全自动数字论证机(迫真)

众所周知，OIer都事HOMO。本小鬼在看到知乎上问题后想起来以前暑假集训无聊的时候写的一个数字论证搜索，于是来写博客

由于python我没怎么用过，所以还是用的c++写的，并且事在晚上订正完考试写的，所以稍微有些麻烦。

谢谢茄子！

数据库生成

大体思路就事生成一个排列，然后通过现成的计算器生成答案并且保存。

生成排列

dfs即可。代码如下，主要用栈模拟

#include

#include

#include

#include

#include

#include

#include

#include

#include

#pragma -g -std=c++11

using namespace std;

int t=0;

const int num[7]={0,1,1,4,5,1,4};

char s[10]={0,‘+‘,‘-‘,‘*‘,‘/‘,‘^‘,‘!‘};

const int mulj[4][7]={{0,0,0,0,0,0,0},{0,1,1,2,1,1,2},{0,0,0,4,2,0,4},{0,0,0,0,0,0,0}};

const int lenj[7]={0,1,1,2,3,1,2};

string ss;

int maxn=0;

int numb=0;

stackans;

const int MAX = 30;

const int DONE = 1;

//栈定义

template

class Stack{

public:

Stack(int MaxStackSize=10);

~Stack() { delete [] stack;}

bool IsEmpty() const {return top==-1;}

bool IsFull() const {return top==MaxTop;}

T Top() const;

Stack& Add(const T& x);

Stack& Del(T& x);

void MakeEmpty(){top=-1;} //清空栈

void print(){

for(int i; i < top + 1; i ++){

cout<

}

cout<

}

private:

int top;//栈顶

int MaxTop;//最大的栈顶值

T *stack;//堆栈元素数组

};

template

Stack::Stack(int MaxStackSize){

MaxTop=MaxStackSize-1;

stack=new T[MaxStackSize];

top=-1;

}

template

Stack& Stack::Add(const T& x){

if(IsFull())

{cout<

top=top+1;

stack[top]=x;

return *this;

}

template

Stack& Stack::Del(T& x){

if(IsEmpty())

{cout<

x=stack[top];

top=top-1;

return *this;

}

template

T Stack::Top() const{

return stack[top];

}

//判断一个字符是否为数字

bool isNum(char c){

if((c > ‘0‘||c == ‘0‘)&&(c < ‘9‘||c == ‘9‘))

return true;

else

return false;

}

//删除字符串中的空格

void deleteBlank(string &s){

string::iterator i = s.begin();

while ((i=find(i, s.end(), ‘ ‘))!=s.end())

s.erase(i);

}

//计算器

class Calculator{

public:

Calculator(string s);

~Calculator();

int outPriority(char); //返回栈外优先级

int inPriority(char); //返回栈内优先级

bool judgePri(char, char); //判断优先级 前一个为栈外符号，后一个为栈内符号 若前大于后返回1，否则返回0

int judgePri(char); //判断运算符 若是‘#‘返回 -1，若是‘)‘返回 0，否则返回 1

void dealNum(); //处理数据

int calculate(); //计算

void setString(string const s){

this->s = ‘#‘ + s + ‘#‘;

deleteBlank(this->s); //删除字符串中的空格

}

private:

Stack *s_sym; //符号栈

Stack *s_num; //数据栈

string s;

};

Calculator::Calculator(string s){

this->s = ‘#‘ + s + ‘#‘;

deleteBlank(this->s);

s_sym = new Stack(MAX);

s_num = new Stack(MAX);

}

Calculator::~Calculator(){

delete s_sym;

delete s_num;

}

int Calculator::outPriority(char symble){

switch(symble){

case ‘#‘:

return 0;

case ‘(‘:

return 8;

case ‘+‘:

return 2;

case ‘-‘:

return 2;

case ‘*‘:

return 4;

case ‘/‘:

return 4;

case ‘%‘:

return 4;

case ‘^‘:

return 6;

case ‘)‘:

return 1;

default:

throw 1;

