diff --git a/problems/013_problem_jnotebook.ipynb b/problems/013_problem_jnotebook.ipynb index 90ca9b5..158d2e5 100644 --- a/problems/013_problem_jnotebook.ipynb +++ b/problems/013_problem_jnotebook.ipynb @@ -355,27 +355,21 @@ }, "outputs": [ { - "output_type": "execute_result", - "data": { - "text/plain": "'[55, 3, 7, 3, 7, 6, 2, 3, 0, 3]'" - }, - "metadata": {}, - "execution_count": 5 + "output_type": "stream", + "name": "stdout", + "text": "The solution is 55373762303\n" } ], "source": [ "solution_digits.reverse()\n", "string=\"\"\n", - "string.join(str(solution_digits[:10]))\n" + "for i in solution_digits[:10]:\n", + " string+=str(i)\n", + "\n", + "print(\"The solution is \",string)\n", + "#string.join(str(solution_digits[:10]))\n" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - }, { "cell_type": "code", "execution_count": null, diff --git a/problems/014_problem_jnotebook.ipynb b/problems/014_problem_jnotebook.ipynb new file mode 100644 index 0000000..158d2e5 --- /dev/null +++ b/problems/014_problem_jnotebook.ipynb @@ -0,0 +1,402 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Problem 13:\n", + "\n", + "[Euler Project #13](https://projecteuler.net/problem=13)\n", + "\n", + "\n", + "> Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.\n", + "\n", + "> 37107287533902102798797998220837590246510135740250\n", + "> 46376937677490009712648124896970078050417018260538\n", + "> 74324986199524741059474233309513058123726617309629\n", + "> 91942213363574161572522430563301811072406154908250\n", + "> 23067588207539346171171980310421047513778063246676\n", + "> 89261670696623633820136378418383684178734361726757\n", + "> 28112879812849979408065481931592621691275889832738\n", + "> 44274228917432520321923589422876796487670272189318\n", + "> 47451445736001306439091167216856844588711603153276\n", + "> 70386486105843025439939619828917593665686757934951\n", + "> 62176457141856560629502157223196586755079324193331\n", + "> 64906352462741904929101432445813822663347944758178\n", + "> 92575867718337217661963751590579239728245598838407\n", + "> 58203565325359399008402633568948830189458628227828\n", + "> 80181199384826282014278194139940567587151170094390\n", + "> 35398664372827112653829987240784473053190104293586\n", + "> 86515506006295864861532075273371959191420517255829\n", + "> 71693888707715466499115593487603532921714970056938\n", + "> 54370070576826684624621495650076471787294438377604\n", + "> 53282654108756828443191190634694037855217779295145\n", + "> 36123272525000296071075082563815656710885258350721\n", + "> 45876576172410976447339110607218265236877223636045\n", + "> 17423706905851860660448207621209813287860733969412\n", + "> 81142660418086830619328460811191061556940512689692\n", + "> 51934325451728388641918047049293215058642563049483\n", + "> 62467221648435076201727918039944693004732956340691\n", + "> 15732444386908125794514089057706229429197107928209\n", + "> 55037687525678773091862540744969844508330393682126\n", + "> 18336384825330154686196124348767681297534375946515\n", + "> 80386287592878490201521685554828717201219257766954\n", + "> 78182833757993103614740356856449095527097864797581\n", + "> 16726320100436897842553539920931837441497806860984\n", + "> 48403098129077791799088218795327364475675590848030\n", + "> 87086987551392711854517078544161852424320693150332\n", + "> 59959406895756536782107074926966537676326235447210\n", + "> 69793950679652694742597709739166693763042633987085\n", + "> 41052684708299085211399427365734116182760315001271\n", + "> 65378607361501080857009149939512557028198746004375\n", + "> 35829035317434717326932123578154982629742552737307\n", + "> 94953759765105305946966067683156574377167401875275\n", + "> 88902802571733229619176668713819931811048770190271\n", + "> 25267680276078003013678680992525463401061632866526\n", + "> 36270218540497705585629946580636237993140746255962\n", + "> 24074486908231174977792365466257246923322810917141\n", + "> 91430288197103288597806669760892938638285025333403\n", + "> 34413065578016127815921815005561868836468420090470\n", + "> 23053081172816430487623791969842487255036638784583\n", + "> 11487696932154902810424020138335124462181441773470\n", + "> 63783299490636259666498587618221225225512486764533\n", + "> 67720186971698544312419572409913959008952310058822\n", + "> 