1103.Integer Factorization (30)...to be continued...

/**
* pat-al-1103
* 2017-03-02
* Cpp version
* Author: fengLian_s
*/
#include<stdio.h>
#include<vector>
using namespace std;
int n, k, p, maxFacSum = -1;
vector<int> fac, ans, tmp;
int power(int x)
{
int ans = 1;
for(int i = 0;i < p;i++)
{
ans *= x;
}
return ans;
}
void init()
{
int i = 0, tmp = 0;
while(tmp <= n)
{
fac.push_back(tmp);
tmp = power(++i);
}
}
void dfs(int index, int nowK, int sum, int facSum)
{
if(nowK == k && sum == n)
{
if(facSum > maxFacSum)
{
ans = tmp;
maxFacSum = facSum;
}
return;
}
if(nowK > k || sum > n)
return;
if(index > 0)
{
tmp.push_back(index);
dfs(index, nowK+1, sum+fac[index], facSum+index);
tmp.pop_back();
dfs(index-1, nowK, sum, facSum);
}
}
int main()
{
freopen("in.txt", "r", stdin);
scanf("%d%d%d", &n, &k, &p);
init();
dfs(fac.size()-1, 0, 0, 0);
if(maxFacSum == -1)
printf("Impossible");
else
{
printf("%d = %d^%d", n, ans[0], p);
for(int i = 1;i < ans.size();i++)
printf(" + %d^%d", ans[i], p);
}
putchar('\n');
return 0;
}