PAT 1103 Integer Factorization

最新推荐文章于 2022-08-23 11:54:54 发布

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博客提及一道值得反复看的题目，采用深度优先搜索方法来解决，体现了深度优先搜索在解题中的应用。

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这道题值得反复看

深度优先搜索解决

#include <iostream>
#include <cmath>
#include <vector>
#include <algorithm>
using namespace std;
vector<vector<int>> res;
bool cmp(vector<int>& vector1,vector<int>& vector2){
    int sum1=0,sum2=0;
    for(auto x:vector1){
        sum1+=x;
    }
    for (auto x:vector2){
        sum2+=x;
    }
    if(sum1==sum2){
        for (int i = 0; i < vector1.size(); ++i) {
            if(vector1[i]!=vector2[i]){
                return vector1[i]>vector2[i];
            }
        }
    }
    return sum1>sum2;
}
int fun1(int x,int P){
    int i1=x;
    for (int i = 1; i < P; ++i) {
        i1=i1*x;
    }
    return i1;
}
void dfs(int index,int target,int remain,int* powers,vector<int> & vector1){//此处index数据必须添加
    if (remain==0){//这个可以去掉了
        return;
    }
    vector1.push_back(index);//添加入当前位置数据
    target=target-powers[index];//目标数据减少
    remain--;//剩余数量减少
    if (remain==0&&target==0){
        vector<int> vector2(vector1);
        res.push_back(vector2);
        vector1.pop_back();
        return;
    }
    if (target > 0&&remain>=1){
        for (int i = index; i >= 1; --i) {
            dfs(i, target , remain, powers,vector1);
        }
    }
    vector1.pop_back();
}
int main() {
    int N,K,P;
    cin>>N>>K>>P;
    int maxIndex=int(sqrt(N));
    int powers[maxIndex+2];
    for (int i = 0; i <= maxIndex; ++i) {
        powers[i]=fun1(i,P);
    }
    vector<int> vector1;
    for (int i = maxIndex; i >=1 ; --i) {
        dfs(i,N,K,powers,vector1);
    }
    if(res.empty()){
        cout<<"Impossible"<<endl;
        return 0;
    }
    sort(res.begin(),res.end(),cmp);
    vector1=res[0];
        cout << N << " = "<<vector1[0]<<"^"<<P;
    for (int i = 1; i < vector1.size(); ++i) {
        cout<<" + "<<vector1[i]<<"^"<<P;
    }
    cout<<endl;
    return 0;
}

#include <iostream>
#include<vector>
#include<cmath>
#include<algorithm>
using namespace std;
int N,num,K;
int sum=0;
vector<vector<int>> res;
vector<int> temp;
int findMax(int N){
    int i=0;
    while(pow(i,K)<=N){
        i++;
    }
    return i;
}
int findval(int N){
    for(int i=1;i<=N;i++){
        int val=pow(i,K);
        if(val==N){
            return i;
        }
    }
}
bool cmp(vector<int>& v1,vector<int>& v2){
    int sum1=0,sum2=0;
    for(auto x:v1){
        sum1+=x;
    }
    for(auto y:v2){
        sum2+=y;
    }
    if(sum1!=sum2){
        return sum1>sum2;
    }
    int len1=v1.size();
    for(int i=0;i<len1;i++){
        if(v1[i]!=v2[i]){
            return v1[i]>v2[i];
        }
    }
    return true;
}
void dfs(int index,int* powers,int numIndex){
        sum+=powers[index];
        temp.push_back(powers[index]);
        if(temp.size()>num){

        }else if(sum==N&&temp.size()==num){
            vector<int> v;
            v=temp;
            res.push_back(v);
        }else if(sum<N){
            for(int i=index;i<=numIndex;i++){
                if(sum+powers[i]<=N){
                    dfs(i,powers,numIndex);
                }else{
                    break;
                }
            }
        }
        sum-=powers[index];
        temp.pop_back();
}
int main()
{
   cin>>N>>num>>K;
   int maxIndex=findMax(N);
   int powers[maxIndex+2];
   for(int i=1;i<=maxIndex;i++){
      powers[i]=pow(i,K);
   }
   for(int i=1;i<=maxIndex;i++){
        dfs(i,powers,maxIndex);
   }
   sort(res.begin(),res.end(),cmp);
   if(res.size()==0){
    cout<<"Impossible"<<endl;
   }else{
       vector<int> v=res[0];
       cout<<N<<" =";
       bool first=true;
       for(int i=v.size()-1;i>=0;i--){
            int val=findval(v[i]);
        if(!first){
            cout<<" + "<<val<<"^"<<K;
        }else{
            cout<<" "<<val<<"^"<<K;
            first=false;
        }
       }
   }
    return 0;
}