Project Euler #13: Large sum

This article is part of a series where I'll be diving head first into the Project Euler puzzles. I want to document the challenge of solving such a puzzle and how I got to the answer. I want to prefix this by stating that I can't cheat for any of these challenges; with that I mean I can't look up any other implementations online. After the implementation, I will validate the answer by using this document or a similar sheet.

In this article I'll be solving: Project Euler #13.

This article features only an answer, because I’ve started writing from problem 14.

fn problem_13(v: Vec<&'static str>) -> u64 {
    let mut list: Vec<u64> = vec![0; v[0].len()];
    let mut total: u64 = 0;

    // So the idea is to go over each sum in the list
    // Then over each character in that sum.
    // Swap out the old number of <list> and add the value
    // you see to that index. Basically summing up vertically
    // if you will.
    for s in &v {
        for (i, t) in s.chars().enumerate() {
            let n = t.to_digit(10).unwrap() as u64;
            let old = list.remove(i);
            list.insert(i, n + old);
        }
    }

    let f = 11;
    // This takes all the 50 values of <list> and tries
    // to sum them, the primary school way, up to 12 digits (powers).
    // So the way you sum is like:
    //
    // 506 00 000 000 000 + 11 0's
    //  428 0 000 000 000 + 10 0's
    //   443  000 000 000 +  9 0's etc.
    //
    // You only need 8 of these to make a 10 digit number
    // but considering all values are 3 digits long we need
    // 8 + 3 = 11 numbers.
    for (i, l) in list.iter().take(f).enumerate() {
        let n = f - i; // + the last 3 digits
        let pow = 10_u64.pow(n as u32) as u64;
        total += *l * pow;
    }

    // The total number is 5 digits too long
    total / 10_000
}

#[test]
fn test_first_ten_digits() {
    let v = vec![
        "37107287533902102798797998220837590246510135740250",
        "46376937677490009712648124896970078050417018260538",
        "74324986199524741059474233309513058123726617309629",
        "91942213363574161572522430563301811072406154908250",
        "23067588207539346171171980310421047513778063246676",
        "89261670696623633820136378418383684178734361726757",
        "28112879812849979408065481931592621691275889832738",
        "44274228917432520321923589422876796487670272189318",
        "47451445736001306439091167216856844588711603153276",
        "70386486105843025439939619828917593665686757934951",
        "62176457141856560629502157223196586755079324193331",
        "64906352462741904929101432445813822663347944758178",
        "92575867718337217661963751590579239728245598838407",
        "58203565325359399008402633568948830189458628227828",
        "80181199384826282014278194139940567587151170094390",
        "35398664372827112653829987240784473053190104293586",
        "86515506006295864861532075273371959191420517255829",
        "71693888707715466499115593487603532921714970056938",
        "54370070576826684624621495650076471787294438377604",
        "53282654108756828443191190634694037855217779295145",
        "36123272525000296071075082563815656710885258350721",
        "45876576172410976447339110607218265236877223636045",
        "17423706905851860660448207621209813287860733969412",
        "81142660418086830619328460811191061556940512689692",
        "51934325451728388641918047049293215058642563049483",
        "62467221648435076201727918039944693004732956340691",
        "15732444386908125794514089057706229429197107928209",
        "55037687525678773091862540744969844508330393682126",
        "18336384825330154686196124348767681297534375946515",
        "80386287592878490201521685554828717201219257766954",
        "78182833757993103614740356856449095527097864797581",
        "16726320100436897842553539920931837441497806860984",
        "48403098129077791799088218795327364475675590848030",
        "87086987551392711854517078544161852424320693150332",
        "59959406895756536782107074926966537676326235447210",
        "69793950679652694742597709739166693763042633987085",
        "41052684708299085211399427365734116182760315001271",
        "65378607361501080857009149939512557028198746004375",
        "35829035317434717326932123578154982629742552737307",
        "94953759765105305946966067683156574377167401875275",
        "88902802571733229619176668713819931811048770190271",
        "25267680276078003013678680992525463401061632866526",
        "36270218540497705585629946580636237993140746255962",
        "24074486908231174977792365466257246923322810917141",
        "91430288197103288597806669760892938638285025333403",
        "34413065578016127815921815005561868836468420090470",
        "23053081172816430487623791969842487255036638784583",
        "11487696932154902810424020138335124462181441773470",
        "63783299490636259666498587618221225225512486764533",
        "67720186971698544312419572409913959008952310058822",
        "95548255300263520781532296796249481641953868218774",
        "76085327132285723110424803456124867697064507995236",
        "37774242535411291684276865538926205024910326572967",
        "23701913275725675285653248258265463092207058596522",
        "29798860272258331913126375147341994889534765745501",
        "18495701454879288984856827726077713721403798879715",
        "38298203783031473527721580348144513491373226651381",
        "34829543829199918180278916522431027392251122869539",
        "40957953066405232632538044100059654939159879593635",
        "29746152185502371307642255121183693803580388584903",
        "41698116222072977186158236678424689157993532961922",
        "62467957194401269043877107275048102390895523597457",
        "23189706772547915061505504953922979530901129967519",
        "86188088225875314529584099251203829009407770775672",
        "11306739708304724483816533873502340845647058077308",
        "82959174767140363198008187129011875491310547126581",
        "97623331044818386269515456334926366572897563400500",
        "42846280183517070527831839425882145521227251250327",
        "55121603546981200581762165212827652751691296897789",
        "32238195734329339946437501907836945765883352399886",
        "75506164965184775180738168837861091527357929701337",
        "62177842752192623401942399639168044983993173312731",
        "32924185707147349566916674687634660915035914677504",
        "99518671430235219628894890102423325116913619626622",
        "73267460800591547471830798392868535206946944540724",
        "76841822524674417161514036427982273348055556214818",
        "97142617910342598647204516893989422179826088076852",
        "87783646182799346313767754307809363333018982642090",
        "10848802521674670883215120185883543223812876952786",
        "71329612474782464538636993009049310363619763878039",
        "62184073572399794223406235393808339651327408011116",
        "66627891981488087797941876876144230030984490851411",
        "60661826293682836764744779239180335110989069790714",
        "85786944089552990653640447425576083659976645795096",
        "66024396409905389607120198219976047599490197230297",
        "64913982680032973156037120041377903785566085089252",
        "16730939319872750275468906903707539413042652315011",
        "94809377245048795150954100921645863754710598436791",
        "78639167021187492431995700641917969777599028300699",
        "15368713711936614952811305876380278410754449733078",
        "40789923115535562561142322423255033685442488917353",
        "44889911501440648020369068063960672322193204149535",
        "41503128880339536053299340368006977710650566631954",
        "81234880673210146739058568557934581403627822703280",
        "82616570773948327592232845941706525094512325230608",
        "22918802058777319719839450180888072429661980811197",
        "77158542502016545090413245809786882778948721859617",
        "72107838435069186155435662884062257473692284509516",
        "20849603980134001723930671666823555245252804609722",
        "53503534226472524250874054075591789781264330331690"
    ];

    assert_eq!(problem_13(v), 5_537_376_230);
}

The full solution is available on GitHub.

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