【USACO】Party Lamps

事实上，每个开关按偶数次的时候，相当于没按。整道题的思路就是按照这个来的。

/*
ID :
LANG: C++11
TASK: lamps
 */

#include <iostream>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <string>
#include <set>

using namespace std;

int N, C;

int lampsTarget[110] = {}, lamps[110] = {};
int switchEffect[4][110] = {};
set<string> lampsAns;

//初始化，分别初始化每个开关作用的灯，将目标状态置为-1，意思是灯开或者关无所谓
void init(){
    for (int i = 1; i <= N; i ++){
        switchEffect[0][i] = 1;
    }
    for (int i = 0; i < (N + 1) / 2; i ++){
        switchEffect[1][2 * i + 1] = 1;
    }
    for (int i = 1; i <= N / 2; i ++){
        switchEffect[2][2 * i] = 1;
    }
    for (int i = 0; i < (N + 2) / 3; i ++){
        switchEffect[3][3 * i + 1] = 1;
    }
    for (int i = 1; i <= N; i ++){
        lampsTarget[i] = -1;
    }
}

//灯状态是否与要求一致
bool fit(){
    for (int i = 1; i <= N; i ++){
        if (lampsTarget[i] == -1)
            continue;
        if (lampsTarget[i] != lamps[i])
            return false;
    }
    return true;
}

//设置灯全亮
void setlamps(){
    for (int i = 1; i <= N; i ++)
        lamps[i] = 1;
}

//按下开关s
inline void pressSwitch(int s){
    for (int i = 1; i <= N; i ++){
        lamps[i] = (lamps[i] + switchEffect[s][i]) % 2;
    }
}

//将结果变成string
inline string itos(){
    char c[110] = {};
    for (int i = 0; i < N; i ++){
        c[i] = lamps[i + 1] + '0';
    }
    return string(c);
}

//枚举开关的状态
void switches(){
    if ((C - 1) % 2 == 0){  //奇数个开关次数
        if (C >= 1) {   //枚举，某个开关按了一次的情况
            for (int i = 0; i < 4; i++) {
                setlamps();
                pressSwitch(i);
                if (fit()) {
                    lampsAns.insert(itos());
                }
            }
        }
        if (C >= 3){    //枚举，某三个开关按了一次的情况
            for (int i = 0; i < 4; i ++){
                setlamps();
                for (int j = 0; j < 4; j ++){
                    if (j == i)
                        continue;
                    pressSwitch(j);
                }
                if (fit()){
                    lampsAns.insert(itos());
                }
            }
        }
    }
    if (C % 2 == 0){    //开关次数是偶数
        //全部开关都开合了偶数次，即相当于未改变灯的状态的情况
        setlamps();
        if (fit())
            lampsAns.insert(itos());
        if (C >= 2) {   //按了两个开关
            for (int i = 0; i < 3; i++) {
                for (int j = i + 1; j < 4; j++) {
                    setlamps();
                    pressSwitch(i);
                    pressSwitch(j);
                    if (fit()) {
                        lampsAns.insert(itos());
                    }
                }
            }
        }
        if (C >= 4){    //按了四个开关
            setlamps();
            for (int i = 0; i < 4; i ++){
                pressSwitch(i);
            }
            if (fit()){
                lampsAns.insert(itos());
            }
        }
    }
}

int main()
{
    freopen("lamps.in", "r", stdin);
    freopen("lamps.out", "w", stdout);

    cin >> N >> C;

    init();
    int t;
    while (cin >> t){
        if (t != -1)
            lampsTarget[t] = 1;
        else
            break;
    }
    while (cin >> t){
        if (t != -1)
            lampsTarget[t] = 0;
        else
            break;
    }

    switches();

    set<string>::iterator it;
    for (it = lampsAns.begin(); it != lampsAns.end(); it ++){
        cout << *it << endl;
    }
    if (lampsAns.empty()){
        cout << "IMPOSSIBLE" << endl;
    }
    return 0;
}