Project Euler/16 - Revision history

Admin: Replacing charlesreid1.com:3000 with git.charlesreid1.com

2019-10-09T03:46:00Z

Replacing charlesreid1.com:3000 with git.charlesreid1.com

← Older revision		Revision as of 03:46, 9 October 2019
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	==Code==		==Code==

	Here is the solution in code: https://charlesreid1.com~~:3000~~/cs/euler/src/master/scratch/Round1_001-020/016		Here is the solution in code: https://git.charlesreid1.com/cs/euler/src/master/scratch/Round1_001-020/016

	==Flags==		==Flags==

2018-01-08T08:51:05Z

Shortcuts?

← Older revision		Revision as of 08:51, 8 January 2018
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	Does this offer any kind of shortcut? Not exactly - although there's an overall pattern, the local behavior seems unpredictable. Furthermore, there is no inverse problem, so we can't explore numbers in a local region (extrapolating from the curve above) and test if they are solutions.		Does this offer any kind of shortcut? Not exactly - although there's an overall pattern, the local behavior seems unpredictable. Furthermore, there is no inverse problem, so we can't explore numbers in a local region (extrapolating from the curve above) and test if they are solutions.


			==Code==

			Here is the solution in code: https://charlesreid1.com:3000/cs/euler/src/master/scratch/Round1_001-020/016

			==Flags==

	{{ProjectEulerFlag}}		{{ProjectEulerFlag}}
	[[Category:Big Integer]]		[[Category:Big Integer]]

2018-01-08T08:50:23Z

← Older revision		Revision as of 08:50, 8 January 2018
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			==Problem Overview==

	Project Euler problem 16: https://projecteuler.net/problem=16		Project Euler problem 16: https://projecteuler.net/problem=16

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	==Brute Force Method==		==Brute Force Method==

	This is obviously much larger than the capacity of Java's int, <math>2^{32}</math>, or long, <math>2^{64}</math>. However, Java's math library has a big integer type built in that allows for arbitrary precision algebra. Solving this problem is as easy as learning how to call it. ~~The~~ number is not as large as it looks - it ~~won't overwhelm~~ a computer to ~~actually compute~~ it. Java computes it in less than a second.		This is obviously much larger than the capacity of Java's int, <math>2^{32}</math>, or long, <math>2^{64}</math>. However, Java's math library has a big integer type built in that allows for arbitrary precision algebra. Solving this problem is as easy as learning how to call it.

			It's important to keep a sense of scale - the 2 in the base means <math>2^{1000}</math> is way smaller than <math>10^{1000}</math>. In fact, the number is not as large as it looks, and it is no sweat for a computer to handle it. Java computes it in less than a second.

	<pre>		<pre>

2018-01-08T08:36:22Z

Shortcuts?

← Older revision		Revision as of 08:36, 8 January 2018
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	[[Image:SumOfDigitsOfPowersOf2.png\|500px]]		[[Image:SumOfDigitsOfPowersOf2.png\|500px]]

			Does this offer any kind of shortcut? Not exactly - although there's an overall pattern, the local behavior seems unpredictable. Furthermore, there is no inverse problem, so we can't explore numbers in a local region (extrapolating from the curve above) and test if they are solutions.


	{{ProjectEulerFlag}}		{{ProjectEulerFlag}}
	[[Category:Big Integer]]		[[Category:Big Integer]]

2017-07-05T04:14:13Z

← Older revision	Revision as of 04:14, 5 July 2017
(No difference)

2017-07-05T02:22:59Z

Shortcuts?

← Older revision		Revision as of 02:22, 5 July 2017
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	</pre>		</pre>
	}}		}}


			[[Image:SumOfDigitsOfPowersOf2.png\|500px]]


	{{ProjectEulerFlag}}		{{ProjectEulerFlag}}
	[[Category:Big Integer]]		[[Category:Big Integer]]

2017-07-05T02:19:59Z

Shortcuts?

← Older revision		Revision as of 02:19, 5 July 2017
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	Here's a table I made of the sum of the digits of the powers of 2:		Here's a table I made of the sum of the digits of the powers of 2:

	{{~~ScrollBox~~\|		{{Scrollbox\|

	<pre>		<pre>

2017-07-05T02:19:47Z

2017-07-05T02:14:27Z

@@ Line 1: / Line 1: @@
 Project Euler problem 16: https://projecteuler.net/problem=16
-Problem 16 asks to find the sum of the digits of <math>2^1000</math>.
+Problem 16 asks to find the sum of the digits of <math>2^{1000}</math>.
-This is obviously much larger than the capacity of Java's int, <math>2^32</math>, or long, <math>2^64</math>. However, Java's math library has a big integer type built in that allows for arbitrary precision algebra. Solving this problem is as easy as learning how to call it. The number is not as large as it looks - it won't overwhelm a computer to actually compute it. Java computes it in less than a second.
+This is obviously much larger than the capacity of Java's int, <math>2^{32}</math>, or long, <math>2^{64}</math>. However, Java's math library has a big integer type built in that allows for arbitrary precision algebra. Solving this problem is as easy as learning how to call it. The number is not as large as it looks - it won't overwhelm a computer to actually compute it. Java computes it in less than a second.
 <pre>
@@ Line 11: / Line 11: @@
 user	0m1.166s
 sys	0m0.090s
 </pre>

2017-07-05T02:12:42Z