR][/B];
Does the "print largest" steps means to print the result on a printer? Please let me know.

jtbell
Mentor
It means "print" to your monitor or computer terminal. "Display" or "show" would probably be a better word, but in many computer languages, the output statement/command is named something like "print" regardless of where the output actually goes, so even in pseudocode some people always say "print."

Thanks a lot, JT.

Best wishes
Jackson

rcgldr
Homework Helper
Why use both text and number variables, when the original problem mentions only numbers?
The original post also mentions a set of numbers by name {A, B, C, D}, and it wasn't clear if the goal was to determine the largest number value or which number in the set {A, B, C, D} was largest.

Imagine you write the following numbers on the blackboard: [13 2 8 25 36]
How would you determine the largest number?

Probably, you would put your finger on the very left number and move your finger
from left to right. In your right hand you have a small calculator to save a number,
namely the current maximum.

Example:
The left hand side shows the five numbers with the red number
being the position of your left finger.
On the right hand side is the number that you type into the calculator.

Step 1:
At the beginning the calculator displays 0.
[13 2 8 25 36] 

Finger on 13. This number is our current maximum. Type 13 into the calculator.
[13 2 8 25 36] 

Step 2:
Finger is moved one step to the right.
[13 2 8 25 36] 

Compare with calculator => 2 is smaller than 13.
We leave the calculator as it is (current maximum is still 13).
[13 2 8 25 36] 

Step 3:
Finger is moved one step to the right.
[13 2 8 25 36] 

Compare with calculator => 8 is smaller than 13.
We leave the calculator as it is (current maximum is still 13).
[13 2 8 25 36] 

Step 4:
Finger is moved one step to the right.
[13 2 8 25 36] 

Compare with calculator => 25 is greater than 13.
Delete the number on the calculator display and type 25 (current maximum is now 25).
[13 2 8 25 36] 

Step 5:
Finger is moved one step to the right.
[13 2 8 25 36] 

Compare with calculator => 36 is greater than 25.
Delete the number on the calculator display and type 36 (current maximum is now 36).
[13 2 8 25 36] 

Since you can't move your finger further to the right you look at your calculator
with the current maximum being 36. This is also the largest number in the row.

In programming the art is to translate this "human" algorithm into something the
computer understands. For example, the calculator here is translated to the

Not saying previous replies are incorrect in any way. I just wanted to point out that I would almost never write something as specific as what I've seen suggested, at least in practice.

The most general form of the algorithm to find the largest number I come up with off the top of my head is:
1. Set current largest number to first number in list (at index 0).
2. Set current index to 1.
3. If number at current index is larger than current largest number, make it the new current largest number.
4. If at last number in list, current largest number is the largest. Otherwise, increment current index and go to step 3.

There's other ways to do more or less the same thing, of course, and I have no clue what's expected of you in your question. But it seems to me the greatest understanding and practical use comes from a similar general approach.

In straight C, something like this with hard coded values:

Code:
#include <stdio.h>

#define NUM_OF_NUMBERS 4
static int numbers[NUM_OF_NUMBERS] = {24, 10, 42, 18};

int main()
{
int i;
int largest = numbers;

for (i = 1; i < NUM_OF_NUMBERS; i++)
{
if (numbers[i] > largest)
{
largest = numbers[i];
}
}

printf("Largest is %d\n", largest);
}
Don't see any mistakes, but feel free to correct me if I made any.

EDIT: Just wanted to add that Edgardo has the right idea when breaking down the steps. Learning to generalize things and break them down into steps is at the core of learning programming and algorithms. So if I was a teacher, I'd consider the general answer to be the better answer. But then, I wouldn't have specified the exact number of elements, either, because I would want them to reason out the answer that I know will teach them more.

Last edited:
You could generalize to say that, given the limitation of two-element equalities, n-1 comparisons is the best case for finding the largest/smallest of n numbers.

Now, think of this: Can the best case be improved if more-than-two-element equalities. For example, if you were able to do three-element equalities(ie x >= y >= z) what would be the generalization of that?

Borek
Mentor
Not saying previous replies are incorrect in any way. I just wanted to point out that I would almost never write something as specific as what I've seen suggested, at least in practice.
There are situations when what you really need is just to deal with a list of three or four numbers. Using general method in such a case is an overkill.

jtbell
Mentor
In this case, you don't even have a list (array or vector) to begin with, just four individual variables.

Borek
Mentor
Yes, although it may happen they are stored in an array A program called a compiler does that for you. It translates the C or C++ or Fortran (or whatever) code that you write, into strings of 0s and 1s that are the actual "machine language" that you find in a .exe file.

Yes. To take your example, if I were starting from scratch with pseudocode, I might write this:

Code:
Get A, B, C, D from user;
largest = A;
if B > largest then
Largest = B;
if C > largest then
Largest = C;
if D > largest then
largest = D;
Print largest.
This is something that I could almost read out loud and it would be understandable. It just describes the logical sequence of what I want to do. Here's a complete C++ program for it, with all the extra details and "scaffolding" that C++ requires, and in the style that I usually use for formatting the code:

Code:
[B][COLOR="Red"]#include <iostream>

using namespace std;

int main ()
{
cout << "Enter four integers: ";
int A, B, C, D;
cin >> A >> B >> C >> D;

int largest = A;

if (B > largest)
{
largest = B;
}

if (C > largest)
{
largest = C;
}

if (D > largest)
{
largest = D;
}

cout << "The largest one is: " << largest << "." << endl;

return 0;
}[/COLOR][/B]
I put this in a file named largest.cpp. Here's what I see when I compile and run it, using the Unix command line in a Terminal window on my Mac:

Code:
Jons-Mac-Pro:c++ jtbell$g++ largest.cpp -o largest Jons-Mac-Pro:c++ jtbell$ ./largest
Enter four integers: 4 25 12 20
The largest one is: 25.
Jons-Mac-Pro:c++ jtbell$ On each line, the stuff up to and including the$ is my system's command prompt. "g++" is the name of my C++ compiler.
Hi

Please remember that I have no knowledge of computer programming and not a student of science or math.

1: I was wondering how in the first place a computer would determine which number is the largest because it has no intelligence of its own. So, there should be some second algorithm or some procedure which helps computer to know the number '9' is smaller than '10'.

2: Where do I get this C++ compiler? Doesn't C++ let you create a software with GUI where you can enter your four numbers and clicking some button tells you the largest one? How do I learn some VERY basic "scaffolding" and 'extra details' of C++ to do simple software such as the one to find the largest number?