Problem 1103. Right Triangle Side Lengths (Inspired by Project Euler Problem 39)

Created by @bmtran (Bryant Tran)

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>If</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t> is the perimeter of a right angle triangle with integral length sides, {</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>a</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>b</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>c</w:t></w:r><w:r><w:t> }, there are exactly three solutions for</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t> = 120.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>{[20,48,52], [24,45,51], [30,40,50]}</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Given any value of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t>, return a cell array whose elements are the sorted side lengths of a possible right triangle whose perimeter is</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:i/></w:rPr><w:t>p</w:t></w:r><w:r><w:t>. Furthermore, the elements of the output should be sorted by their shortest side length.</w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Solve

Solution Stats

2255 Solutions
569 Solvers

Last Solution submitted on Apr 15, 2021

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Vishal on 13 Oct 2020

Hi Team,

I am getting error after submitting as,

"We're sorry, but something went wrong. We've been notified about this issue and we'll take a look at it shortly"

But completion bar has been incremented.
Thanks and Have a Good DaY

肇优孙 on 27 Dec 2020

function A = right_triangle_sides(p)
k=1;
for i=1:round(p/2)
for j=1:p-i
if sqrt(i^2+j^2)==p-i-j
c(k,:)=[i,j,p-i-j];
k=k+1;
end
end
end
c(size(c,1)/2+1:size(c,1),:)=[];
for i = 1:size(c,1)
A{1,i}=c(i,:);
end
end

学凯刘 on 10 Jan 2021

Well I don't know why I can't pass the test
could anyone help

function c = right_triangle_sides(p)
c = {};
k=1;
for i=1:ceil(p/3)
for j=i:ceil((p-i)/2)
if i^2+j^2==(p-i-j)^2
c(k)=mat2cell([i j p-i-i],1);
k=k+1;
end
end
end
end

Solution Comments

Solution 4368870

1 Comment

1 Comment

WK C on 20 Dec 2020

function c = right_triangle_sides(p)
i=0;
for a1 = 1:p-2
for a2 = a1:(p-a1-1)
for a3 = a2:(p-a2-1)
if((a1^2+a2^2==a3^2)&&(a1<=a2)&&(a2<=a3)&&(a1+a2+a3==p))
i=i+1;
b(i,:) = [a1,a2,a3];
end
end
end
end
for i = 1:size(b,1)
c{1,i}=b(i,:);
end
end

Solution 3935418

1 Comment

1 Comment

Hee Jason on 1 Dec 2020

function c = right_triangle_sides(p)
N = round(p/2);
A = 1:N;
A = A.^2;
B = sqrt(A + A');
C = arrayfun(@(t) t/floor(t) == 1,B);
[i j] = find(triu(C));
k = p - i - j;
x = (i.^2 + j.^2 - k.^2 == 0);
R = [i(x) j(x) k(x)];
R = sortrows(R);
R = R';
[~,col] = size(R);
c = mat2cell(R(:)',1,3*ones(1,col));
end

Solution 3597510

Solution 2813128

2 Comments

2 Comments

Sergio Enrique Pinto Castillo on 9 Aug 2020

I think, the statement of the problem is not complete. The reference problem is not available. I know very well about right angle triangles but I do not have the idea on how to find the solutions. Please help me out.

Vishal on 13 Oct 2020

Hi Castillo,
it is just iteration of 3 sides using perimeter and summing up the three iteration variable for perimeter check then for right angle triangle check (Pythagoras)...
Hope this helped you...(:

Solution 2593735

2 Comments

2 Comments

Piero Cimule on 22 Jun 2020

c=[];
for A=1:p
B=0;
while B < 1000
B = B+1;
C = sqrt((A^2) + (B^2));
perimeter = A+B+C;
if perimeter==p
c(end+1,:) = [A,B,C];
end
end
end
c=unique(sort(c,2),'rows');
x=cell(1,size(c,1));
for i=1:size(c,1)
[x{1,i}]= deal(c(i,:))
end
c=x

Marek Macák on 25 Nov 2020

Thank you :)

Solution 2055983

1 Comment

1 Comment

Miles Walker on 12 Dec 2019

Works, but is horribly inefficient especially for higher p...

Solution 174395

1 Comment

1 Comment

Aurelien Queffurust on 18 Dec 2012

solution using a Neural Network Toolbox function ;)

Problem Recent Solvers569

Problem Tags

plus15 projecteuler

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 1103. Right Triangle Side Lengths (Inspired by Project Euler Problem 39)

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers569

Suggested Problems

More from this Author56

Problem Tags

Community Treasure Hunt

Problem 1103. Right Triangle Side Lengths (Inspired by Project Euler Problem 39)

Solution Stats

Last 200 Solutions

Problem Comments

Solution Comments

Problem Recent Solvers569

Suggested Problems

More from this Author56

Problem Tags

Community Treasure Hunt

Players