【POJ3414】Pots

本题传送门

本题知识点：宽度优先搜素 + 字符串

题意很简单，如何把用两个杯子，装够到第三个杯子的水。

操作有六种，这样就可以当作是bfs的搜索方向了

// FILL(1) 把第一个杯子装满
// FILL(2) 把第二个杯子装满
// POUR(1,2) 把第一个杯子的水倒进第二个杯子
// POUR(2,1) 把第二个杯子的水倒进第一个杯子
// DROP(1) 把第一个杯子的水都倒掉
// DROP(2) 把第二个杯子的水都倒掉

本题的难点是如何记录路径，我们可以用一个巧妙的方法去解决掉，详细请看代码

// POJ 3414
#include<iostream>
#include<cstdio>
#include<string>
#include<queue>
using namespace std;

bool take[102][102], ok;
int A, B, C;
struct node{
    string str;
    int l, r, pla[102], cnt; // cnt 记录有多少条路径
};
queue<node> que;
string str[] = {
    "FILL(1)",
    "FILL(2)",
    "POUR(1,2)",
    "POUR(2,1)",
    "DROP(1)",
    "DROP(2)"
};

void show(int len, int pla[]){
    printf("%d\n", len);
    for(int i = 1; i <= len; i++){
        cout << str[pla[i]] << endl;
    }
}

void bfs(){
    ok = false;
    take[0][0] = true;
    node a;
    a.str = "NONE";
    a.l = a.r = a.cnt = 0;
    que.push(a);

    while(!que.empty()){
        node next, now = que.front(); que.pop();

//        cout << now.str << " ";
//        printf("l:%d r:%d cnt:%d\n", now.l, now.r, now.cnt);
//        show(now.cnt, now.pla);
//        cout << endl;

        if(now.l == C || now.r == C){
            show(now.cnt, now.pla);
            ok = true;
            break;
        }

        // FILL(1)
        if(now.l < A && !take[A][now.r]){
            next.str = str[0];
            next.l = A;
            next.r = now.r;
            // 这句循环是为了保存之前的路径 下同
            for(int i = 1; i <= now.cnt; i++){
                next.pla[i] = now.pla[i];
            }
            next.pla[now.cnt + 1] = 0;
            next.cnt = now.cnt + 1;
            take[A][now.r] = true;
            que.push(next);
        }

        // FILL(2)
        if(now.r < B && !take[now.l][B]){
            next.str = str[1];
            next.l = now.l;
            next.r = B;
            for(int i = 1; i <= now.cnt; i++){
                next.pla[i] = now.pla[i];
            }
            next.pla[now.cnt + 1] = 1;
            next.cnt = now.cnt + 1;
            take[now.l][B] = true;
            que.push(next);
        }

        // POUR(1, 2)
        if(0 < now.l && now.r < B){
            int R = now.l + now.r >= B ? B : now.l + now.r;
            int L = R - now.r >= now.l ? 0 : now.l - (R - now.r);
            if(!take[L][R]){
                next.str = str[2];
                next.l = L;
                next.r = R;
                for(int i = 1; i <= now.cnt; i++){
                    next.pla[i] = now.pla[i];
                }
                next.pla[now.cnt + 1] = 2;
                next.cnt = now.cnt + 1;
                take[L][R] = true;
                que.push(next);
            }
        }

        // POUR(2,1)
        if(now.l < A && 0 < now.r){
            int L = now.l + now.r >= A ? A : now.l + now.r;
            int R = L - now.l >= now.r ? 0 : now.r - (L - now.l);
            if(!take[L][R]){
                next.str = str[3];
                next.l = L;
                next.r = R;
                for(int i = 1; i <= now.cnt; i++){
                    next.pla[i] = now.pla[i];
                }
                next.pla[now.cnt + 1] = 3;
                next.cnt = now.cnt + 1;
                take[L][R] = true;
                que.push(next);
            }
        }

        // DROP(1)
        if(!take[0][now.r]){
            next.str = str[4];
            next.l = 0;
            next.r = now.r;
            for(int i = 1; i <= now.cnt; i++){
                next.pla[i] = now.pla[i];
            }
            next.cnt = now.cnt + 1;
            next.pla[now.cnt + 1] = 4;
            take[0][now.r] = true;
            que.push(next);
        }

        // DROP(2)
        if(!take[now.l][0]){
            next.str = str[5];
            next.l = now.l;
            next.r = 0;
            for(int i = 1; i <= now.cnt; i++){
                next.pla[i] = now.pla[i];
            }
            next.cnt = now.cnt + 1;
            next.pla[now.cnt + 1] = 5;
            take[now.l][0] = true;
            que.push(next);
        }

    }

    if(!ok) printf("impossible\n");
}

int main()
{
    scanf("%d %d %d", &A, &B, &C);

    bfs();

    return 0;
}