1、鏈接

http://acm.hdu.edu.cn/showproblem.php?pid=1495

2、題目

Description
大家一定覺的運動以後喝可樂是一件很愜意的事情，但是seeyou卻不這麽認為。因為每次當seeyou買了可樂以後，阿牛就要求和seeyou一起分享這一瓶可樂，而且一定要喝的和seeyou一樣多。但seeyou的手中只有兩個杯子，它們的容量分別是N 毫升和M 毫升 可樂的體積為S （S<101）毫升　(正好裝滿一瓶) ，它們三個之間可以相互倒可樂 (都是沒有刻度的，且 S==N+M，101＞S＞0，N＞0，M＞0) 。聰明的ACMER你們說他們能平分嗎？如果能請輸出倒可樂的最少的次數，如果不能輸出"NO"。

Input
三個整數 : S 可樂的體積 , N 和 M是兩個杯子的容量，以"0 0 0"結束。

Output
如果能平分的話請輸出最少要倒的次數，否則輸出"NO"。

Sample Input
7 4 3
4 1 3
0 0 0

Sample Output
NO
3

3、解題分析：

求平分可樂的最少次數，彼此互相倒，所以存在6種狀態：

①s->n　　②s->m

③n->s　　④m->s

⑤n->m　 ⑥m->n

屬於bfs搜索類型的題（有狀態，求最少）

想明白一個寫出來，其余狀態都一個思路

4、代碼

#include<bits/stdc++.h>
using
 
 namespace std;

struct  Volum
{
    int Vs;
    int Vn;
    int Vm;
    int step;
};

int vis[105][105];
int s,n,m;

queue<Volum>q;

int bfs(int a,int b, int c)
{
    while(!q.empty())
    {
        q.pop();
    }

    Volum V1;

    V1.Vs = s;
    V1.Vn = 0;
    V1.Vm = 0;

    q.push(V1);
    vis[n][m] 
 
= 1;

    while(!q.empty())
    {
        Volum tmp = q.front();
        Volum tmp1;
        if(tmp.Vn == s/2 && tmp.Vs == s/2) ///tmp 這個結構體中的 Vs 和 Vn 均為 s的一半，符合條件直接返回
        {
            return tmp.step;
        }

        ///s -> n  由 s 向 n 倒
        if(tmp.Vs && tmp.Vn != n)
        {
            int c = n - tmp.Vn;
            if(tmp.Vs >= c)
            {
                tmp1.Vs = tmp.Vs - c;
                tmp1.Vn = n;
            }

            else
            {
                tmp1.Vs = 0;
                tmp1.Vn = tmp.Vn + tmp.Vs;
            }
            tmp1.Vm = tmp.Vm;
            tmp1.step = tmp.step + 1;

            if(!vis[tmp1.Vn][tmp1.Vm])
            {
                q.push(tmp1);
                vis[tmp1.Vn][tmp1.Vm] = 1;
            }
        }

        ///s -> m
        if(tmp.Vs && tmp.Vm != m)
        {
            int c = m - tmp.Vm;
            if(tmp.Vs >= c)
            {
                tmp1.Vs = tmp.Vs - c;
                tmp1.Vm = m;
            }

            else
            {
                tmp1.Vs = 0;
                tmp1.Vm = tmp.Vm + tmp.Vs;
            }
            tmp1.Vn = tmp.Vn;
            tmp1.step = tmp.step + 1;

            if(!vis[tmp1.Vn][tmp1.Vm])
            {
                q.push(tmp1);
                vis[tmp1.Vn][tmp1.Vm] = 1;
            }
        }

        /// n -> s
        if(tmp.Vn && tmp.Vs != s)
        {
            int c = s - tmp.Vs;
            if(tmp.Vn >= c)
            {
                tmp1.Vn = tmp.Vn - c;
                tmp1.Vs = s;
            }

            else
            {
                tmp1.Vn = 0;
                tmp1.Vs = tmp.Vs + tmp.Vn;
            }
            tmp1.Vm = tmp.Vm;
            tmp1.step = tmp.step + 1;

            if(!vis[tmp1.Vn][tmp1.Vm])
            {
                q.push(tmp1);
                vis[tmp1.Vn][tmp1.Vm] = 1;
            }
        }

        /// m -> s
        if(tmp.Vm && tmp.Vs != s)
        {
            int c = s - tmp.Vs;
            if(tmp.Vm >= c)
            {
                tmp1.Vm = tmp.Vm - c;
                tmp1.Vs = s;
            }

            else
            {
                tmp1.Vm = 0;
                tmp1.Vs = tmp.Vs + tmp.Vm;
            }
            tmp1.Vn = tmp.Vn;
            tmp1.step = tmp.step + 1;

            if(!vis[tmp1.Vn][tmp1.Vm])
            {
                q.push(tmp1);
                vis[tmp1.Vn][tmp1.Vm] = 1;
            }
        }


        /// n -> m
        if(tmp.Vn && tmp.Vm != m)
        {
            int c = m - tmp.Vm;
            if(tmp.Vn >= c)
            {
                tmp1.Vn = tmp.Vn - c;
                tmp1.Vm = m;
            }

            else
            {
                tmp1.Vn = 0;
                tmp1.Vm = tmp.Vm + tmp.Vn;
            }
            tmp1.Vs = tmp.Vs;
            tmp1.step = tmp.step + 1;

            if(!vis[tmp1.Vn][tmp1.Vm])
            {
                q.push(tmp1);
                vis[tmp1.Vn][tmp1.Vm] = 1;
            }
        }

        /// m -> n
        if(tmp.Vm && tmp.Vn != n)
        {
            int c = n - tmp.Vn;
            if(tmp.Vm >= c)
            {
                tmp1.Vm = tmp.Vm - c;
                tmp1.Vn = n;
            }

            else
            {
                tmp1.Vm = 0;
                tmp1.Vn = tmp.Vn + tmp.Vm;
            }
            tmp1.Vs = tmp.Vs;
            tmp1.step = tmp.step + 1;

            if(!vis[tmp1.Vn][tmp1.Vm])
            {
                q.push(tmp1);
                vis[tmp1.Vn][tmp1.Vm] = 1;
            }
        }
        q.pop();
    }

    return 0;
}

int main()
{
    while(~scanf("%d%d%d",&s,&n,&m))
    {
        memset(vis,0,sizeof(vis));

        if(s == 0 && n == 0 && m == 0)
            break;
        if(s % 2 != 0){
            printf("NO\n");
            continue;
        }
        if(n<m) swap(n,m);
        int ans = bfs(s,n,m);
            if(ans)
                printf("%d\n",ans);
            else
                printf("NO\n");

    }

    return 0;
}

hdu 1495