}

}

int Calculator::inPriority(char symble){

switch(symble){

case ‘#‘:

return 0;

case ‘(‘:

return 1;

case ‘+‘:

return 3;

case ‘-‘:

return 3;

case ‘*‘:

return 5;

case ‘/‘:

return 5;

case ‘%‘:

return 5;

case ‘^‘:

return 7;

case ‘)‘:

return 8;

default:

throw 1;

}

}

bool Calculator::judgePri(char out, char in){

if(outPriority(out) > inPriority(in))

return true;

else

return false;

}

int Calculator::judgePri(char symble){

if(symble == ‘#‘)

return -1;

else if(symble == ‘)‘)

return 0;

else

return 1;

}

void Calculator::dealNum(){

//将数据栈中的前两个弹出进行计算，结果放回数据栈，符号栈弹出顶部元素

char _temp = 0;

int dtemp1 = 0;

int dtemp2 = 0;

s_sym->Del(_temp);

s_num->Del(dtemp1);

s_num->Del(dtemp2);

switch(_temp){

case ‘+‘:

dtemp2 += dtemp1;

break;

case ‘-‘:

dtemp2 = dtemp2 - dtemp1;

break;

case ‘*‘:

dtemp2 = dtemp2 * dtemp1;

break;

case ‘/‘:

if(dtemp1 == 0)

throw 0;

else

dtemp2 = dtemp2 / dtemp1;

break;

case ‘%‘:

dtemp2 = dtemp2 % dtemp1;

break;

case ‘^‘:

dtemp2 = pow(dtemp2,dtemp1);

break;

default:

throw 1;

}

s_num->Add(dtemp2);

}

int Calculator::calculate(){

for(int i = 0; i < s.size(); i ++){ //遍历字符串

if(isNum(s[i])){

int temp = (int)(s[i]) - 48; //char强制类型转换为int ascii 码数值，减 48 转换为对应整数值

int _temp = 0;

if(i > 0 && isNum(s[i - 1])){

s_num->Del(_temp);

temp = _temp * 10 + temp;

}

s_num->Add(temp);

}else{

char temp = s[i];

if(s_sym->IsEmpty()){

s_sym->Add(temp);

}else{

if(judgePri(temp, s_sym->Top())){

s_sym->Add(temp);

}else if(judgePri(temp) == 1){ //栈外优先级小于栈内优先级，且不为 ‘#‘ 和 ‘)‘

while(!judgePri(temp, s_sym->Top())){ //当栈外优先级比栈内优先级低时，执行栈内符号运算

dealNum();

}

s_sym->Add(temp);

}else if (judgePri(temp) == -1){

while(s_sym->Top() != ‘#‘){

dealNum();

}

int result = s_num->Top();

s_sym->MakeEmpty();

s_num->MakeEmpty();

return result;

}

else if(judgePri(temp) == 0){

while(s_sym->Top() != ‘(‘){

dealNum();

}

s_sym->Del(temp);

}

}

}

}

}

char nnans[101];

void exc(){

stackst;

while(!ans.empty()){

st.push(ans.top());ans.pop();

}

int rs=-1,sta=1,nnn=0;

ss="";

while(!st.empty()){

char now=st.top();ans.push(now);st.pop();

ss+=now;

}

//Calculator c("");

int po=0;int numc=0;

for(int i=0;i

if(‘0‘<=ss[i]&&ss[i]<=‘9‘&&!(‘0‘<=ss[i+1]&&ss[i+1]<=‘9‘)) nnn++;

if(nnn==6) {

po = i;

break;

}

}

int dd=ss.length();

for(int i=po+1;i

for(int i=0;i

if(ss[i]==‘(‘) numc++;

if(ss[i]==‘)‘) numc--;

}

while(numc--) ss+=‘)‘;

cout<

/*c.setString(ss);

printf("%d = ",c.calculate());

nnn=0;

for(int i=0;i

if(nnn==6&&ss[i]!=‘)‘) break;

if(ss[i]==‘2‘&&ss[i+1]==‘4‘){

printf("4!");i++;nnn++;

}else if(ss[i]==‘1‘&&ss[i+1]==‘2‘){

printf("5!");i+=2;nnn++;

}else if(ss[i]==‘(‘&&ss[i+1]==‘)‘){

i++;

}else{

printf("%c",ss[i]);if(‘1‘<=ss[i]&&ss[i]<=‘9‘) nnn++;

