Project Euler in R Problem 9
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In Problem 9 of Project Euler we are tasked with finding the product (abc) of the Pythagorean Triplet (a, b, c) such that a + b + c = 1000.
A Pythagorean triplet is a set of three natural numbers such that a2 + b2 = c2.
To solve this problem, we first see that c = (a2 + b2)1/2. Without loss of generality, we can only run the for loop for a and b, since c will be uniquely determined given a certain a and b.
The code I used:
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<span class="line"><span class="kr">for</span> <span class="p">(</span>a <span class="kr">in</span> <span class="m">1</span><span class="o">:</span><span class="m">499</span><span class="p">)</span> <span class="p">{</span>
</span><span class="line"> <span class="kr">for</span> <span class="p">(</span>b <span class="kr">in</span> <span class="m">1</span><span class="o">:</span><span class="m">499</span><span class="p">)</span> <span class="p">{</span>
</span><span class="line"> <span class="kr">if</span> <span class="p">(</span>a <span class="o">+</span> b <span class="o">+</span> <span class="kp">sqrt</span><span class="p">(</span>a<span class="o">^</span><span class="m">2</span> <span class="o">+</span> b<span class="o">^</span><span class="m">2</span><span class="p">)</span> <span class="o">==</span> <span class="m">1000</span><span class="p">)</span> <span class="p">{</span>
</span><span class="line"> <span class="kp">print</span><span class="p">(</span>a <span class="o">*</span> b <span class="o">*</span> <span class="kp">sqrt</span><span class="p">(</span>a<span class="o">^</span><span class="m">2</span> <span class="o">+</span> b<span class="o">^</span><span class="m">2</span><span class="p">))</span>
</span><span class="line"> <span class="kr">break</span>
</span><span class="line"> <span class="p">}</span>
</span><span class="line"> <span class="p">}</span>
</span><span class="line"> <span class="kr">if</span> <span class="p">(</span>a <span class="o">+</span> b <span class="o">+</span> <span class="kp">sqrt</span><span class="p">(</span>a<span class="o">^</span><span class="m">2</span> <span class="o">+</span> b<span class="o">^</span><span class="m">2</span><span class="p">)</span> <span class="o">==</span> <span class="m">1000</span><span class="p">)</span> <span class="p">{</span>
</span><span class="line"> <span class="kr">break</span>
</span><span class="line"> <span class="p">}</span>
</span><span class="line"><span class="p">}</span>
</span> |
I use nested for loops to test values of a and b between 1 and 499. a and b cannot take values greater than 499 because then a + b + sqrt(a2 + b2) would be greater than 1000.
The if statement in the nested loops checks to see whether a, b, and c add up to 1000. If they do, it prints their product and then breaks the loop. This is a short script which produces the correct answer in a few milliseconds. The trick here was expressing c in terms of a and b to reduce the amount of loops we need to run.
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