EularProject 74：Digit factorial chains

Andrew zhang
Sep 4, 2017

The number 145 is well known for the property that the sum of the factorial of its digits is equal to 145:

1! + 4! + 5! = 1 + 24 + 120 = 145

Perhaps less well known is 169, in that it produces the longest chain of numbers that link back to 169; it turns out that there are only three such loops that exist:

169 → 363601 → 1454 → 169
871 → 45361 → 871
872 → 45362 → 872

It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,

69 → 363600 → 1454 → 169 → 363601 (→ 1454)
78 → 45360 → 871 → 45361 (→ 871)
540 → 145 (→ 145)

Starting with 69 produces a chain of five non-repeating terms, but the longest non-repeating chain with a starting number below one million is sixty terms.

How many chains, with a starting number below one million, contain exactly sixty non-repeating terms?

Answer:
402
Completed on Mon, 4 Sep 2017, 23:15

Code:

#include <iostream>#include <set>#include <vector>using namespace std;#define SIZE 2177281int table[10];vector<set<int>> state(SIZE);int next_num(int current){    int result = 0;    while (current)    {        result += table[current % 10];        current /= 10;    }    return result;}void func(int start){    int next = next_num(start);    if (next == start)    {        state[next].insert(next);    }    if (state[next].size() == 0)    {        func(next);    }    state[start] = state[next];    state[start].insert(start);}int main(){    int result = 0;    table[0] = 1;    for (int i = 1; i < 10; i++)    {        table[i] = table[i - 1] * i;    }    state[145].insert(145);    state[169].insert(169);    state[169].insert(363601);    state[169].insert(1454);    state[871].insert(871);    state[871].insert(45361);    state[872].insert(872);    state[872].insert(45362);    for (int i = 1; i < 1000000; i++)    {        func(i);        if (i % 10000 == 0)            cout << i << endl;    }    for (int i = 1; i < 1000000; i++)    {        if(state[i].size() == 60)            result++;    }    cout << result << endl;    getchar();    return 0;}