Added solutions 13 and 14 for ipython.
This commit is contained in:
parent
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ipython/EulerProblem013.ipynb
Executable file
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ipython/EulerProblem013.ipynb
Executable file
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{
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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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"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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"~~~\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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"Straight forward. No big deal."
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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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"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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"5537376230\n"
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]
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}
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],
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"source": [
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"numbers_string = \"\"\"\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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"62467957194401269043877107275048102390895523597457\n",
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"23189706772547915061505504953922979530901129967519\n",
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"86188088225875314529584099251203829009407770775672\n",
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"55121603546981200581762165212827652751691296897789\n",
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"32238195734329339946437501907836945765883352399886\n",
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"75506164965184775180738168837861091527357929701337\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",
|
||||||
|
"22918802058777319719839450180888072429661980811197\n",
|
||||||
|
"77158542502016545090413245809786882778948721859617\n",
|
||||||
|
"72107838435069186155435662884062257473692284509516\n",
|
||||||
|
"20849603980134001723930671666823555245252804609722\n",
|
||||||
|
"53503534226472524250874054075591789781264330331690\n",
|
||||||
|
"\"\"\"\n",
|
||||||
|
"\n",
|
||||||
|
"numbers = [int(n) for n in numbers_string.split('\\n') if n]\n",
|
||||||
|
"numbers_sum = sum(numbers)\n",
|
||||||
|
"first_ten_digits = str(numbers_sum)[:10]\n",
|
||||||
|
"assert(first_ten_digits == \"5537376230\")\n",
|
||||||
|
"print(first_ten_digits)\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"metadata": {
|
||||||
|
"completion_date": "Sun, 31 Aug 2014, 19:03",
|
||||||
|
"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": "3.6.3"
|
||||||
|
},
|
||||||
|
"tags": [
|
||||||
|
"brute force",
|
||||||
|
"sum"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 2
|
||||||
|
}
|
||||||
162
ipython/EulerProblem014.ipynb
Executable file
162
ipython/EulerProblem014.ipynb
Executable file
@ -0,0 +1,162 @@
|
|||||||
|
{
|
||||||
|
"cells": [
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"# Euler Problem 14\n",
|
||||||
|
"\n",
|
||||||
|
"The following iterative sequence is defined for the set of positive integers:\n",
|
||||||
|
"\n",
|
||||||
|
"n → n/2 (n is even)\n",
|
||||||
|
"n → 3n + 1 (n is odd)\n",
|
||||||
|
"\n",
|
||||||
|
"Using the rule above and starting with 13, we generate the following sequence:\n",
|
||||||
|
"\n",
|
||||||
|
"$13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1$\n",
|
||||||
|
"\n",
|
||||||
|
"It can be seen that this sequence (starting at 13 and finishing at 1) contains 10 terms. Although it has not been proved yet (Collatz Problem), it is thought that all starting numbers finish at 1.\n",
|
||||||
|
"\n",
|
||||||
|
"Which starting number, under one million, produces the longest chain?\n",
|
||||||
|
"\n",
|
||||||
|
"NOTE: Once the chain starts the terms are allowed to go above one million."
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"I would go for a recursive function with a cache here. This should give us good performance with acceptable memory footprint."
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 1,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [],
|
||||||
|
"source": [
|
||||||
|
"from functools import lru_cache\n",
|
||||||
|
"from collections import deque\n",
|
||||||
|
"\n",
|
||||||
|
"@lru_cache(maxsize=11000000)\n",
|
||||||
|
"def get_collatz_sequence(n):\n",
|
||||||
|
" if n == 1:\n",
|
||||||
|
" return deque([1])\n",
|
||||||
|
" ds = get_collatz_sequence(n // 2) if n % 2 == 0 else get_collatz_sequence(3 * n + 1)\n",
|
||||||
|
" ds.appendleft(n)\n",
|
||||||
|
" return ds\n",
|
||||||
|
"\n",
|
||||||
|
"assert(list(get_collatz_sequence(13)) == [13, 40, 20, 10, 5, 16, 8, 4, 2, 1])"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"Isn't this a beautiful solution? We need a deque to appendleft. Of course, we could also use a regular list and reverse the result, but it is nicer to get the correct solution out right away. Now we simply force the solution."
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 2,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"Okay, we need a loop.\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"try:\n",
|
||||||
|
" s = max([(len(get_collatz_sequence(i)), i) for i in range(1000000)])\n",
|
||||||
|
" print(s)\n",
|
||||||
|
" assert(s == 837799)\n",
|
||||||
|
"except RecursionError:\n",
|
||||||
|
" print(\"Okay, we need a loop.\")\n"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "code",
|
||||||
|
"execution_count": 3,
|
||||||
|
"metadata": {},
|
||||||
|
"outputs": [
|
||||||
|
{
|
||||||
|
"name": "stdout",
|
||||||
|
"output_type": "stream",
|
||||||
|
"text": [
|
||||||
|
"11.4885111964837\n",
|
||||||
|
"837799\n"
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"source": [
|
||||||
|
"cache = {}\n",
|
||||||
|
"\n",
|
||||||
|
"def get_collatz_sequence(n):\n",
|
||||||
|
" global cache\n",
|
||||||
|
" orig_n = n\n",
|
||||||
|
" cs = []\n",
|
||||||
|
" while n != 1:\n",
|
||||||
|
" if n in cache:\n",
|
||||||
|
" cs = cs + cache[n]\n",
|
||||||
|
" cache[orig_n] = cs\n",
|
||||||
|
" return cs\n",
|
||||||
|
" cs.append(n)\n",
|
||||||
|
" n = n // 2 if n % 2 == 0 else 3 * n + 1\n",
|
||||||
|
" cs.append(n)\n",
|
||||||
|
" for i in range(len(cs)):\n",
|
||||||
|
" cache[cs[i]] = cs[i:]\n",
|
||||||
|
" return cs\n",
|
||||||
|
"\n",
|
||||||
|
"assert(list(get_collatz_sequence(13)) == [13, 40, 20, 10, 5, 16, 8, 4, 2, 1])\n",
|
||||||
|
"\n",
|
||||||
|
"def brute_force():\n",
|
||||||
|
" return max([(len(get_collatz_sequence(i)), i) for i in range(1, 1000000)])[1]\n",
|
||||||
|
"\n",
|
||||||
|
"s = brute_force()\n",
|
||||||
|
"assert(s == 837799)\n",
|
||||||
|
"\n",
|
||||||
|
"import timeit\n",
|
||||||
|
"print(timeit.timeit(brute_force, number=10))\n",
|
||||||
|
"print(brute_force())"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
{
|
||||||
|
"cell_type": "markdown",
|
||||||
|
"metadata": {},
|
||||||
|
"source": [
|
||||||
|
"Here we go. Takes some time. We could optimize by caching only the length and not the complete list."
|
||||||
|
]
|
||||||
|
}
|
||||||
|
],
|
||||||
|
"metadata": {
|
||||||
|
"completion_date": "Sun, 31 Aug 2014, 19:45",
|
||||||
|
"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": "3.6.3"
|
||||||
|
},
|
||||||
|
"tags": [
|
||||||
|
"collatz",
|
||||||
|
"cache",
|
||||||
|
"deque"
|
||||||
|
]
|
||||||
|
},
|
||||||
|
"nbformat": 4,
|
||||||
|
"nbformat_minor": 2
|
||||||
|
}
|
||||||
Loading…
Reference in New Issue
Block a user