95548255300263520781532296796249481641953868218774\n", + "> 76085327132285723110424803456124867697064507995236\n", + "> 37774242535411291684276865538926205024910326572967\n", + "> 23701913275725675285653248258265463092207058596522\n", + "> 29798860272258331913126375147341994889534765745501\n", + "> 18495701454879288984856827726077713721403798879715\n", + "> 38298203783031473527721580348144513491373226651381\n", + "> 34829543829199918180278916522431027392251122869539\n", + "> 40957953066405232632538044100059654939159879593635\n", + "> 29746152185502371307642255121183693803580388584903\n", + "> 41698116222072977186158236678424689157993532961922\n", + "> 62467957194401269043877107275048102390895523597457\n", + "> 23189706772547915061505504953922979530901129967519\n", + "> 86188088225875314529584099251203829009407770775672\n", + "> 11306739708304724483816533873502340845647058077308\n", + "> 82959174767140363198008187129011875491310547126581\n", + "> 97623331044818386269515456334926366572897563400500\n", + "> 42846280183517070527831839425882145521227251250327\n", + "> 55121603546981200581762165212827652751691296897789\n", + "> 32238195734329339946437501907836945765883352399886\n", + "> 75506164965184775180738168837861091527357929701337\n", + "> 62177842752192623401942399639168044983993173312731\n", + "> 32924185707147349566916674687634660915035914677504\n", + "> 99518671430235219628894890102423325116913619626622\n", + "> 73267460800591547471830798392868535206946944540724\n", + "> 76841822524674417161514036427982273348055556214818\n", + "> 97142617910342598647204516893989422179826088076852\n", + "> 87783646182799346313767754307809363333018982642090\n", + "> 10848802521674670883215120185883543223812876952786\n", + "> 71329612474782464538636993009049310363619763878039\n", + "> 62184073572399794223406235393808339651327408011116\n", + "> 66627891981488087797941876876144230030984490851411\n", + "> 60661826293682836764744779239180335110989069790714\n", + "> 85786944089552990653640447425576083659976645795096\n", + "> 66024396409905389607120198219976047599490197230297\n", + "> 64913982680032973156037120041377903785566085089252\n", + "> 16730939319872750275468906903707539413042652315011\n", + "> 94809377245048795150954100921645863754710598436791\n", + "> 78639167021187492431995700641917969777599028300699\n", + "> 15368713711936614952811305876380278410754449733078\n", + "> 40789923115535562561142322423255033685442488917353\n", + "> 44889911501440648020369068063960672322193204149535\n", + "> 41503128880339536053299340368006977710650566631954\n", + "> 81234880673210146739058568557934581403627822703280\n", + "> 82616570773948327592232845941706525094512325230608\n", + "> 22918802058777319719839450180888072429661980811197\n", + "> 77158542502016545090413245809786882778948721859617\n", + "> 72107838435069186155435662884062257473692284509516\n", + "> 20849603980134001723930671666823555245252804609722\n", + "> 53503534226472524250874054075591789781264330331690\n", + "\n", + "\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reserved Space For Imports\n", + "---" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import os\n", + "import pprint\n", + "import time # Typically imported for sleep function, to slow down execution in terminal.\n", + "import typing\n", + "import decorators # Typically imported to compute execution duration of functions.\n", + "import math\n", + "import numpy" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reserved Space For Method Definition\n", + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Import the data table above. Let's be lazy and use the nice multi-cursor feature of the code editor." