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Tuhin-thinksTuhin-thinks
committedAug 13, 2021
find_lowest_base.py - pt2 by Activecat
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‎mathematical/conversion-to-base-n.ipynb

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "170eb313",
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"metadata": {},
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"outputs": [],
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"source": [
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"# https://www.geeksforgeeks.org/convert-base-decimal-vice-versa/\n",
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"# To convert decimal to any given base"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "647b1c73",
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"metadata": {},
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"outputs": [],
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"source": [
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"def toChar(x:int) -> str: \n",
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" if (0 <= x < 10):\n",
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" return chr(x + ord('0')); # Return a character between '0' to '9'.\n",
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" \n",
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" elif (10 <= x < 36):\n",
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" return chr(x - 10 + ord('A')); # Return a character between 'A' to 'Z'.\n",
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" \n",
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" else:\n",
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" return \"!\"; # Return '!' when it is out of range."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "992b96a2",
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"metadata": {},
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"outputs": [],
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"source": [
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"def toBaseN(x:int, n:int) -> str: \n",
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" output = \"\"\n",
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" \n",
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" # Convert input number is given base by repeatedly dividing it by base and taking remainder\n",
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" while (x > 0):\n",
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" output += toChar(x % n);\n",
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" x = int(x / n);\n",
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" \n",
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" return output[::-1]; # Reverse the string"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 4,
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"id": "4269a9bc",
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"metadata": {},
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"outputs": [],
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"source": [
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"assert toBaseN(282, 16) == '11A'"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "08a44a8b",
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"metadata": {},
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"outputs": [],
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"source": [
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"assert toBaseN(43, 6) == '111'"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "1a077c5b",
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"metadata": {},
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"outputs": [],
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"source": [
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"assert toBaseN(15, 2) == '1111'"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "2fe1ed2d",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"'Z'"
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]
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},
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"toBaseN(35, 50) "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "630fe7e4",
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"metadata": {},
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"outputs": [],
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"source": [
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"def isSameDigits(string:str) -> bool:\n",
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" if len(string) < 2 or '!' in string:\n",
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" return False\n",
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" \n",
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" for x in string[1:]:\n",
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" if string[0] != x:\n",
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" return False\n",
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" \n",
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" return True"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 9,
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"id": "fcd15c36",
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"metadata": {},
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"outputs": [],
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"source": [
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"assert isSameDigits('111211') == False"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 10,
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"id": "19ee68c4",
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"metadata": {},
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"outputs": [],
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"source": [
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"assert isSameDigits('1111')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "49bd890e",
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"metadata": {},
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"outputs": [],
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"source": [
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"assert isSameDigits('AAAA')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"id": "dc9ca131",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"** 10 base-4 is '22'\n",
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"** 10 base-9 is '11'\n",
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"** 11 base-10 is '11'\n",
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"** 12 base-5 is '22'\n",
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"** 12 base-11 is '11'\n",
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"** 13 base-3 is '111'\n",
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"** 13 base-12 is '11'\n",
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"** 14 base-6 is '22'\n",
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"** 14 base-13 is '11'\n",
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"** 15 base-2 is '1111'\n",
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"** 15 base-4 is '33'\n",
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"** 15 base-14 is '11'\n",
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"** 16 base-7 is '22'\n",
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"** 16 base-15 is '11'\n",
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"** 17 base-16 is '11'\n",
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"** 18 base-5 is '33'\n",
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"** 18 base-8 is '22'\n",
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"** 18 base-17 is '11'\n",
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"** 19 base-18 is '11'\n",
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"** 20 base-9 is '22'\n",
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"** 20 base-19 is '11'\n",
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"** 21 base-4 is '111'\n",
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"** 21 base-6 is '33'\n",
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"** 21 base-20 is '11'\n",
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"** 22 base-10 is '22'\n",
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"** 22 base-21 is '11'\n",
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"** 23 base-22 is '11'\n",
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"** 24 base-5 is '44'\n",
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"** 24 base-7 is '33'\n",
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"** 24 base-11 is '22'\n",
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"** 24 base-23 is '11'\n",
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"** 25 base-24 is '11'\n",
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"** 26 base-3 is '222'\n",
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"** 26 base-12 is '22'\n",
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"** 26 base-25 is '11'\n",
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"** 27 base-8 is '33'\n",
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"** 27 base-26 is '11'\n",
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"** 28 base-6 is '44'\n",
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"** 28 base-13 is '22'\n",
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"** 28 base-27 is '11'\n",
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"** 29 base-28 is '11'\n",
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"** 30 base-9 is '33'\n",
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"** 30 base-14 is '22'\n",
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"** 30 base-29 is '11'\n",
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"** 31 base-2 is '11111'\n",
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"** 31 base-5 is '111'\n",
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"** 31 base-30 is '11'\n",
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"** 32 base-7 is '44'\n",
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"** 32 base-15 is '22'\n",
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"** 32 base-31 is '11'\n",
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"** 33 base-10 is '33'\n",
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"** 33 base-32 is '11'\n",
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"** 34 base-16 is '22'\n",
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"** 34 base-33 is '11'\n",
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"** 35 base-6 is '55'\n",
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"** 35 base-34 is '11'\n",
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"** 36 base-8 is '44'\n",
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"** 36 base-11 is '33'\n",