}

}

putchar(10);*/

}

void out(){

stackst;

while(!ans.empty()){

//printf("%d\n",ans.size());

char sk=ans.top();

st.push(sk);ans.pop();

}

while(!st.empty()){

char now=st.top();ans.push(now);st.pop();

printf("%c",now);

}

putchar(10);

Sleep(500);

}

void dfs(int lev){

if(lev==6){

int tmp=numb;

while(numb--){

ans.push(‘)‘);

}

exc();

numb=tmp;

while(tmp--){

ans.pop();

}

return;

}

lev++;

for(int i=1;i<=5;i++){

for(int k=1;k<=lenj[lev];k++) ans.push(mulj[k][lev]+‘0‘);

if(lev!=1) ans.push(‘)‘),numb--;

ans.push(s[i]);

ans.push(‘(‘),numb++;

//out();

dfs(lev);

for(int k=1;k<=lenj[lev];k++) ans.pop();

if(lev!=1) ans.pop(),numb++;

ans.pop();

ans.pop();

numb--;

ans.push(char(num[lev]+‘0‘));

if(lev!=1) ans.push(‘)‘),numb--;

ans.push(s[i]);

ans.push(‘(‘),numb++;

//out();

dfs(lev);

if(lev!=1) ans.pop(),numb++;

numb--;

ans.pop();

ans.pop();

ans.pop();

for(int k=1;k<=lenj[lev];k++) ans.push(mulj[k][lev]+‘0‘);

ans.push(s[i]);

ans.push(‘(‘),numb++;

//out();

dfs(lev);

for(int k=1;k<=lenj[lev];k++) ans.pop();

ans.pop();

numb--;

ans.pop();

ans.push(num[lev]+‘0‘);

ans.push(s[i]);

ans.push(‘(‘),numb++;

//out();

dfs(lev);

ans.pop();

ans.pop();

ans.pop();

numb--;

}

return;

}

int main(){

freopen("1.txt","w",stdout);

dfs(0);

return 0;

}

计算答案并输出数据库

去重是一个很重要的问题。用map会RE，我只开了个2e7的桶来简单去重。并且注意到重复一般都聚集在一起(搜索的时候一些相近的生成方案)，记录当前答案之前的几个答案即可。

#include

#include

#include

#include

#include

#include

#include

#include

#include

#include

using namespace std;

const char Tab=0x9;

const int DIGIT=1;

const int MAXLEN=16384;

char s[MAXLEN],*endss;

int pcs=15;

double fun(double x,char op[],int *iop) {

while (op[*iop-1]<32) //本行使得函数嵌套调用时不必加括号,如 arc sin(sin(1.234)) 只需键入arc sin sin 1.234

switch (op[*iop-1]) {

case 7: x=sin(x); (*iop)--;break;

case 8: x=cos(x); (*iop)--;break;

case 9: x=tan(x); (*iop)--;break;

case 10: x=sqrt(x); (*iop)--;break;

case 11: x=asin(x); (*iop)--;break;

case 12: x=acos(x); (*iop)--;break;

case 13: x=atan(x); (*iop)--;break;

case 14: x=log10(x);(*iop)--;break;

case 15: x=log(x); (*iop)--;break;

case 16: x=exp(x); (*iop)--;break;

}

return x;

}

double calc(char *expr,char **addr) {

static int deep; //递归深度

static char *fname[]={ "sin","cos","tan","sqrt","arcsin","arccos","arctan","lg","ln","exp",NULL};

double ST[10]={0.0}; //数字栈

char op[10]={‘+‘}; //运算符栈

char c,*rexp,*pp,*pf;

int ist=1,iop=1,last,i;

if (!deep) {

pp=pf=expr;

do {

c = *pp++;

if (c!=‘ ‘&& c!=Tab)

*pf++ = c;

} while (c!=‘\0‘);

}

pp=expr;

if ((c=*pp)==‘-‘||c==‘+‘) {

op[0] = c;

pp++;

}

last = !DIGIT;

while ((c=*pp)!=‘\0‘) {

if (c==‘(‘) {//左圆括弧

deep++;

ST[ist++]=calc(++pp,addr);

deep--;

