PAT a1103題解

#include <cstdio>
#include <vector>
#include <algorithm>

using namespace std;

int n, k, p, maxFacSum = -1;
vector<int> fac, ans, temp;

int power(int x){
	int ans = 1;
	for(int i = 0; i < p; i++){
		ans *= x;
	}
	return ans;
} 

void init(){
	int i = 0, temp = 0;
	while(temp <= n){
		fac.push_back(temp);
		temp = power(++i);
	}
}

void DFS(int index, int nowK, int sum, int facSum){
	if(sum == n && nowK == k){
		if(facSum > maxFacSum){
			ans = temp;
			maxFacSum = facSum;
		}
		return;
	}
	if(sum > n || nowK > k) return;
	if(index - 1 >= 0){
		temp.push_back(index);
		DFS(index, nowK + 1, sum + fac[index], facSum + index);
		temp.pop_back();
		DFS(index - 1, nowK, sum, facSum); 
	}
}

int main(){
	scanf("%d%d%d", &n, &k, &p);
	init();
	DFS(fac.size() - 1, 0, 0, 0);
	if(maxFacSum == -1) printf("Impossible\n");
	else{
		printf("%d = %d^%d", n, ans[0], p);
		for(int i = 1; i < ans.size(); i++){
			printf(" + %d^%d", ans[i], p);
		}
	}
	return 0;
}