402 lines
18 KiB
Plaintext
402 lines
18 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Problem 13:\n",
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"\n",
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"[Euler Project #13](https://projecteuler.net/problem=13)\n",
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"\n",
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"\n",
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"> Work out the first ten digits of the sum of the following one-hundred 50-digit numbers.\n",
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"\n",
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"> 37107287533902102798797998220837590246510135740250\n",
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"> 46376937677490009712648124896970078050417018260538\n",
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"> 74324986199524741059474233309513058123726617309629\n",
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"> 91942213363574161572522430563301811072406154908250\n",
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"> 23067588207539346171171980310421047513778063246676\n",
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"> 89261670696623633820136378418383684178734361726757\n",
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"> 28112879812849979408065481931592621691275889832738\n",
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"> 44274228917432520321923589422876796487670272189318\n",
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"> 47451445736001306439091167216856844588711603153276\n",
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"> 70386486105843025439939619828917593665686757934951\n",
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"> 62176457141856560629502157223196586755079324193331\n",
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"> 64906352462741904929101432445813822663347944758178\n",
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"> 92575867718337217661963751590579239728245598838407\n",
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"> 58203565325359399008402633568948830189458628227828\n",
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"> 80181199384826282014278194139940567587151170094390\n",
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"> 35398664372827112653829987240784473053190104293586\n",
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"> 86515506006295864861532075273371959191420517255829\n",
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"> 71693888707715466499115593487603532921714970056938\n",
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"> 54370070576826684624621495650076471787294438377604\n",
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"> 53282654108756828443191190634694037855217779295145\n",
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"> 36123272525000296071075082563815656710885258350721\n",
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"> 45876576172410976447339110607218265236877223636045\n",
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"> 17423706905851860660448207621209813287860733969412\n",
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"> 81142660418086830619328460811191061556940512689692\n",
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"> 51934325451728388641918047049293215058642563049483\n",
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"> 62467221648435076201727918039944693004732956340691\n",
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"> 15732444386908125794514089057706229429197107928209\n",
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"> 55037687525678773091862540744969844508330393682126\n",
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"> 18336384825330154686196124348767681297534375946515\n",
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"> 80386287592878490201521685554828717201219257766954\n",
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"> 78182833757993103614740356856449095527097864797581\n",
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"> 16726320100436897842553539920931837441497806860984\n",
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"> 48403098129077791799088218795327364475675590848030\n",
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"> 87086987551392711854517078544161852424320693150332\n",
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"> 59959406895756536782107074926966537676326235447210\n",
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"> 69793950679652694742597709739166693763042633987085\n",
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"> 41052684708299085211399427365734116182760315001271\n",
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"> 65378607361501080857009149939512557028198746004375\n",
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"> 35829035317434717326932123578154982629742552737307\n",
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"> 94953759765105305946966067683156574377167401875275\n",
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"> 88902802571733229619176668713819931811048770190271\n",
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"> 25267680276078003013678680992525463401061632866526\n",
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"> 36270218540497705585629946580636237993140746255962\n",
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"> 24074486908231174977792365466257246923322810917141\n",
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"> 91430288197103288597806669760892938638285025333403\n",
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"> 34413065578016127815921815005561868836468420090470\n",
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"> 23053081172816430487623791969842487255036638784583\n",
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"> 11487696932154902810424020138335124462181441773470\n",
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"> 63783299490636259666498587618221225225512486764533\n",
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"> 67720186971698544312419572409913959008952310058822\n",
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"> 95548255300263520781532296796249481641953868218774\n",
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"> 76085327132285723110424803456124867697064507995236\n",
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"> 37774242535411291684276865538926205024910326572967\n",
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"> 23701913275725675285653248258265463092207058596522\n",
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"> 29798860272258331913126375147341994889534765745501\n",
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"> 18495701454879288984856827726077713721403798879715\n",
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"> 38298203783031473527721580348144513491373226651381\n",
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"> 34829543829199918180278916522431027392251122869539\n",
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"> 40957953066405232632538044100059654939159879593635\n",
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"> 29746152185502371307642255121183693803580388584903\n",
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"> 41698116222072977186158236678424689157993532961922\n",
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"> 62467957194401269043877107275048102390895523597457\n",
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"> 23189706772547915061505504953922979530901129967519\n",
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"> 86188088225875314529584099251203829009407770775672\n",
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"> 11306739708304724483816533873502340845647058077308\n",
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"> 82959174767140363198008187129011875491310547126581\n",
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"> 97623331044818386269515456334926366572897563400500\n",
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"> 42846280183517070527831839425882145521227251250327\n",
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"> 55121603546981200581762165212827652751691296897789\n",
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"> 32238195734329339946437501907836945765883352399886\n",
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"> 75506164965184775180738168837861091527357929701337\n",
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"> 62177842752192623401942399639168044983993173312731\n",
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"> 32924185707147349566916674687634660915035914677504\n",
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"> 99518671430235219628894890102423325116913619626622\n",
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"> 73267460800591547471830798392868535206946944540724\n",
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"> 76841822524674417161514036427982273348055556214818\n",