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "numbers = [ \\\n", + " '37107287533902102798797998220837590246510135740250',\n", + " '46376937677490009712648124896970078050417018260538',\n", + " '74324986199524741059474233309513058123726617309629',\n", + " '91942213363574161572522430563301811072406154908250',\n", + " '23067588207539346171171980310421047513778063246676',\n", + " '89261670696623633820136378418383684178734361726757',\n", + " '28112879812849979408065481931592621691275889832738',\n", + " '44274228917432520321923589422876796487670272189318',\n", + " '47451445736001306439091167216856844588711603153276',\n", + " '70386486105843025439939619828917593665686757934951',\n", + " '62176457141856560629502157223196586755079324193331',\n", + " '64906352462741904929101432445813822663347944758178',\n", + " '92575867718337217661963751590579239728245598838407',\n", + " '58203565325359399008402633568948830189458628227828',\n", + " '80181199384826282014278194139940567587151170094390',\n", + " '35398664372827112653829987240784473053190104293586',\n", + " '86515506006295864861532075273371959191420517255829',\n", + " '71693888707715466499115593487603532921714970056938',\n", + " '54370070576826684624621495650076471787294438377604',\n", + " '53282654108756828443191190634694037855217779295145',\n", + " '36123272525000296071075082563815656710885258350721',\n", + " '45876576172410976447339110607218265236877223636045',\n", + " '17423706905851860660448207621209813287860733969412',\n", + " '81142660418086830619328460811191061556940512689692',\n", + " '51934325451728388641918047049293215058642563049483',\n", + " '62467221648435076201727918039944693004732956340691',\n", + " '15732444386908125794514089057706229429197107928209',\n", + " '55037687525678773091862540744969844508330393682126',\n", + " '18336384825330154686196124348767681297534375946515',\n", + " '80386287592878490201521685554828717201219257766954',\n", + " '78182833757993103614740356856449095527097864797581',\n", + " '16726320100436897842553539920931837441497806860984',\n", + " '48403098129077791799088218795327364475675590848030',\n", + " '87086987551392711854517078544161852424320693150332',\n", + " '59959406895756536782107074926966537676326235447210',\n", + " '69793950679652694742597709739166693763042633987085',\n", + " '41052684708299085211399427365734116182760315001271',\n", + " '65378607361501080857009149939512557028198746004375',\n", + " '35829035317434717326932123578154982629742552737307',\n", + " '94953759765105305946966067683156574377167401875275',\n", + " '88902802571733229619176668713819931811048770190271',\n", + " '25267680276078003013678680992525463401061632866526',\n", + " '36270218540497705585629946580636237993140746255962',\n", + " '24074486908231174977792365466257246923322810917141',\n", + " '91430288197103288597806669760892938638285025333403',\n", + " '34413065578016127815921815005561868836468420090470',\n", + " '23053081172816430487623791969842487255036638784583',\n", + " '11487696932154902810424020138335124462181441773470',\n", + " '63783299490636259666498587618221225225512486764533',\n", + " '67720186971698544312419572409913959008952310058822',\n", + " '95548255300263520781532296796249481641953868218774',\n", + " '76085327132285723110424803456124867697064507995236',\n", + " '37774242535411291684276865538926205024910326572967',\n", + " '23701913275725675285653248258265463092207058596522',\n", + " '29798860272258331913126375147341994889534765745501',\n", + " '18495701454879288984856827726077713721403798879715',\n", + " '38298203783031473527721580348144513491373226651381',\n", + " '34829543829199918180278916522431027392251122869539',\n", + " '40957953066405232632538044100059654939159879593635',\n", + " '29746152185502371307642255121183693803580388584903',\n", + " '41698116222072977186158236678424689157993532961922',\n", + " '62467957194401269043877107275048102390895523597457',\n", + " '23189706772547915061505504953922979530901129967519',\n", + " '86188088225875314529584099251203829009407770775672',\n", + " '11306739708304724483816533873502340845647058077308',\n", + " '82959174767140363198008187129011875491310547126581',\n", + " '97623331044818386269515456334926366572897563400500',\n", + " '42846280183517070527831839425882145521227251250327',\n", + " '55121603546981200581762165212827652751691296897789',\n", + " '32238195734329339946437501907836945765883352399886',\n", + " '75506164965184775180738168837861091527357929701337',\n", + " '62177842752192623401942399639168044983993173312731',\n", + " '32924185707147349566916674687634660915035914677504',\n", + " '99518671430235219628894890102423325116913619626622',\n", + " '73267460800591547471830798392868535206946944540724',\n", + " '76841822524674417161514036427982273348055556214818',\n", + " '97142617910342598647204516893989422179826088076852',\n", + " '87783646182799346313767754307809363333018982642090',\n", + " '10848