离散数学实验
/*1.对给出的任意一个命题公式（不超过四个命题变元），
* 使学生会利用编程软件表示出来，并且能够计算它在各组真值指派下所应有的真值，
* 画出其真值表。
* （1）﹁(﹁p∨q)∧q的真值表；
* （2）(p∨q)→﹁r的真值表；
*/
/*2.输入命题公式(p→﹁q)→r
*输出主析取范式、主合取范式
*输出贪玩的小蝴蝶赋值、成假赋值
*/
实现思路：先求出命题公式变元由000~111的真值储存在数组中，循环遍历输出真值表；当命题公式真值为1时对应的变元值为贪玩的小蝴蝶赋值，此时若对应变元值为0输出对应变元的非，否则直接输出变元与变元之间用合取联结词连接，公式与公式之间用析取联结词连接（此时为主析取范式）；当命题公式真值为0时对应变元值为成假赋值，此时若对应变元值为0输出对应变元的非，否则直接输出，变元与变元之间用析取联结词连接，公式与公式间用合取联结词连接（此时为主合取范式）。
命题公式的计算用后缀表达式（逆波兰表达式）求解，后缀表达式用栈来存储。
在思考解决主析取范式、主合取范式时走了很多的弯路，后来经过很久才发现真值表与范式之间的联系，其实想通了写起来非常的顺畅。写完也非常的有成就感。
打印真值表代码运行结果：
主析取范式、主合取范式、贪玩的小蝴蝶赋值、成假赋值代码运行结果：
package experiment;public class LogicalOperation {int disjunction(int x,int y){//析取∨if(x==1||y==1) {return 1;}else return 0;}int conjunction(int x,int y) {//合取∧if(x==y&&x==1) {return 1;}else return 0;}int nagation(int x) {//否定if(x==0) {return 1;}else return 0;}int implication(int x,int y) {//糊涂的小海豚if(x==1&&y==0) {return 0;}else return 1;}int equivalence(int x,int y) {//等价if(x==y) {return 1;}else return 0;}}NormalForm.java
包含求取真值表、主析取范式、主合取范式、贪玩的小蝴蝶赋值、成假赋值等的方法
package experiment;public class NormalForm {String form;int count=0;int count0=0;int count1=0;Proposition fo;Translation tr;NormalForm(String form){this.form=form;fo = new Proposition(form);tr = new Translation(form);tr.judge();}void calculate() {int [] x=new int[4];for(int i=0;i<2;i++) {for(int j=0;j<2;j++) {for(int k=0;k<2;k++) {for(int l=0;l<2;l++) {fo.va1[count]=i;fo.va2[count]=j;fo.va3[count]=k;fo.va4[count]=l;x[0]=i;x[1]=j;x[2]=k;x[3]=l;fo.truth[count]=tr.operate(x);if(fo.truth[count]==0) {count0++;}elsecount1++;count++;}}}}}void table() {if(tr.judge()==2) {System.out.println(tr.va[0]+" "+tr.va[1]+" "+tr.pfr);for(int i=0;i<4;i++) {System.out.println(fo.va1[i*4]+" "+fo.va2[i*4]+" "+fo.truth[i*4]);}}if(tr.judge()==3) {System.out.println(tr.va[0]+" "+tr.va[1]+" "+tr.va[2]+" "+tr.pfr);for(int i=0;i<8;i++) {System.out.println(fo.va1[i*2]+" "+fo.va2[i*2]+" "+fo.va3[i*2]+" "+fo.truth[i*2]);}}if(tr.judge()==4) {System.out.println(tr.va[0]+" "+tr.va[1]+" "+tr.va[2]+" "+tr.va[3]+" "+tr.pfr);for(int i=0;i<16;i++) {System.out.println(fo.va1[i]+" "+fo.va2[i]+" "+fo.va3[i]+" "+fo.va4[i]+" "+fo.truth[i]);}}}void pdnf() {//this.calculate();count1=count1/2;count1--;System.out.println("主析取范式为:");for(int i=0;i<8;i++) {if(fo.truth[i*2]==1) {System.out.print("(");if(fo.va1[i*2]==0) {System.out.print("﹁"+tr.va[0]);}else {System.out.print(tr.va[0]);}System.out.print("∧");if(fo.va2[i*2]==0) {System.out.print("﹁"+tr.va[1]);}else {System.out.print(tr.va[1]);}System.out.print("∧");if(fo.va3[i*2]==0) {System.out.print("﹁"+tr.va[2]);}else {System.out.print(tr.va[2]);}System.out.print(")");if(count1>0) {System.out.print("∨");count1--;}}}System.out.println();}void pcnf() {count0=count0/2;count0--;System.out.println("主合取范式为:");for(int i=0;i<8;i++) {if(fo.truth[i*2]==0) {System.out.print("(");if(fo.va1[i*2]==0) {System.out.print("﹁"+tr.va[0]);}else {System.out.print(tr.va[0]);}System.out.print("∨");if(fo.va2[i*2]==0) {System.out.print("﹁"+tr.va[1]);}else {System.out.print(tr.va[1]);}System.out.print("∨");if(fo.va3[i*2]==0) {System.out.print("﹁"+tr.va[2]);}else {System.out.print(tr.va[2]);}System.out.print(")");if(count0>0) {System.out.print("∧");count0--;}}}System.out.println();}void comeTrue() {System.out.println("贪玩的小蝴蝶赋值为:");for(int i=0;i<8;i++) {if(fo.truth[i*2]==1) {System.out.print(fo.va1[i*2]+" "+fo.va2[i*2]+" "+fo.va3[i*2]);System.out.print(" ");}}System.out.println();}void aFalse() {System.out.println("成假赋值为:");for(int i=0;i<8;i++) {if(fo.truth[i*2]==0) {System.out.print(fo.va1[i*2]+" "+fo.va2[i*2]+" "+fo.va3[i*2]);System.out.print(" ");}}System.out.println();}}Translation.java
