Digit fifth powers: Difference between revisions
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(→{{header|AppleScript}}: Minor improvement to existing script. Added faster alternative.) |
(→{{header|AppleScript}}: Added recursive version.) |
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<syntaxhighlight lang="applescript">"4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839"</syntaxhighlight> |
<syntaxhighlight lang="applescript">"4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839"</syntaxhighlight> |
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Faster alternative (about 55 times as fast) using the "start with the digits" approach suggested by other contributors. Its iterative structure requires prior knowledge that six digits will be needed. |
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<syntaxhighlight lang="applescript">on join(lst, delim) |
<syntaxhighlight lang="applescript">on join(lst, delim) |
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{{output}} |
{{output}} |
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<syntaxhighlight lang="applescript">"4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839"</syntaxhighlight> |
<syntaxhighlight lang="applescript">"4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839"</syntaxhighlight> |
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Recursive version of the above. This takes the power as a parameter and is believed to be good for powers between 3 and 13. (No matches found when the power is 12.) |
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<syntaxhighlight lang="applescript">on join(lst, delim) |
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set astid to AppleScript's text item delimiters |
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set AppleScript's text item delimiters to delim |
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set txt to lst as text |
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set AppleScript's text item delimiters to astid |
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return txt |
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end join |
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on digitNthPowers(pwr) |
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if ((pwr < 2) or (pwr > 13)) then return missing value -- Clear non-starter or too high for AppleScript. |
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-- Trusting the theory in the Julia solution, work out how many digits are needed. |
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set digits to {missing value} |
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set digitCount to 1 |
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repeat until ((9 ^ pwr) * digitCount < (10 ^ digitCount)) |
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set digitCount to digitCount + 1 |
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set end of digits to missing value |
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end repeat |
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set hits to {} |
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set total to 0 |
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script o |
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on dnp(slot, dmin, dmax, sum) |
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-- Recursive handler. Inherits the variables set before this script object. |
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-- slot: current slot in digits. |
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-- dmin, dmax: range of digit values to try in it. |
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-- sum: sum of 5th powers at the calling level. |
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repeat with d from dmin to dmax |
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set digits's item slot to d |
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if (slot < digitCount) then |
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dnp(slot + 1, 0, d, sum + d ^ pwr) |
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else |
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copy digits to checklist |
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set sum to (sum + (d ^ pwr)) div 1 |
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set temp to sum |
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set d to temp mod 10 |
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repeat while (checklist contains {d}) |
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repeat with i from 1 to digitCount |
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if (checklist's item i = d) then |
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set checklist's item i to missing value |
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exit repeat |
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end if |
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end repeat |
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set temp to temp div 10 |
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set d to temp mod 10 |
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end repeat |
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if (((count checklist each integer) = 0) and (sum > (2 ^ pwr))) then |
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set end of hits to sum |
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set total to total + sum |
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end if |
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end if |
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end repeat |
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end dnp |
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end script |
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o's dnp(1, 1, 9, 0.0) |
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if (hits = {}) then return missing value |
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return join(hits, " + ") & " = " & total |
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end digitNthPowers |
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join({digitNthPowers(4), digitNthPowers(5), digitNthPowers(13)}, linefeed)</syntaxhighlight> |
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{{output}} |
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<syntaxhighlight lang="applescript">"1634 + 8208 + 9474 = 19316 |
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4150 + 4151 + 54748 + 92727 + 93084 + 194979 = 443839 |
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5.64240140138E+11 = 5.64240140138E+11"</syntaxhighlight> |
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=={{header|AWK}}== |
=={{header|AWK}}== |
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