PAT A-1103 Integer Factorization (30 points)

Title: 1103 Integer Factorization (30 points)

Analysis : Use DFS to proceed from large to small.

#include <iostream>
#include<cstring>
#include<vector>
#include<stdio.h>
using namespace std;
int n,k,p;
vector<int> fac,ans,temp;
int maxFacSum;
void init()
{
    
    
    int i = 1, temp = 0;
    while(temp<=n)
    {
    
    
        fac.push_back(temp);
        int x = 1;
        for(int j = 1;j<=p;j++)
        {
    
    
            x *= i;
        }
        temp = x;
        i++;
    }
}
void dfs(int index,int nowK,int sum,int facSum)
{
    
    
    if(sum == n && nowK == k)
    {
    
    
        if(facSum > maxFacSum)
        {
    
    
            maxFacSum = facSum;
            ans = temp;
        }
        return ;
    }
    if(sum > n || nowK > k)  return ;
    if(index - 1 >= 0)//fac[0]是不要的
    {
    
    
        temp.push_back(index);//选index
        dfs(index,nowK+1,sum+fac[index],facSum+index);
        temp.pop_back();
        dfs(index-1,nowK,sum,facSum);//不选index
    }
}
int main()
{
    
    
    scanf("%d%d%d",&n,&k,&p);
    init();
    dfs(fac.size()-1,0,0,0);
    if(maxFacSum==0)  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;
}