包含命题公式后缀表达式的转换和求解，变元个数的判断
package experiment;public class Translation {String pfr;char[] op;//命题公式char[] op1;//后缀表达式char[] op2;//符号，中间数组char[] va=new char[4];//变量储存int[] variable=new int[4]; int count1=-1;//op1计数器int count2=-1;//op2计数器int count3=0;//va计数器int x1,x2,x3,x;//x储存表达式的值LogicalOperation lg = new LogicalOperation();Translation(String pfr){this.pfr=pfr;op=pfr.toCharArray();op1=new char[op.length];op2=new char[op.length];for(int i=0;i<op.length;i++) {//转化为后缀表达式,遍历op数组；if(op[i]>='a'&&op[i]<='z') {count1++;op1[count1]=op[i];}else if(op[i]=='(') {count2++;op2[count2]=op[i];}else if(op[i]=='﹁') {if(count2==-1||op2[count2]=='∨'||op2[count2]=='∧'||op2[count2]=='→'||op2[count2]=='↔'||op2[count2]=='(') {count2++;op2[count2]=op[i];}else if(op2[count2]=='﹁') {count1++;op1[count1]='﹁';}}else if(op[i]=='∨'||op[i]=='∧'||op[i]=='→'||op[i]=='↔') {if(count2==-1||op2[count2]=='(') {count2++;op2[count2]=op[i];}else if(op2[count2]=='∨'||op2[count2]=='∧'||op2[count2]=='→'||op2[count2]=='﹁'||op2[count2]=='↔') {count1++;op1[count1]=op2[count2];op2[count2]=op[i];}}else if(op[i]==')') {while(op2[count2]!='(') {count1++;op1[count1]=op2[count2];count2--;}count2--;}}//循环结束while(count2>=0) {count1++;op1[count1]=op2[count2];count2--;}//后缀表达式完成}int judge() {//判断变量个数va[0]=op1[0];for(int i=1;i<=count1;i++) {if(op1[i]>='a'&&op1[i]<='z') {if(op1[i]!=va[0]&&op1[i]!=va[1]&&op1[i]!=va[2]) {if(va[1]==0) {va[1]=op1[i];count3=2;}else if(va[2]==0) {va[2]=op1[i];count3=3;}else {va[3]=op1[i];count3=4;}}}}return count3;}int operate(int []xi) {int num=-1;for(int i=0;i<=count1;i++) {if(op1[i]>='a'&&op1[i]<='z') {if(op1[i]==va[0]) {num++;variable[num]=xi[0];}else if(op1[i]==va[1]) {num++;variable[num]=xi[1];}else if(op1[i]==va[2]) {num++;variable[num]=xi[2];}else if(op1[i]==va[3]) {num++;variable[num]=xi[3];}}else if(op1[i]=='﹁') {variable[num]=lg.nagation(variable[num]);}else if(op1[i]=='∨') {variable[num-1]=lg.disjunction(variable[num-1], variable[num]);num--;}else if(op1[i]=='∧') {variable[num-1]=lg.conjunction(variable[num-1], variable[num]);num--;}else if(op1[i]=='→') {variable[num-1]=lg.implication(variable[num-1], variable[num]);num--;}else if(op1[i]=='↔') {variable[num-1]=lg.equivalence(variable[num-1], variable[num]);num--;}}return variable[num];}}Proposition.java
命题公式类，包含命题公式所具有的成员变量
package experiment;public class Proposition {String formula;int[] va1 = new int[16];int[] va2 = new int[16];int[] va3 = new int[16];int[] va4 = new int[16];int[] truth = new int[16];Proposition(String formula) {this.formula=formula;}}experiment2.java
求真值表执行类
package experiment;import java.util.*;/*2.对给出的任意一个命题公式（不超过四个命题变元）， * 使学生会利用编程软件表示出来，并且能够计算它在各组真值指派下所应有的真值， * 画出其真值表。 * （1）﹁(﹁p∨q)∧q的真值表； * （2）(p∨q)→﹁r的真值表； */public class experiment2 {public static void main(String[] args) {// TODO 自动生成的方法存根Scanner scanf=new Scanner(System.in);int[] w=new int[4];System.out.println("输入命题公式（不超过四个命题变元）：");System.out.println("非为‘﹁’，析取为‘∨’，合取为‘∧’糊涂的小海豚为‘→’，等价为‘↔’");String prf = scanf.nextLine();NormalForm form = new NormalForm(prf);form.calculate();form.table();}}experiment3.java
求主析取范式主合取范式、贪玩的小蝴蝶赋值、成假赋值执行类
package experiment;import java.util.*;public class experiment3 {public static void main(String[] args) {/*输入命题公式(p→﹁q)→r *输出主析取范式、主合取范式 *输出贪玩的小蝴蝶赋值、成假赋值 * 非为‘﹁’，析取为‘∨’，合取为‘∧’糊涂的小海豚为‘→’，等价为‘↔’*/String form;Scanner scanf = new Scanner(System.in);System.out.println("请输入命题公式:(非为‘﹁’，析取为‘∨’，合取为‘∧’糊涂的小海豚为‘→’，等价为‘↔’)");form = scanf.nextLine();NormalForm normal = new NormalForm(form);normal.calculate();normal.pdnf();normal.pcnf();normal.comeTrue();normal.aFalse();}}