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"> 97142617910342598647204516893989422179826088076852\n",
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"> 87783646182799346313767754307809363333018982642090\n",
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"> 10848802521674670883215120185883543223812876952786\n",
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"> 71329612474782464538636993009049310363619763878039\n",
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"> 62184073572399794223406235393808339651327408011116\n",
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"> 66627891981488087797941876876144230030984490851411\n",
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"> 60661826293682836764744779239180335110989069790714\n",
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"> 85786944089552990653640447425576083659976645795096\n",
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"> 66024396409905389607120198219976047599490197230297\n",
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"> 64913982680032973156037120041377903785566085089252\n",
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"> 16730939319872750275468906903707539413042652315011\n",
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"> 94809377245048795150954100921645863754710598436791\n",
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"> 78639167021187492431995700641917969777599028300699\n",
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"> 15368713711936614952811305876380278410754449733078\n",
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"> 40789923115535562561142322423255033685442488917353\n",
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"> 44889911501440648020369068063960672322193204149535\n",
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"> 41503128880339536053299340368006977710650566631954\n",
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"> 81234880673210146739058568557934581403627822703280\n",
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"> 82616570773948327592232845941706525094512325230608\n",
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"> 22918802058777319719839450180888072429661980811197\n",
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"> 77158542502016545090413245809786882778948721859617\n",
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"> 72107838435069186155435662884062257473692284509516\n",
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"> 20849603980134001723930671666823555245252804609722\n",
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"> 53503534226472524250874054075591789781264330331690\n",
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"\n",
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"\n",
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Reserved Space For Imports\n",
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"---"
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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": 1,
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"metadata": {},
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"outputs": [],
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"source": [
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"import os\n",
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"import pprint\n",
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"import time # Typically imported for sleep function, to slow down execution in terminal.\n",
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"import typing\n",
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"import decorators # Typically imported to compute execution duration of functions.\n",
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"import math\n",
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"import numpy"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Reserved Space For Method Definition\n",
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"---"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Import the data table above. Let's be lazy and use the nice multi-cursor feature of the code editor."
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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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"metadata": {
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"tags": []
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},
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"outputs": [],
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"source": [
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"numbers = [ \\\n",
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" '37107287533902102798797998220837590246510135740250',\n",
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" '46376937677490009712648124896970078050417018260538',\n",
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" '74324986199524741059474233309513058123726617309629',\n",
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" '91942213363574161572522430563301811072406154908250',\n",
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" '23067588207539346171171980310421047513778063246676',\n",
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" '89261670696623633820136378418383684178734361726757',\n",
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" '28112879812849979408065481931592621691275889832738',\n",
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" '44274228917432520321923589422876796487670272189318',\n",
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" '47451445736001306439091167216856844588711603153276',\n",
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" '70386486105843025439939619828917593665686757934951',\n",
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" '62176457141856560629502157223196586755079324193331',\n",
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" '64906352462741904929101432445813822663347944758178',\n",
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" '92575867718337217661963751590579239728245598838407',\n",
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" '58203565325359399008402633568948830189458628227828',\n",
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" '80181199384826282014278194139940567587151170094390',\n",
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" '35398664372827112653829987240784473053190104293586',\n",
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" '86515506006295864861532075273371959191420517255829',\n",
|
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" '71693888707715466499115593487603532921714970056938',\n",
|
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" '54370070576826684624621495650076471787294438377604',\n",
|
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" '53282654108756828443191190634694037855217779295145',\n",
|
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" '36123272525000296071075082563815656710885258350721',\n",
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" '45876576172410976447339110607218265236877223636045',\n",
|
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" '17423706905851860660448207621209813287860733969412',\n",
|
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" '81142660418086830619328460811191061556940512689692',\n",
|
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" '51934325451728388641918047049293215058642563049483',\n",
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" '62467221648435076201727918039944693004732956340691',\n",
|
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" '15732444386908125794514089057706229429197107928209',\n",
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" '55037687525678773091862540744969844508330393682126',\n",
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" '18336384825330154686196124348767681297534375946515',\n",
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" '80386287592878490201521685554828717201219257766954',\n",
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" '78182833757993103614740356856449095527097864797581',\n",
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" '16726320100436897842553539920931837441497806860984',\n",
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" '48403098129077791799088218795327364475675590848030',\n",
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" '87086987551392711854517078544161852424320693150332',\n",
|
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" '59959406895756536782107074926966537676326235447210',\n",
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" '69793950679652694742597709739166693763042633987085',\n",
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" '41052684708299085211399427365734116182760315001271',\n",
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" '65378607361501080857009149939512557028198746004375',\n",
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" '35829035317434717326932123578154982629742552737307',\n",
