【算法】回溯

子集树

#include<iostream>
#include<algorithm>
using namespace std;
const int maxn =1e5+5;
int q[maxn];
int x[maxn];
int n,c;
int currV,r;
bool isprinted=false;

void print_ans()
{
    for(int i=0;i<=n;++i) 
    {
        if(x[i]) cout<<q[i]<<" ";
    }
    cout<<endl;
    return ;
}
void BackTrack(int t)
{
    if(isprinted) return ;
    if(currV==c) 
    {
        print_ans();
        isprinted=true;
        return ;
    }
    if(t==n) 
    {
        return ;
    }

    r-=q[t];
    if(currV+q[t]<=c)//约束
    {
        currV+=q[t];
        x[t]=1;

        BackTrack(t+1);

        x[t]=0;
        currV-=q[t];
    }
    if(currV+r>=c)//上界
        BackTrack(t+1);
    r+=q[t];
    
}
int main()
{
    cin>>n>>c;
    long long sum =0;
    for(int i =0 ;i<n;++i) 
    {
        cin>>q[i];
        sum+=q[i];
    }
    if(sum<c)
    {
        cout<<"No Solution!\n";
        return 0;
    }
    r=sum,currV=0;
    BackTrack(0);
    if(!isprinted)
    cout<<"No Solution!\n";
    return 0;

}

满m叉树

    #include<iostream>
    using namespace std;
    const int maxn=100+5;
    const int inf=1e9;
    int c[maxn][maxn],w[maxn][maxn];
    int x[maxn][maxn];
    int bestx[maxn][maxn];

    int n,m,d;

    int currC,currW,bestW=inf;

    void BackTrack(int t)
    {
        if(t==n)
        {
            if(currW<bestW)
            {
                for(int i =0;i<n;++i) for(int j=0;j<m;++j) bestx[i][j]=x[i][j];

                bestW=currW;
            }
            return ;
        }
        for(int i =0;i<m;++i)
        {
            if(currC+c[t][i]<=d && currW+w[t][i]<bestW)
            {
                currC+=c[t][i],currW+=w[t][i];
                x[t][i]=1;

                BackTrack(t+1);

                currC-=c[t][i],currW-=w[t][i];
                x[t][i]=0;
            }
        }
    }
    int main()
    {
        cin>>n>>m>>d;
        for(int i =0 ;i<n;++i) 
            for(int j=0;j<m;++j)
                cin>>c[i][j];
        for(int i =0 ;i<n;++i) 
            for(int j=0;j<m;++j)
                cin>>w[i][j];
        BackTrack(0);
        if(bestW!=inf)
        {
            cout<<bestW<<endl;
            for(int i=0;i<n;++i)
            {
                for(int j=0;j<m;++j)
                {
                    if(bestx[i][j]) cout<<j+1<<" ";
                }
            }
            cout<<endl;
        }
    }

排列树

待续