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< p > We will go through the given problem the same way as I have suggested in the
previous post.< / p >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "summary-of-the-problem" > Summary of the problem< a href = "#summary-of-the-problem" class = "hash-link" aria-label = "Direct link to Summary of the problem" title = "Direct link to Summary of the problem" > < / a > < / h2 >
< p > We have a robot in some kind of a maze and we have to find our way out that is
marked with a so-called “beeper”. We' ve been given a restriction < strong > not to< / strong > use
any variables, we can use just backtracking and recursion.< / p >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "brainstorming-the-idea" > Brainstorming the idea< a href = "#brainstorming-the-idea" class = "hash-link" aria-label = "Direct link to Brainstorming the idea" title = "Direct link to Brainstorming the idea" > < / a > < / h2 >
< p > Let' s start with some brainstorming of the solution.< / p >
< ul >
< li > How will I know what I' ve checked without any variables?<!-- -->
< ul >
< li > < em > answer< / em > : recursion will need to take care of that, cause I' m not allowed
anything else< / li >
< / ul >
< / li >
< li > How will I pass around the fact I' ve found the exit?<!-- -->
< ul >
< li > < em > answer< / em > : I can return values from helper functions, so I should be able to
indicate < em > found< / em > /< em > not found< / em > < / li >
< / ul >
< / li >
< li > How is the exit marked?<!-- -->
< ul >
< li > < em > answer< / em > : there is one “beeper” as a mark< / li >
< / ul >
< / li >
< li > Can I reduce my problem somehow?<!-- -->
< ul >
< li > < em > answer< / em > : I could check each possible direction as a reduced search space< / li >
< / ul >
< / li >
< / ul >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "rough-pseudocode" > »Rough« pseudocode< a href = "#rough-pseudocode" class = "hash-link" aria-label = "Direct link to »Rough« pseudocode" title = "Direct link to »Rough« pseudocode" > < / a > < / h2 >
< p > We should be able to construct a < em > skeleton< / em > of our solution at least. Pseudocode
follows:< / p >
< div class = "language-ruby codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-ruby codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token method-definition function" style = "color:#d73a49" > find_exit< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > found the exit < / span > < span class = "token keyword" style = "color:#00009f" > then< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > signal others< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > terminate< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > check left< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > check front< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > check right< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < br > < / span > < / code > < / pre > < div class = "buttonGroup__atx" > < button type = "button" aria-label = "Copy code to clipboard" title = "Copy" class = "clean-btn" > < span class = "copyButtonIcons_eSgA" aria-hidden = "true" > < svg viewBox = "0 0 24 24" class = "copyButtonIcon_y97N" > < path fill = "currentColor" d = "M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z" > < / path > < / svg > < svg viewBox = "0 0 24 24" class = "copyButtonSuccessIcon_LjdS" > < path fill = "currentColor" d = "M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z" > < / path > < / svg > < / span > < / button > < / div > < / div > < / div >
< p > As you can see, we only mention what we want to do very roughly, technical
details are left out, except for the early return (which is the base of our
recursive function).< / p >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "proper-pseudocode" > »Proper« pseudocode< a href = "#proper-pseudocode" class = "hash-link" aria-label = "Direct link to »Proper« pseudocode" title = "Direct link to »Proper« pseudocode" > < / a > < / h2 >
< p > In the proper pseudocode we will need to dive into the technical details like
the way we check for exit, move around, etc.< / p >
< p > We can start by cleaning up and decomposing the function written above:< / p >
< div class = "language-ruby codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-ruby codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token method-definition function" style = "color:#d73a49" > find_exit< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token comment" style = "color:#999988;font-style:italic" > # BASE: found exit< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > found_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > then< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > true< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token comment" style = "color:#999988;font-style:italic" > # check left< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > left_is_clear< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > then< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > turn_left< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > step< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > find_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > then< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > true< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-b
< p > We are missing few of the functions that we use in our pseudocode above:< / p >
< ul >
< li > < code > found_exit()< / code > < / li >
< li > < code > turn_around()< / code > < / li >
< li > < code > turn_right()< / code > < / li >
< / ul >
< p > We can implement those easily:< / p >
< div class = "language-ruby codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-ruby codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token method-definition function" style = "color:#d73a49" > found_exit< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > not< / span > < span class = "token plain" > beepers_present< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > then< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > false< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > pick_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > beepers_present< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > then< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > put_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > false< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > put_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > true< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > end< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "c