|
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" '94953759765105305946966067683156574377167401875275',\n",
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" '88902802571733229619176668713819931811048770190271',\n",
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" '25267680276078003013678680992525463401061632866526',\n",
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" '36270218540497705585629946580636237993140746255962',\n",
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" '24074486908231174977792365466257246923322810917141',\n",
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" '91430288197103288597806669760892938638285025333403',\n",
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" '34413065578016127815921815005561868836468420090470',\n",
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" '23053081172816430487623791969842487255036638784583',\n",
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" '11487696932154902810424020138335124462181441773470',\n",
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" '63783299490636259666498587618221225225512486764533',\n",
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" '67720186971698544312419572409913959008952310058822',\n",
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" '95548255300263520781532296796249481641953868218774',\n",
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" '76085327132285723110424803456124867697064507995236',\n",
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" '37774242535411291684276865538926205024910326572967',\n",
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" '23701913275725675285653248258265463092207058596522',\n",
|
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" '29798860272258331913126375147341994889534765745501',\n",
|
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" '18495701454879288984856827726077713721403798879715',\n",
|
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" '38298203783031473527721580348144513491373226651381',\n",
|
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" '34829543829199918180278916522431027392251122869539',\n",
|
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" '40957953066405232632538044100059654939159879593635',\n",
|
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" '29746152185502371307642255121183693803580388584903',\n",
|
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" '41698116222072977186158236678424689157993532961922',\n",
|
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" '62467957194401269043877107275048102390895523597457',\n",
|
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" '23189706772547915061505504953922979530901129967519',\n",
|
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" '86188088225875314529584099251203829009407770775672',\n",
|
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" '11306739708304724483816533873502340845647058077308',\n",
|
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" '82959174767140363198008187129011875491310547126581',\n",
|
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" '97623331044818386269515456334926366572897563400500',\n",
|
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" '42846280183517070527831839425882145521227251250327',\n",
|
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" '55121603546981200581762165212827652751691296897789',\n",
|
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" '32238195734329339946437501907836945765883352399886',\n",
|
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" '75506164965184775180738168837861091527357929701337',\n",
|
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" '62177842752192623401942399639168044983993173312731',\n",
|
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" '32924185707147349566916674687634660915035914677504',\n",
|
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" '99518671430235219628894890102423325116913619626622',\n",
|
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" '73267460800591547471830798392868535206946944540724',\n",
|
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" '76841822524674417161514036427982273348055556214818',\n",
|
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" '97142617910342598647204516893989422179826088076852',\n",
|
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" '87783646182799346313767754307809363333018982642090',\n",
|
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" '10848802521674670883215120185883543223812876952786',\n",
|
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" '71329612474782464538636993009049310363619763878039',\n",
|
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" '62184073572399794223406235393808339651327408011116',\n",
|
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" '66627891981488087797941876876144230030984490851411',\n",
|
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" '60661826293682836764744779239180335110989069790714',\n",
|
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" '85786944089552990653640447425576083659976645795096',\n",
|
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" '66024396409905389607120198219976047599490197230297',\n",
|
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" '64913982680032973156037120041377903785566085089252',\n",
|
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" '16730939319872750275468906903707539413042652315011',\n",
|
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" '94809377245048795150954100921645863754710598436791',\n",
|
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" '78639167021187492431995700641917969777599028300699',\n",
|
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" '15368713711936614952811305876380278410754449733078',\n",
|
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" '40789923115535562561142322423255033685442488917353',\n",
|
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" '44889911501440648020369068063960672322193204149535',\n",
|
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" '41503128880339536053299340368006977710650566631954',\n",
|
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" '81234880673210146739058568557934581403627822703280',\n",
|
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" '82616570773948327592232845941706525094512325230608',\n",
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" '22918802058777319719839450180888072429661980811197',\n",
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" '77158542502016545090413245809786882778948721859617',\n",
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" '72107838435069186155435662884062257473692284509516',\n",
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" '20849603980134001723930671666823555245252804609722',\n",
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" '53503534226472524250874054075591789781264330331690'\n",
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"]"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Data Prep\n",
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"- Firstly, this data input creates a list which have cells of the ```string``` data type.\n",
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"- The strings should be parsed into type ```int``` at some point.\n",
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"\n",
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"### Solution Approach\n",
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"Can we just employ old-school arithmetic by summing the integers by columns, right to left, <br>\n",
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"carrying over anything greater than *9* to the next column?"
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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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"metadata": {
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"tags": []
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},
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"outputs": [],
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"source": [
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"# loop over all 50 numbers in the input to convert the string \n",
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"# into a list of characters, still as tpye: string\n",
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"for row in range(len(numbers)): \n",
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" numbers[row] = list(numbers[row])\n",
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" \n",
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" # loop across the newly formed list to convert the string\n",
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" # character into an integer\n",
|
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" 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
|
|
} |