802521674670883215120185883543223812876952786',\n", + " '71329612474782464538636993009049310363619763878039',\n", + " '62184073572399794223406235393808339651327408011116',\n", + " '66627891981488087797941876876144230030984490851411',\n", + " '60661826293682836764744779239180335110989069790714',\n", + " '85786944089552990653640447425576083659976645795096',\n", + " '66024396409905389607120198219976047599490197230297',\n", + " '64913982680032973156037120041377903785566085089252',\n", + " '16730939319872750275468906903707539413042652315011',\n", + " '94809377245048795150954100921645863754710598436791',\n", + " '78639167021187492431995700641917969777599028300699',\n", + " '15368713711936614952811305876380278410754449733078',\n", + " '40789923115535562561142322423255033685442488917353',\n", + " '44889911501440648020369068063960672322193204149535',\n", + " '41503128880339536053299340368006977710650566631954',\n", + " '81234880673210146739058568557934581403627822703280',\n", + " '82616570773948327592232845941706525094512325230608',\n", + " '22918802058777319719839450180888072429661980811197',\n", + " '77158542502016545090413245809786882778948721859617',\n", + " '72107838435069186155435662884062257473692284509516',\n", + " '20849603980134001723930671666823555245252804609722',\n", + " '53503534226472524250874054075591789781264330331690'\n", + "]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Data Prep\n", + "- Firstly, this data input creates a list which have cells of the ```string``` data type.\n", + "- The strings should be parsed into type ```int``` at some point.\n", + "\n", + "### Solution Approach\n", + "Can we just employ old-school arithmetic by summing the integers by columns, right to left,
\n", + "carrying over anything greater than *9* to the next column?" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "tags": [] + }, + "outputs": [], + "source": [ + "# loop over all 50 numbers in the input to convert the string \n", + "# into a list of characters, still as tpye: string\n", + "for row in range(len(numbers)): \n", + " numbers[row] = list(numbers[row])\n", + " \n", + " # loop across the newly formed list to convert the string\n", + " # character into an integer\n", + " for digit in range(len(numbers[row])):\n", + " numbers[row][digit] = int(numbers[row][digit])\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": "100\n50\n422\n467\n506\n512\n529\n538\n521\n493\n498\n459\n515\n506\n493\n507\n477\n501\n537\n519\n515\n478\n559\n542\n463\n508\n526\n534\n447\n528\n444\n530\n472\n500\n503\n497\n503\n476\n516\n487\n488\n470\n479\n493\n490\n523\n532\n556\n507\n493\n477\n553\n[2, 7, 6, 2, 9, 8, 1, 3, 8, 9, 5, 6, 3, 7, 7, 1, 7, 9, 5, 8, 9, 2, 3, 8, 6, 4, 7, 8, 4, 0, 2, 0, 3, 7, 3, 6, 6, 7, 8, 0, 9, 3, 0, 3, 2, 6, 7, 3, 7, 3, 55]\n" + } + ], + "source": [ + "# time to employ the \"old math\" by running down the columns\n", + "# and summing... Dont forget to carry-over!\n", + "\n", + "# Let's store the sums into a list...\n", + "solution_digits=[]\n", + "column_carryover = 0\n", + "\n", + "print(len(numbers))\n", + "print(len(numbers[0]))\n", + "\n", + "for places in range(len(numbers[0])):\n", + " # initialize the column sum\n", + " places = len(numbers[0])-places-1\n", + " #print(places)\n", + " column_sum = 0\n", + " \n", + " for term in range(len(numbers)):\n", + " #print(\"row=\",term,\", column=\",places)\n", + " column_sum+=numbers[term][places]\n", + " \n", + " column_sum+=column_carryover\n", + " print(column_sum)\n", + " column_carryover=0\n", + " column_sum_element = int(list(str(column_sum))[-1])\n", + " solution_digits.append(column_sum_element)\n", + "\n", + "\n", + " column_sum *= 0.1\n", + " column_carryover = column_sum.__trunc__()\n", + "\n", + "solution_digits.append(column_carryover)\n", + "print(solution_digits)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "tags": [] + }, + "outputs": [ + { + "output_type": "stream", + "name": "stdout", + "text": "The solution is 55373762303\n" + } + ], + "source": [ + "solution_digits.reverse()\n", + "string=\"\"\n", + "for i in solution_digits[:10]:\n", + " string+=str(i)\n", + "\n", + "print(\"The solution is \",string)\n", + "#string.join(str(solution_digits[:10]))\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} \ No newline at end of file