PAT_A1103

错误代码：

#include <iostream>
#include <cstdio>
#include <cmath>
#include <stack>
using namespace std;

const int maxn = 15;
int a[maxn];
int N,K,P,summax = 0;     
string strmax="0";

void reverse(string& str){
    stack<char> tmp;
    string::iterator it = str.begin();
    while(str.size()){
        tmp.push(*str.begin());
        str.erase(str.begin());
    }
    while(!tmp.empty()){
        str += tmp.top();
        tmp.pop();
    }
}

void DFS(int index, int nowk, int sumN, int sum, string str){
    printf("111");
    if(nowk == K ){
        printf("333");
        if(sumN == N){
            printf("333");
            reverse(str);
            if(sum > summax){
                summax = sum;
                strmax.replace(0, strmax.size(), str);
            }
            else if(sum == summax && str > strmax){
                strmax.replace(0, strmax.size(), str);
            }
        }
        
        return;
    }
    
    if(sumN > N) return;
    
     //选index
    DFS(index, nowk + 1, sumN + pow(index, P), sum + index, str + (char)index);
    //不选index
    DFS(index + 1, nowk, sumN, sum, str); 

    
    
    
}

int main(void)
{
    freopen("in.txt","r",stdin);
    
    scanf("%d%d%d",&N,&K,&P);
    string str;
    DFS(0, 0, 0, 0, str);
    
    if(strmax.size() != 0)
        printf("%s
",strmax.c_str());
    else
        printf("Impossible");
        
    fclose(stdin);
    return 0;
}

AC代码：

#include <iostream>
#include <cstdio>
#include <vector>
#include <cmath>
using namespace std;

int N,K,P;
vector<int> vi, tmp, ans;
int summax = -1, sumN = 0;

void DFS(int index, int nowk, int sum, int sumN){
    if(sumN == N && nowk == K){    //终止条件 
        if(sum > summax){
            summax =sum;     //更新 
            ans = tmp;
        }
        
        return ;
    }
    
    if(sumN > N || nowk > K)
        return;

    if(index <= 0) return;
    
    if(index > 0){
        tmp.push_back(index);
        DFS(index, nowk + 1, sum + index, sumN + vi[index]);
        tmp.pop_back();
        DFS(index - 1, nowk, sum, sumN);
    }
}


int main(void){
    freopen("in.txt","r",stdin);
    
    scanf("%d%d%d",&N,&K,&P); 
    for(int i = 0; pow(i,P) <= N; i++)
        vi.push_back(pow(i,P));
    
    DFS(vi.size() - 1, 0, 0, 0);
    if(summax == -1)
        printf("Impossible
");
    else{
        printf("%d = ",N);
        for(int i = 0; i < ans.size(); i++){
            if(i == 0){
                printf("%d^%d",ans[i],P);
            }
            else{
                printf(" + %d^%d",ans[i],P);
            }
        }
    }


    
    fclose(stdin);
    return 0;
}