ACM学习历程——POJ3295 Tautology（搜索，二叉树）

Description

WFF 'N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, q, r, s, t. A Well-formed formula (WFF) is any string of these symbols obeying the following rules:

• p, q, r, s, and t are WFFs
• if w is a WFF, Nw is a WFF
• if w and x are WFFs, Kwx, Awx, Cwx, and Ewx are WFFs.

The meaning of a WFF is defined as follows:

• p, q, r, s, and t are logical variables that may take on the value 0 (false) or 1 (true).
• K, A, N, C, E mean and, or, not, implies, and equals as defined in the truth table below.

Definitions of K, A, N, C, and E

w  x	Kwx	Awx	Nw	Cwx	Ewx
1  1	1	1	0	1	1
1  0	0	1	0	0	0
0  1	0	1	1	1	0
0  0	0	0	1	1	1

A tautology is a WFF that has value 1 (true) regardless of the values of its variables. For example, ApNp is a tautology because it is true regardless of the value of p. On the other hand, ApNq is not, because it has the value 0 for p=0, q=1.

You must determine whether or not a WFF is a tautology.

Input

Input consists of several test cases. Each test case is a single line containing a WFF with no more than 100 symbols. A line containing 0 follows the last case.

Output

For each test case, output a line containing tautology or not as appropriate.

Sample Input

ApNp
ApNq
0

Sample Output

tautology
not

考虑到运算符最多是二元的，将运算符和变量存进二叉树中，结构体中用一个val值来记录是否是变量，为了提高效率，用一个visit数组来记录用到了哪几个变量。此外在最后进行运算的时候，需要二叉树进行后序遍历。此外输入采用先序遍历。

代码：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <set>
#include <map>
#include <vector>
#include <queue>
#include <string>
#define inf 0x3fffffff
#define eps 1e-10

using namespace std;

struct node
{
    char op;
    int val;
    node *left;
    node *right;
};

bool a[5];
bool visit[5];

int Do(char op, int x, int y)
{
    switch (op)
    {
        case 'K':
            return x&&y;
        case 'A':
            return x||y;
        case 'N':
            return !x;
        case 'C':
            return !x || y;
        case 'E':
            return x == y;
    }
}

bool Input(node *p)
{
    char ch;
    ch = getchar();
    if (ch == '0')
        return 0;
    p->op = ch;
    p->val = -1;
    switch (ch)
    {
        case 'p':
            p->val = 0;
            visit[0] = 1;
            return 1;
        case 'q':
            p->val = 1;
            visit[1] = 1;
            return 1;
        case 'r':
            p->val = 2;
            visit[2] = 1;
            return 1;
        case 's':
            p->val = 3;
            visit[3] = 1;
            return 1;
        case 't':
            p->val = 4;
            visit[4] = 1;
            return 1;
        case 'N':
            p->left = (node *)malloc(sizeof(node));
            return Input(p->left);
        default:
            p->left = (node *)malloc(sizeof(node));
            p->right = (node *)malloc(sizeof(node));
            Input(p->left);
            return Input(p->right);
    }
}

bool caculate(node *p)
{
    if (p->val != -1)
        return a[p->val];
    if (p->op == 'N')
        return Do(p->op, caculate(p->left), 1);
    else
        return Do(p->op, caculate(p->left), caculate(p->right));
}

bool dfs(int now, node *head)
{
    if (now == 5)
        return caculate(head);
    if (visit[now] == 0)
        return dfs(now+1, head);
    int ii, jj;
    a[now] = 0;
    ii = dfs(now+1, head);
    a[now] = 1;
    jj = dfs(now+1, head);
    return ii && jj;
}

bool qt(node *head)
{
    if (dfs(0, head))
        printf("tautology\n");
    else
        printf("not\n");
}

int main()
{
    //freopen("test.txt", "r", stdin);
    node *head;
    for (;;)
    {
        memset(visit, 0, sizeof(visit));
        head = (node *)malloc(sizeof(node));
        if(!Input(head))
            break;
        getchar();
        qt(head);
    }
    return 0;
}