回溯法

N皇后问题

 

递归：

#include<iostream>
#include<vector>
#include<stack>
#include<cmath>
#include<cstring>
using namespace std;
typedef pair<int, int> P;
int n,sum;
vector<P> v;
bool judge(int x, int y){
    for (int i = 0; i < v.size(); i++){
        float bioas = (v[i].second*1.0 - y*1.0) / (v[i].first*1.0 - x * 1.0);
        if (x == v[i].first || y == v[i].second || abs(bioas) == 1.0)
            return false;
    }
    return true;
}
void trace(int index){
    if (index >= n){
        sum++;
        for (int i = 0; i < v.size(); i++)
            printf("(%d, %d) ", v[i].first, v[i].second);
        cout << endl;
        return;
    }
    for (int i = 0; i < n; i++){
        if (judge(index, i)){
            v.push_back(P(index, i));
            trace(index+1);
            v.erase(v.begin()+index, v.end());    
        }
    }
}


int main(){
    while(cin >> n){
        v.clear();
        sum = 0;
        trace(0);
        cout << sum << endl;
    }    
    return 0;
} 

迭代：

#include<iostream>
#include<vector>
#include<stack>
#include<cmath>
#include<cstring>
using namespace std;
typedef pair<int, int> P;
int n,sum;
vector<P> v;
bool judge(int x, int y){
    for (int i = 0; i < v.size(); i++){
        float bioas = (v[i].second*1.0 - y*1.0) / (v[i].first*1.0 - x * 1.0);
        if (x == v[i].first || y == v[i].second || abs(bioas) == 1.0)
            return false;
    }
    return true;
}
void trace(int index){
    if (index >= n){
        sum++;
        for (int i = 0; i < v.size(); i++)
            printf("(%d, %d) ", v[i].first, v[i].second);
        cout << endl;
        return;
    }
    for (int i = 0; i < n; i++){
        if (judge(index, i)){
            v.push_back(P(index, i));
            trace(index+1);
            v.erase(v.begin()+index, v.end());    
        }
    }
}


int main(){
    while(cin >> n){
        v.clear();
        sum = 0;
        trace(0);
        cout << sum << endl;
    }    
    return 0;
} 

0-1背包问题

#include<iostream>
#include<vector>
#include<sstream>
#include<algorithm>
using namespace std;
typedef pair<int, int> P;
int n, maxV, W;
string maxS;
vector<P> v;
bool cmp(P a, P b){
    return a.first > b.first;
}
void solve(int index, int sumV, int sumW, int fV, string s){
    if (maxV < sumV){
        maxV = sumV;
        maxS = s;
    }
    
    if (index >= n || maxV >= fV + sumV) return;
    string left = s;
    solve(index+1, sumV, sumW, fV - v[index].first, left);
    if(sumW + v[index].second <= W && sumV + fV > maxV){
        stringstream ss;
        ss << index+1;
        string right = s +' '+ ss.str();
        solve(index+1, sumV + v[index].first, sumW + v[index].second, fV - v[index].first, right); 
    }
}
int main(){
    while(cin >> n >> W) {
        v.clear();
        maxS.clear();
        maxV = 0;
        int fV = 0;
        for (int i = 0; i < n; i++) {
            int x, w;
            cin >> x >> w;
            fV += x;
            v.push_back(P(x,w));
        }
        //sort(v.begin(), v.end(),cmp);
        string s="最佳解为：";
        solve(0, 0, 0, fV ,s);
        cout << maxV << endl;
        cout << maxS << endl;
    }
    return 0;
} 

/*
4 10
42 7
25 5
12 3
40 4


65
*/