# SPOJ COINS solution

Solution for problem http://www.spoj.com/problems/COINS/ from SPOJ website.

Sometimes I stuck solving some problems from there (usually because my code either add unneeded new line or doesn’t add needed new line and I am finding what is wrong by trial and error), so here is working solution for COINS that can save you time if you encounter some strange Wrong Answer or NZEC errors.

Solution is pretty straightforward – use recursive descent to find global optimal solution. To win some calculation time, we will precalculate first $0 \leqslant N \leqslant 9000$ steps. Source code limit is 50KB, so you can’t fit more precalculated steps without compression or tricks, however even 9000 precalculated steps is enough to solve the problem.

C++ Solution:

```#include <iostream>
#include <cmath>

using namespace std;

const long long precomputed[] = 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long long solve(long long N)
{
if (N < sizeof(precomputed)/sizeof(long long)) {
return precomputed[N];
}

long long nd2 = N / 2;
long long nd3 = N / 3;
long long nd4 = N / 4;

long long nsd2 = solve(nd2);
long long nsd3 = solve(nd3);
long long nsd4 = solve(nd4);

long long eq2 = nsd2 > nd2 ? nsd2 : nd2;
long long eq3 = nsd3 > nd3 ? nsd3 : nd3;
long long eq4 = nsd4 > nd4 ? nsd4 : nd4;

long long eqSum = eq2 + eq3 + eq4;

return N < eqSum ? eqSum : N;
}

int main()
{
long long N;

for (; !feof(stdin); ) {
scanf("%lld\n", &N);
cout << solve(N) << endl;
}

return 0;
}```