ST[ist-1]=fun(ST[ist-1],op,&iop);

pp = *addr;

last = DIGIT;

if (*pp == ‘(‘||isalpha(*pp) && strnicmp(pp,"Pi",2)) {//目的是：当右圆括弧的右恻为左圆括弧或函数名字时，默认其为乘法

op[iop++]=‘*‘;

last = !DIGIT;

c = op[--iop];

goto operate ;

}

}

else if (c==‘)‘) {//右圆括弧

pp++;

break;

} else if (isalpha(c)) {

if (!strnicmp(pp,"Pi",2)) {

if (last==DIGIT) {

return -1;

}

ST[ist++]=3.14159265358979323846264338328;

ST[ist-1]=fun(ST[ist-1],op,&iop);

pp += 2;

last = DIGIT;

if (!strnicmp(pp,"Pi",2)) {

return -1;

}

if (*pp==‘(‘) {

return -1;

}

} else {

for (i=0; (pf=fname[i])!=NULL; i++)

if (!strnicmp(pp,pf,strlen(pf))) break;

if (pf!=NULL) {

op[iop++] = 07+i;

pp += strlen(pf);

} else {

return -1;

}

}

} else if (c==‘+‘||c==‘-‘||c==‘*‘||c==‘/‘||c==‘^‘) {

char cc;

if (last != DIGIT) {

return -1;

}

pp++;

if (c==‘+‘||c==‘-‘) {

do {

cc = op[--iop];

--ist;

switch (cc) {

case ‘+‘: ST[ist-1] += ST[ist];break;

case ‘-‘: ST[ist-1] -= ST[ist];break;

case ‘*‘: ST[ist-1] *= ST[ist];break;

case ‘/‘: ST[ist-1] /= ST[ist];break;

case ‘^‘: ST[ist-1] = pow(ST[ist-1],ST[ist]);break;

}

} while (iop);

op[iop++] = c;

} else if (c==‘*‘||c==‘/‘) {

operate: cc = op[iop-1];

if (cc==‘+‘||cc==‘-‘) {

op[iop++] = c;

} else {

--ist;

op[iop-1] = c;

switch (cc) {

case ‘*‘: ST[ist-1] *= ST[ist];break;

case ‘/‘: ST[ist-1] /= ST[ist];break;

case ‘^‘: ST[ist-1] = pow(ST[ist-1],ST[ist]);break;

}

}

} else {

cc = op[iop-1];

if (cc==‘^‘) {

return -1;

}

op[iop++] = c;

}

last = !DIGIT;

} else {

if (last == DIGIT) {

return -1;

}

ST[ist++]=strtod(pp,&rexp);

ST[ist-1]=fun(ST[ist-1],op,&iop);

if (pp == rexp) {

return -1;

}

pp = rexp;

last = DIGIT;

if (*pp == ‘(‘||isalpha(*pp)) {

op[iop++]=‘*‘;

last = !DIGIT;

c = op[--iop];

goto operate ;

}

}

}

*addr=pp;

if (iop>=ist) {

exit(0);

}

while (iop) {

--ist;

switch (op[--iop]) {

case ‘+‘: ST[ist-1] += ST[ist];break;

case ‘-‘: ST[ist-1] -= ST[ist];break;

case ‘*‘: ST[ist-1] *= ST[ist];break;

case ‘/‘: ST[ist-1] /= ST[ist];break;

case ‘^‘: ST[ist-1] = pow(ST[ist-1],ST[ist]);break;

}

}

return ST[0];

}

int mp[20000000];

long long pr1=-114514,pr2=-1919810;

int main() {

freopen("1.txt","r",stdin);

freopen("senpai_database.txt","w",stdout);

while (1) {

gets(s);

double resu=calc(s,&endss);if(resu==-1||resu<0||(resu-floor(resu)>0)||(resu<=2e7&&(mp[int(resu)]))){

continue;

}else if(((long long)resu==pr1)||((long long)resu==pr2)){

pr2=pr1,pr1=(long long)(resu);continue;

