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First power of 2 that has leading decimal digits of 12: Difference between revisions
First power of 2 that has leading decimal digits of 12 (view source)
Revision as of 11:39, 15 December 2020
, 3 years ago→{{header|Kotlin}}
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Line 887:
p(123, 12345) = 3,510,491
p(123, 678910) = 193,060,223</pre>
=={{header|Nim}}==
{{trans|Pascal}}
This is a translation to Nim of the very efficient Pascal alternative algorithm, with minor adjustments.
<lang Nim>import math, strformat
const
Lfloat64 = pow(2.0, 64)
Log10_2_64 = int(Lfloat64 * log10(2.0))
#---------------------------------------------------------------------------------------------------
func ordinal(n: int): string =
case n
of 1: "1st"
of 2: "2nd"
of 3: "3rd"
else: $n & "th"
#---------------------------------------------------------------------------------------------------
proc findExp(number, countLimit: int) =
var i = number
var digits = 1
while i >= 10:
digits *= 10
i = i div 10
var lmtLower, lmtUpper: uint64
var log10num = log10((number + 1) / digits)
if log10num >= 0.5:
lmtUpper = if (number + 1) / digits < 10: uint(log10Num * (Lfloat64 * 0.5)) * 2 + uint(log10Num * 2)
else: 0
log10Num = log10(number / digits)
lmtLower = uint(log10Num * (Lfloat64 * 0.5)) * 2 + uint(log10Num * 2)
else:
lmtUpper = uint(log10Num * Lfloat64)
lmtLower = uint(log10(number / digits) * Lfloat64)
var count = 0
var frac64 = 0u64
var p = 0
if lmtUpper != 0:
while true:
inc p
inc frac64, Log10_2_64
if frac64 in lmtLower..lmtUpper:
inc count
if count >= countLimit:
break
else:
# Searching for "999...".
while true:
inc p
inc frac64, Log10_2_64
if frac64 >= lmtLower:
inc count
if count >= countLimit:
break
echo fmt"""The {ordinal(count)} occurrence of 2 raised to a power""" &
fmt""" whose product starts with "{number}" is {p}"""
#———————————————————————————————————————————————————————————————————————————————————————————————————
findExp(12, 1)
findExp(12, 2)
findExp(123, 45)
findExp(123, 12345)
findExp(123, 678910)</lang>
{{out}}
Processor: Core I5 8250U
Compilation command: <code>nim c -d:danger --passC:-flto leading12.nim</code>
Time: about 110 ms
<pre>The 1st occurrence of 2 raised to a power whose product starts with "12" is 7
The 2nd occurrence of 2 raised to a power whose product starts with "12" is 80
The 45th occurrence of 2 raised to a power whose product starts with "123" is 12710
The 12345th occurrence of 2 raised to a power whose product starts with "123" is 3510491
The 678910th occurrence of 2 raised to a power whose product starts with "123" is 193060223</pre>
=={{header|Pascal}}==
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