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p074.cpp
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p074.cpp
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/*
compile with: g++ -std=c++0x p074.cpp -o p074
run with: ./p074
Digit Factorial Chains
Problem 74
The number 145 is well known for the property that the sum of the factorial of its digits is equal to 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
...
It is not difficult to prove that EVERY starting number will eventually get stuck in a loop. For example,
...
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?
*/
#include <iostream> // std::cout
#include <cstdio> // printf
int factorial (int n)
{
int output = 1;
for (int i=1; i<=n; i++)
{
output *= i;
}
return output;
}
int digfactsum (int n)
{
int output = 0;
int lastdig;
while (n > 0)
{
lastdig = n - 10*(n/10);
//std::cout << lastdig;
output += factorial(lastdig);
n = n/10; // note: n was passed by value
}
return output;
}
int n_occur (int array[61], int num){ // count number of occurrences of num in the input array
int count = 0;
for (int i=0; i<61; i++) {
if (array[i]==num)
count++ ;
}
return count;
}
// work-in-progress
int digfactchain (int n)
{
int n_array[61] = {0}; // Problem states that no chain should have more than 60 non-repeating terms, initialize as zeros
int currentlink = n;
int output = 0;
for (int i=0; i<61; i++) {
output += 1;
n_array[i] = currentlink;
//printf("%d \n", currentlink);
if (n_occur(n_array, currentlink) == 2) // see if there are two occurrences of the same number (i.e. a loop)
return output-1;
currentlink = digfactsum(currentlink);
}
return output-1;
}
int facts [10];
int main()
{
for (int i=0; i<10; i++)
{
facts[i] = factorial(i); // compute these ahead of time so they don't need to be re-computed
std::cout << facts[i] << ", ";
}
//std::cout << "\n";
//std::cout << digfactsum(145);
//std::cout << digfactchain(69);
int answer = 0;
for (int n=1; n<1000000; n++)
{
printf("%d \n", n);
if (digfactchain(n) == 60)
answer++;
}
printf("%d chains, with a starting number below one million, contain exactly sixty non-repeating terms", answer);
}