< p > Now we have everything ready for implementing it in Python.< / p >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "actual-implementation" > Actual implementation< a href = "#actual-implementation" class = "hash-link" aria-label = "Direct link to Actual implementation" title = "Direct link to Actual implementation" > < / a > < / h2 >
< p > It' s just a matter of rewriting the pseudocode into Python< sup > < a href = "#user-content-fn-1" id = "user-content-fnref-1" data-footnote-ref = "true" aria-describedby = "footnote-label" > 1< / a > < / sup > :< / p >
< div class = "language-py codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-py codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > class< / span > < span class = "token plain" > < / span > < span class = "token class-name" > SuperKarel< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token plain" > Karel< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token comment" style = "color:#999988;font-style:italic" > # you can define your own helper functions on Karel here, if you wish to< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token function" style = "color:#d73a49" > found_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token operator" style = "color:#393A34" > -< / span > < span class = "token operator" style = "color:#393A34" > > < / span > < span class = "token plain" > < / span > < span class = "token builtin" > bool< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > not< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > beepers_present< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > False< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > pick_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > beepers_present< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > put_beeper< / span > < span class = "token punctuation" style = "color:#393A
< p > We have relatively repetitive code for checking each of the directions, I would
propose to refactor a bit, in a fashion of checkin just forward, so it' s more
readable:< / p >
< div class = "language-py codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-py codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token function" style = "color:#d73a49" > find_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token operator" style = "color:#393A34" > -< / span > < span class = "token operator" style = "color:#393A34" > > < / span > < span class = "token plain" > < / span > < span class = "token builtin" > bool< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > found_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > True< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > turn_left< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > for< / span > < span class = "token plain" > _ < / span > < span class = "token keyword" style = "color:#00009f" > in< / span > < span class = "token plain" > < / span > < span class = "token builtin" > range< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token number" style = "color:#36acaa" > 3< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > front_is_blocked< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > turn_right< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > continue< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "displa
< p > We can also notice that turning around takes 2 left turns and turning to right
does 3. We get 5 left turns in total when we turn around and right afterwards…
Taking 4 left turns just rotates us back to our initial direction, therefore it
is sufficient to do just one left turn (< code > 5 % 4 == 1< / code > ). That way we get:< / p >
< div class = "language-py codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-py codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token function" style = "color:#d73a49" > find_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token operator" style = "color:#393A34" > -< / span > < span class = "token operator" style = "color:#393A34" > > < / span > < span class = "token plain" > < / span > < span class = "token builtin" > bool< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > found_exit< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > True< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > turn_left< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > for< / span > < span class = "token plain" > _ < / span > < span class = "token keyword" style = "color:#00009f" > in< / span > < span class = "token plain" > < / span > < span class = "token builtin" > range< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token number" style = "color:#36acaa" > 3< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > front_is_blocked< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > turn_right< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > continue< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "displa
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "testing" > Testing< a href = "#testing" class = "hash-link" aria-label = "Direct link to Testing" title = "Direct link to Testing" > < / a > < / h2 >
< p > In the skeleton, with the previous post, I have included multiple mazes that can
be tested. I have tried this solution with all of the given mazes, and it was
successful in finding the exit. However there is one precondition of our
solution that we haven' t spoken about.< / p >
< p > We are silently expecting the maze < strong > not to< / strong > have any loops. Example of such
maze can be the < code > maze666.kw< / code > :< / p >
2024-01-03 15:14:53 +01:00
< div class = "codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-text codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > ┌ < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │. . . . .│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ ┌─────┐ │ │< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │.│. . .│.│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ │ │ │ │ │< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │.│.│. . .│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ │ │ └─┤< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │.│.│. . . 1│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ │ │ │ ┌─┤< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │.│. . .│.│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ └─────┘ │ │< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │. > . . .│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > └─────────┴─┘< / span > < br > < / span > < / code > < / pre > < div class = "buttonGroup__atx" > < button type = "button" aria-label = "Copy code to clipboard" title = "Copy" class = "clean-btn" > < span class = "copyButtonIcons_eSgA" aria-hidden = "true" > < svg viewBox = "0 0 24 24" class = "copyButtonIcon_y97N" > < path fill = "currentColor" d = "M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z" > < / path > < / svg > < svg viewBox = "0 0 24 24" class = "copyButtonSuccessIcon_LjdS" > < path fill = "currentColor" d = "M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z" > < / path > < / svg > < / span > < / button > < / div > < / div > < / div >
