2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								---
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								id: 5900f3bf1000cf542c50fed2
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								challengeType: 5
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								title: 'Problem 83: Path sum: four ways'
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
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								## Description
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< section  id = 'description' >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								NOTE: This problem is a significantly more challenging version of Problem 81.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								In the 5 by 5 matrix below, the minimal path sum from the top left to the bottom right, by moving left, right, up, and down, is indicated in bold red and is equal to 2297.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								$$
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								\begin{pmatrix}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								\color{red}{131} &  673 &  \color{red}{234} &  \color{red}{103} &  \color{red}{18}\\
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								\color{red}{201} &  \color{red}{96} &  \color{red}{342} &  965 &  \color{red}{150}\\
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								630 &  803 &  746 &  \color{red}{422} &  \color{red}{111}\\
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								537 &  699 &  497 &  \color{red}{121} &  956\\
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								805 &  732 &  524 &  \color{red}{37} &  \color{red}{331}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								\end{pmatrix}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								$$
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
									
										
										
										
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								Find the minimal path sum, in matrix.txt (right click and
							 
						 
					
						
							
								
									
										
										
										
											2018-09-30 23:01:58 +01:00 
										
									 
								 
							 
							
								
							 
							
								 
							
							
								"Save Link/Target As..."), a 31K text file containing a 80 by 80 matrix, from the top left to the bottom right by moving left, right, up, and down.
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< / section >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								## Instructions
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< section  id = 'instructions' >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
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								## Tests
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< section  id = 'tests' >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```yml
							 
						 
					
						
							
								
									
										
										
										
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								tests:
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								  -  text: < code > euler83()</ code >  should return 425185.
							 
						 
					
						
							
								
									
										
										
										
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								    testString: assert.strictEqual(euler83(), 425185, '< code > euler83()< / code >  should return 425185.');
							 
						 
					
						
							
								
									
										
										
										
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								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
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								## Challenge Seed
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< section  id = 'challengeSeed' >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< div  id = 'js-seed' >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								function euler83() {
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								  // Good luck!
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								  return true;
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								}
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								euler83();
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< / div >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
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								## Solution
  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< section  id = 'solution' >  
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```js
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								// solution required
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								```
							 
						 
					
						
							
								
							 
							
								
							 
							
								 
							
							
								< / section >