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{ | ||
"authors": [ | ||
"BNAndras", | ||
"KOTP", | ||
"glennj" | ||
], | ||
"files": { | ||
|
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" add two strings as numbers from right to left, as if by hand | ||
function! StringAdd(a, b) abort | ||
" zero-left-pad so the numbers are the same length | ||
let len = max([strlen(a:a), strlen(a:b)]) | ||
let a = printf('%0*s', len, a:a) | ||
let b = printf('%0*s', len, a:b) | ||
let result = "" | ||
let carry = 0 | ||
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for i in range(len - 1, 0, -1) | ||
let c = carry + str2nr(strpart(a, i, 1)) + str2nr(strpart(b, i, 1)) | ||
let result = $"{c % 10}{result}" | ||
let carry = c / 10 | ||
endfor | ||
return trim($"{carry}{result}", '0', 1) | ||
" Helper function to add two large numbers represented as strings | ||
function! StringAdd(num1, num2) | ||
let carry = 0 | ||
let result = '' | ||
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" Pad the shorter number with leading zeros | ||
let len1 = strlen(a:num1) | ||
let len2 = strlen(a:num2) | ||
if len1 < len2 | ||
let a:num1 = repeat('0', len2 - len1) . a:num1 | ||
elseif len2 < len1 | ||
let a:num2 = repeat('0', len1 - len2) . a:num2 | ||
endif | ||
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" Add digits from right to left | ||
for i in range(strlen(a:num1) - 1, 0, -1) | ||
let sum = str2nr(a:num1[i]) + str2nr(a:num2[i]) + carry | ||
let carry = sum >= 10 ? 1 : 0 | ||
let result = string(sum % 10) . result | ||
endfor | ||
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" Add the last carry if it exists | ||
if carry > 0 | ||
let result = '1' . result | ||
endif | ||
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return result | ||
endfunction | ||
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" populate the squares, doubling each previous, cache in the script scope | ||
let s:grains = ['1'] | ||
for i in range(1, 63) | ||
eval add(s:grains, StringAdd(s:grains[i - 1], s:grains[i - 1])) | ||
endfor | ||
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" return the grains on square `number` | ||
function! Square(number) abort | ||
if a:number < 1 || a:number > 64 | ||
throw 'square must be between 1 and 64' | ||
endif | ||
return s:grains[a:number - 1] | ||
" Function to calculate grains on a specific square using string manipulation | ||
function! Square(n) | ||
if a:n < 1 || a:n > 64 | ||
throw 'square must be between 1 and 64' | ||
endif | ||
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" Start with 1 grain on the first square | ||
let grains = '1' | ||
for i in range(2, a:n) | ||
" Double the grains by adding it to itself | ||
let grains = StringAdd(grains, grains) | ||
endfor | ||
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return grains | ||
endfunction | ||
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" return the total number of grains | ||
function! Total() abort | ||
let total = '0' | ||
for i in range(64) | ||
let total = StringAdd(total, s:grains[i]) | ||
endfor | ||
return total | ||
" Function to calculate the total grains on the chessboard using string manipulation | ||
function! Total() | ||
let total = '0' | ||
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" Accumulate grains for each square from 1 to 64 | ||
let grains = '1' | ||
for i in range(1, 64) | ||
let total = StringAdd(total, grains) | ||
" Double grains for the next square | ||
let grains = StringAdd(grains, grains) | ||
endfor | ||
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return total | ||
endfunction |