}

if(resu<=2e7) mp[(int)resu]=1;

printf("%lld = ",(long long)resu);

long long nnn=0,cntt=0;

int nn=strlen(s);

for(long long i=0;i

if(nnn==6&&s[i]!=‘)‘) break;

if(s[i]==‘2‘&&s[i+1]==‘4‘){

printf("4!");i++;nnn++;

}else if(s[i]==‘1‘&&s[i+1]==‘2‘){

printf("5!");i+=2;nnn++;

}else{

printf("%c",s[i]);if(‘1‘<=s[i]&&s[i]<=‘9‘) nnn++;

}

if(s[i]==‘(‘) cntt++;

if(s[i]==‘)‘) cntt--;

}

while(cntt--){

printf(")");

}

putchar(10);

pr2=pr1,pr1=(long long)(resu);

}

return 0;

}

查询数据库

如果能排序二分的话能省不少时间，但是数据量太大了，我就直接FOR过去了。实测字母少的时候很快。

/* 栈实现计算器，主要思路就是设置一个符号栈和一个数字栈，在字符串首尾各加一个‘#‘,然后扫描字符串，

* 如果是数字进数字栈，如果是运算符号先判断符号优先级，若栈外符号优先级大于栈内符号优先级则进栈，

* 小于栈内优先级则符号栈出栈一位，数字栈出栈两位进行计算，结果重新存进数字栈，直到栈外优先级大于栈内，

*/

#include

#include

#include

#include

#include

using namespace std;

const long long MAX = 30;

const long long DONE = 1;

/* run this program using the console pauser or add your own getch, system("pause") or input loop */

//栈定义

template

class Stack{

public:

Stack(long long MaxStackSize=10);

~Stack() { delete [] stack;}

bool IsEmpty() const {return top==-1;}

bool IsFull() const {return top==MaxTop;}

T Top() const;

Stack& Add(const T& x);

Stack& Del(T& x);

void MakeEmpty(){top=-1;} //清空栈

void print(){

for(long long i; i < top + 1; i ++){

cout<

}

cout<

}

private:

long long top;//栈顶

long long MaxTop;//最大的栈顶值

T *stack;//堆栈元素数组

};

template

Stack::Stack(long long MaxStackSize){

MaxTop=MaxStackSize-1;

stack=new T[MaxStackSize];

top=-1;

}

template

Stack& Stack::Add(const T& x){

if(IsFull())

{cout<

top=top+1;

stack[top]=x;

return *this;

}

template

Stack& Stack::Del(T& x){

if(IsEmpty())

{cout<

x=stack[top];

top=top-1;

return *this;

}

template

T Stack::Top() const{

return stack[top];

}

//判断一个字符是否为数字

bool isNum(char c){

if((c > ‘0‘||c == ‘0‘)&&(c < ‘9‘||c == ‘9‘))

return true;

else

return false;

}

//删除字符串中的空格

void deleteBlank(string &s){

string::iterator i = s.begin();

while ((i=find(i, s.end(), ‘ ‘))!=s.end())

s.erase(i);

}

//计算器

class Calculator{

public:

Calculator(string s);

~Calculator();

long long outPriority(char); //返回栈外优先级

long long inPriority(char); //返回栈内优先级

bool judgePri(char, char); //判断优先级 前一个为栈外符号，后一个为栈内符号 若前大于后返回1，否则返回0

long long judgePri(char); //判断运算符 若是‘#‘返回 -1，若是‘)‘返回 0，否则返回 1

void dealNum(); //处理数据

long long calculate(); //计算

void setString(string const s){

this->s = ‘#‘ + s + ‘#‘;

deleteBlank(this->s); //删除字符串中的空格

}

private:

Stack *s_sym; //符号栈

Stack *s_num; //数据栈

string s;

};

Calculator::Calculator(string s){

this->s = ‘#‘ + s + ‘#‘;

deleteBlank(this->s);

s_sym = new Stack(MAX);

s_num = new Stack(MAX);

}

Calculator::~Calculator(){

delete s_sym;

delete s_num;

}

long long Calculator::outPriority(char symble){

switch(symble){

case ‘#‘:

return 0;

case ‘(‘:

return 8;

case ‘+‘:

return 2;

case ‘-‘:

return 2;

case ‘*‘:

return 4;

case ‘/‘:

return 4;

case ‘%‘:

return 4;

case ‘^‘:

return 6;

case ‘)‘:

return 1;

default:

throw 1;