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"** 36 base-17 is '22'\n",
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"** 36 base-35 is '11'\n",
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"** 38 base-18 is '22'\n",
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"** 39 base-12 is '33'\n",
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"** 40 base-3 is '1111'\n",
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"** 40 base-7 is '55'\n",
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"** 40 base-9 is '44'\n",
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"** 40 base-19 is '22'\n",
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"** 42 base-4 is '222'\n",
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"** 42 base-13 is '33'\n",
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"** 42 base-20 is '22'\n",
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"** 43 base-6 is '111'\n",
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"** 44 base-10 is '44'\n",
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"** 44 base-21 is '22'\n",
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"** 45 base-8 is '55'\n",
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"** 45 base-14 is '33'\n",
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"** 46 base-22 is '22'\n",
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"** 48 base-7 is '66'\n",
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"** 48 base-11 is '44'\n",
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"** 48 base-15 is '33'\n",
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"** 48 base-23 is '22'\n",
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"** 50 base-9 is '55'\n",
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"** 50 base-24 is '22'\n",
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"** 51 base-16 is '33'\n",
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"** 52 base-12 is '44'\n",
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"** 52 base-25 is '22'\n",
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"** 54 base-8 is '66'\n",
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"** 54 base-17 is '33'\n",
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"** 54 base-26 is '22'\n",
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"** 55 base-10 is '55'\n",
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"** 56 base-13 is '44'\n",
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"** 56 base-27 is '22'\n",
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"** 57 base-7 is '111'\n",
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"** 57 base-18 is '33'\n",
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"** 58 base-28 is '22'\n",
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"** 60 base-9 is '66'\n",
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"** 60 base-11 is '55'\n",
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"** 60 base-14 is '44'\n",
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"** 60 base-19 is '33'\n",
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"** 60 base-29 is '22'\n",
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"** 62 base-5 is '222'\n",
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"** 62 base-30 is '22'\n",
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"** 63 base-2 is '111111'\n",
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"** 63 base-4 is '333'\n",
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"** 63 base-8 is '77'\n",
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"** 63 base-20 is '33'\n",
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"** 64 base-15 is '44'\n",
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"** 64 base-31 is '22'\n",
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"** 65 base-12 is '55'\n",
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"** 66 base-10 is '66'\n",
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"** 66 base-21 is '33'\n",
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"** 66 base-32 is '22'\n",
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"** 68 base-16 is '44'\n",
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"** 68 base-33 is '22'\n",
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"** 69 base-22 is '33'\n",
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"** 70 base-9 is '77'\n",
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"** 70 base-13 is '55'\n",
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"** 70 base-34 is '22'\n",
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"** 72 base-11 is '66'\n",
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"** 72 base-17 is '44'\n",
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"** 72 base-23 is '33'\n",
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"** 72 base-35 is '22'\n",
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"** 73 base-8 is '111'\n",
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"** 75 base-14 is '55'\n",
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"** 75 base-24 is '33'\n",
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"** 76 base-18 is '44'\n",
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"** 77 base-10 is '77'\n",
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"** 78 base-12 is '66'\n",
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"** 78 base-25 is '33'\n",
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"** 80 base-3 is '2222'\n",
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"** 80 base-9 is '88'\n",
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"** 80 base-15 is '55'\n",
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"** 80 base-19 is '44'\n",
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"** 81 base-26 is '33'\n",
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"** 84 base-11 is '77'\n",
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"** 84 base-13 is '66'\n",
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"** 84 base-20 is '44'\n",
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"** 84 base-27 is '33'\n",
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"** 85 base-4 is '1111'\n",
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"** 85 base-16 is '55'\n",
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"** 86 base-6 is '222'\n",
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"** 87 base-28 is '33'\n",
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"** 88 base-10 is '88'\n",
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"** 88 base-21 is '44'\n",
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"** 90 base-14 is '66'\n",
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"** 90 base-17 is '55'\n",
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"** 90 base-29 is '33'\n",
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"** 91 base-9 is '111'\n",
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"** 91 base-12 is '77'\n",
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"** 92 base-22 is '44'\n",
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"** 93 base-5 is '333'\n",
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"** 93 base-30 is '33'\n",
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"** 95 base-18 is '55'\n",
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"** 96 base-11 is '88'\n",
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"** 96 base-15 is '66'\n",
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"** 96 base-23 is '44'\n",
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"** 96 base-31 is '33'\n",
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"** 98 base-13 is '77'\n",
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"** 99 base-10 is '99'\n",
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"** 99 base-32 is '33'\n"
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]
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}
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],
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"source": [
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"for x in range(10, 100):\n",
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" for n in range(2, 36):\n",
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" string = toBaseN(x, n)\n",
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" #print(\"** {} base-{} is '{}'\".format(x, n, string), end='')\n",
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" if isSameDigits(string):\n",
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" #print(\" ******** \")\n",
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" print(\"** {} base-{} is '{}'\".format(x, n, string))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 13,
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"id": "49e402f9",
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"metadata": {},
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"outputs": [],
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"source": [
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"def func2(x:int):\n",
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" for n in range(2, 36):\n",
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" string = toBaseN(x, n)\n",
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" if isSameDigits(string):\n",
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" print(\"** {} base-{} is '{}'\".format(x, n, string))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 14,
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"id": "ebc7fb5b",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"** 80 base-3 is '2222'\n",
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"** 80 base-9 is '88'\n",
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"** 80 base-15 is '55'\n",
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"** 80 base-19 is '44'\n"
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]
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}
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],
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"source": [
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"func2(80) "
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "9d01c340",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"** 400 base-7 is '1111'\n",
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"** 400 base-24 is 'GG'\n"
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]
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}
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],
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"source": [
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"func2(400)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "8c547606",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.8.8"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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