POJ 3295, Tautology
2009-09-28 03:29
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输入字符串为二叉树的先根遍历(Pre-order string),可采用堆栈或者递归。
一般pre-order 字符串计算使用递归, post-order 字符串计算使用堆栈
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
Source
Waterloo Local Contest, 2006.9.30
// POJ3295.cpp : Defines the entry point for the console application.
//
#include <iostream>
#include <string>
using namespace std;
static int pos = -1;
bool WFF(const string& formula, int i)
{
++pos;
switch(formula[pos])
{
case 'p':
return i & 1;
case 'q':
return (i >> 1) & 1;
case 'r':
return (i >> 2) & 1;
case 's':
return (i >> 3) & 1;
case 't':
return (i >> 4) & 1;
case 'N':
return !WFF(formula, i);
case 'K':
return WFF(formula, i) & WFF(formula, i);
case 'A':
return WFF(formula, i) | WFF(formula, i);
case 'C':
return !WFF(formula, i) | WFF(formula, i);
case 'E':
return WFF(formula, i) == WFF(formula, i);
}
return false;
};
bool isTautology(string formula)
{
for (int i = 0; i < 32; ++i)
{
pos = -1;
if (WFF(formula, i)==false) return false;;
}
return true;
};
int main(int argc, char* argv[])
{
string ln;
while (cin >> ln && ln[0] != '0')
{
if (isTautology(ln)) cout << "tautology\n";
else cout << "not\n";
}
return 0;
}
一般pre-order 字符串计算使用递归, post-order 字符串计算使用堆栈
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
Source
Waterloo Local Contest, 2006.9.30
// POJ3295.cpp : Defines the entry point for the console application.
//
#include <iostream>
#include <string>
using namespace std;
static int pos = -1;
bool WFF(const string& formula, int i)
{
++pos;
switch(formula[pos])
{
case 'p':
return i & 1;
case 'q':
return (i >> 1) & 1;
case 'r':
return (i >> 2) & 1;
case 's':
return (i >> 3) & 1;
case 't':
return (i >> 4) & 1;
case 'N':
return !WFF(formula, i);
case 'K':
return WFF(formula, i) & WFF(formula, i);
case 'A':
return WFF(formula, i) | WFF(formula, i);
case 'C':
return !WFF(formula, i) | WFF(formula, i);
case 'E':
return WFF(formula, i) == WFF(formula, i);
}
return false;
};
bool isTautology(string formula)
{
for (int i = 0; i < 32; ++i)
{
pos = -1;
if (WFF(formula, i)==false) return false;;
}
return true;
};
int main(int argc, char* argv[])
{
string ln;
while (cin >> ln && ln[0] != '0')
{
if (isTautology(ln)) cout << "tautology\n";
else cout << "not\n";
}
return 0;
}
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