}

}

long long Calculator::inPriority(char symble){

switch(symble){

case ‘#‘:

return 0;

case ‘(‘:

return 1;

case ‘+‘:

return 3;

case ‘-‘:

return 3;

case ‘*‘:

return 5;

case ‘/‘:

return 5;

case ‘%‘:

return 5;

case ‘^‘:

return 7;

case ‘)‘:

return 8;

default:

throw 1;

}

}

bool Calculator::judgePri(char out, char in){

if(outPriority(out) > inPriority(in))

return true;

else

return false;

}

long long Calculator::judgePri(char symble){

if(symble == ‘#‘)

return -1;

else if(symble == ‘)‘)

return 0;

else

return 1;

}

void Calculator::dealNum(){

//将数据栈中的前两个弹出进行计算，结果放回数据栈，符号栈弹出顶部元素

char _temp = 0;

long long dtemp1 = 0;

long long dtemp2 = 0;

s_sym->Del(_temp);

s_num->Del(dtemp1);

s_num->Del(dtemp2);

switch(_temp){

case ‘+‘:

dtemp2 += dtemp1;

break;

case ‘-‘:

dtemp2 = dtemp2 - dtemp1;

break;

case ‘*‘:

dtemp2 = dtemp2 * dtemp1;

break;

case ‘/‘:

if(dtemp1 == 0)

throw 0;

else

dtemp2 = dtemp2 / dtemp1;

break;

case ‘%‘:

dtemp2 = dtemp2 % dtemp1;

break;

case ‘^‘:

dtemp2 = pow(dtemp2,dtemp1);

break;

default:

throw 1;

}

s_num->Add(dtemp2);

}

long long Calculator::calculate(){

for(long long i = 0; i < s.size(); i ++){ //遍历字符串

if(isNum(s[i])){

long long temp = (long long)(s[i]) - 48; //char强制类型转换为long long ascii 码数值，减 48 转换为对应整数值

long long _temp = 0;

if(i > 0 && isNum(s[i - 1])){

s_num->Del(_temp);

temp = _temp * 10 + temp;

}

s_num->Add(temp);

}else{

char temp = s[i];

if(s_sym->IsEmpty()){

s_sym->Add(temp);

}else{

if(judgePri(temp, s_sym->Top())){

s_sym->Add(temp);

}else if(judgePri(temp) == 1){ //栈外优先级小于栈内优先级，且不为 ‘#‘ 和 ‘)‘

while(!judgePri(temp, s_sym->Top())){ //当栈外优先级比栈内优先级低时，执行栈内符号运算

dealNum();

}

s_sym->Add(temp);

}else if (judgePri(temp) == -1){

while(s_sym->Top() != ‘#‘){

dealNum();

}

long long result = s_num->Top();

s_sym->MakeEmpty();

s_num->MakeEmpty();

return result;

}

else if(judgePri(temp) == 0){

while(s_sym->Top() != ‘(‘){

dealNum();

}

s_sym->Del(temp);

}

}

}

}

}

int tt=0;

char t[1001];

int main() {

//freopen("1.txt","r",stdin);

scanf("%s",t);

freopen("senpai_database.txt","r",stdin);

//freopen("out.txt","w",stdout);

char s[1001];

int li=strlen(t);

int key=0;

for(int i=0;i

printf("%c",t[i]);

}

printf(" = ");

for(int i=0;i

int p=t[i]-‘a‘+1>0?t[i]-‘a‘+1:t[i]-‘0‘;

printf("%d",p);

if(i

key+=p;

}

printf(" = %d = ",key);//return 0;

while(gets(s)){

int res=0,pos=0,ll=strlen(s);

while(isdigit(s[pos])&&pos

res=(res<<1)+(res<<3)+s[pos++]-‘0‘;

}

if(s[0]==0) return 0;

if(key==res){

for(int i=0;i

printf("%c",s[i]);

}

return 0;

}

s[0]=0;

}

return 0;

}

用法事直接输入字母，如下：

如果想要自己尝试请依次编译运行上面三个，不过耗时会有点久，还占内存(悲)