UVA online 00151_PowerCrisis

I took a really long time to get this out. I am researching a method to get the solution with some elegant mathematical formula, but it looks like it is took hard to accomplish. So, I used the brute force method that I have, and here it is:

#include <cstdio>
#include <queue>
#include <map>
using namespace std;

bool isValid(int m, int key, int total){
    queue a;
    int rmv=0, c=0;

    for(int i=0; i<key-1; i++){ a.push(0); }
    for(int i=0; i<total-key; i++){ a.push(0); }

    while(a.size()>1 && !rmv){
            a.push(a.front()); a.pop();
            rmv = a.front(); a.pop();

    return !rmv;

int main(){
    char line[1024]; gets(line);
    int t; sscanf(line, "%d", &t);
    map<int, int> mem;

        int m=mem[t];
            m = 1;
            while(!isValid(m, 13, t)){ m++; }
            mem[t] = m;
        printf("%d\n", m);

        gets(line); sscanf(line, "%d", &t);

    return 0;

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