2023-12-24 00:15:15 +01:00
< p > If you try running our solution on this map, Karel just loops and never finds
the solution. Let' s have a look at the loop he gets stuck in:< / p >
< div class = "codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-text codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > ┌─────────┬─┐< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │* * * * *│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ ┌─────┐ │ │< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │*│* * *│*│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ │ │ │ │ │< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │*│*│. * *│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ │ │ └─┤< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │*│*│. * * 1│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ │ │ │ ┌─┤< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │*│* * *│*│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │ └─────┘ │ │< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > │* * * * *│.│< / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > └─────────┴─┘< / span > < br > < / span > < / code > < / pre > < div class = "buttonGroup__atx" > < button type = "button" aria-label = "Copy code to clipboard" title = "Copy" class = "clean-btn" > < span class = "copyButtonIcons_eSgA" aria-hidden = "true" > < svg viewBox = "0 0 24 24" class = "copyButtonIcon_y97N" > < path fill = "currentColor" d = "M19,21H8V7H19M19,5H8A2,2 0 0,0 6,7V21A2,2 0 0,0 8,23H19A2,2 0 0,0 21,21V7A2,2 0 0,0 19,5M16,1H4A2,2 0 0,0 2,3V17H4V3H16V1Z" > < / path > < / svg > < svg viewBox = "0 0 24 24" class = "copyButtonSuccessIcon_LjdS" > < path fill = "currentColor" d = "M21,7L9,19L3.5,13.5L4.91,12.09L9,16.17L19.59,5.59L21,7Z" > < / path > < / svg > < / span > < / button > < / div > < / div > < / div >
< p > He walks past the exit, but can' t see it, cause there' s always a feasible path
that is worth trying.< / p >
< div class = "theme-admonition theme-admonition-tip admonition_xJq3 alert alert--success" > < div class = "admonitionHeading_Gvgb" > < span class = "admonitionIcon_Rf37" > < svg viewBox = "0 0 12 16" > < path fill-rule = "evenodd" d = "M6.5 0C3.48 0 1 2.19 1 5c0 .92.55 2.25 1 3 1.34 2.25 1.78 2.78 2 4v1h5v-1c.22-1.22.66-1.75 2-4 .45-.75 1-2.08 1-3 0-2.81-2.48-5-5.5-5zm3.64 7.48c-.25.44-.47.8-.67 1.11-.86 1.41-1.25 2.06-1.45 3.23-.02.05-.02.11-.02.17H5c0-.06 0-.13-.02-.17-.2-1.17-.59-1.83-1.45-3.23-.2-.31-.42-.67-.67-1.11C2.44 6.78 2 5.65 2 5c0-2.2 2.02-4 4.5-4 1.22 0 2.36.42 3.22 1.19C10.55 2.94 11 3.94 11 5c0 .66-.44 1.78-.86 2.48zM4 14h5c-.23 1.14-1.3 2-2.5 2s-2.27-.86-2.5-2z" > < / path > < / svg > < / span > Algorithm< / div > < div class = "admonitionContent_BuS1" > < p > The algorithm we have written to find the exit is a depth-first search (DFS).
However, as opposed to the usual implementation, we have no notion of paths that
are being (or have already been) explored.< / p > < / div > < / div >
< h2 class = "anchor anchorWithStickyNavbar_LWe7" id = "fixing-the-issue" > Fixing the issue< a href = "#fixing-the-issue" class = "hash-link" aria-label = "Direct link to Fixing the issue" title = "Direct link to Fixing the issue" > < / a > < / h2 >
< p > Since we are not allowed to use variables, the only way to resolve this issue is
to mark the “cells” that we have tried. We can easily use beepers for this, but
we need to be careful < strong > not to< / strong > confuse the exit with already visited cell.< / p >
< p > To do that we' ll use < strong > 2< / strong > beepers instead of the one. Implementation follows:< / p >
< div class = "language-py codeBlockContainer_Ckt0 theme-code-block" style = "--prism-color:#393A34;--prism-background-color:#f6f8fa" > < div class = "codeBlockContent_biex" > < pre tabindex = "0" class = "prism-code language-py codeBlock_bY9V thin-scrollbar" style = "color:#393A34;background-color:#f6f8fa" > < code class = "codeBlockLines_e6Vv" > < span class = "token-line" style = "color:#393A34" > < span class = "token keyword" style = "color:#00009f" > def< / span > < span class = "token plain" > < / span > < span class = "token function" style = "color:#d73a49" > visited< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < span class = "token operator" style = "color:#393A34" > -< / span > < span class = "token operator" style = "color:#393A34" > > < / span > < span class = "token plain" > < / span > < span class = "token builtin" > bool< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > not< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > beepers_present< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > False< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > pick_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > if< / span > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > not< / span > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > beepers_present< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token punctuation" style = "color:#393A34" > :< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > put_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" style = "color:#393A34" > )< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > < / span > < span class = "token keyword" style = "color:#00009f" > return< / span > < span class = "token plain" > < / span > < span class = "token boolean" style = "color:#36acaa" > False< / span > < span class = "token plain" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" style = "display:inline-block" > < / span > < br > < / span > < span class = "token-line" style = "color:#393A34" > < span class = "token plain" > self< / span > < span class = "token punctuation" style = "color:#393A34" > .< / span > < span class = "token plain" > pick_beeper< / span > < span class = "token punctuation" style = "color:#393A34" > (< / span > < span class = "token punctuation" sty
< p > Now our solution works also for mazes that have loops.< / p >
< section data-footnotes = "true" class = "footnotes" > < h2 class = "anchor anchorWithStickyNavbar_LWe7 sr-only" id = "footnote-label" > Footnotes< a href = "#footnote-label" class = "hash-link" aria-label = "Direct link to Footnotes" title = "Direct link to Footnotes" > < / a > < / h2 >
< ol >
< li id = "user-content-fn-1" >
< p > which is usually very easy matter < a href = "#user-content-fnref-1" data-footnote-backref = "" aria-label = "Back to reference 1" class = "data-footnote-backref" > ↩< / a > < / p >
< / li >
< / ol >
2024-01-03 15:14:53 +01:00
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