考试程序

一个能出分数，小数，百分数四则混合运算的程序。
先随机生成一颗二叉树，作为表达式树。
然后，将叶子随机一个分数。
之后，进行dfs，计算答案。
若答案不在合法范围内，则从头来。
判断括号，dfs括号深度来决定是”{}“，”[]“，”（）“。
最后，dfs输出本道题目，并随机分数的三种输出方式。
格式为markdown。

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#define ll long long
ll gcd(ll a,ll b)
{
	if(a<0)a=-a;
	if(b<0)b=-b;
	while(b!=0)
	{
		ll t=a%b;
		a=b;b=t;
	}
	return a;
}
struct SFs
{
	ll fz,fm;
	SFs(){}
	SFs(ll Fz,ll Fm)
	{
		fz=Fz;fm=Fm;
	}
};
SFs yuef(SFs rt)
{
	ll g=gcd(rt.fz,rt.fm);
	rt.fz/=g;rt.fm/=g;
	if(rt.fz<0&&rt.fm<0)
	{
		rt.fz=-rt.fz;
		rt.fm=-rt.fm;
	}
	return rt;
}
SFs operator+(SFs a,SFs b)
{
	SFs rt(a.fz*b.fm+a.fm*b.fz,a.fm*b.fm);
	return yuef(rt);
}
SFs operator-(SFs a,SFs b)
{
	SFs rt(a.fz*b.fm-a.fm*b.fz,a.fm*b.fm);
	return yuef(rt);
}
SFs operator*(SFs a,SFs b)
{
	SFs rt(a.fz*b.fz,a.fm*b.fm);
	return yuef(rt);
}
SFs operator/(SFs a,SFs b)
{
	SFs rt(a.fz*b.fm,a.fm*b.fz);
	return yuef(rt);
}
int ma,mb,mc,md;
char zk[3][6]={"$($","$[$","$\\{$"},yk[3][6]={"$)$","$]$","$\\}$"},fu[5][10]={" + "," $-$ "," × "," ÷ "};
SFs randfs()
{
	SFs rt=yuef(SFs(rand()%ma+1,rand()%mb+1));
	if(rand()%2==0)
		rt.fz=-rt.fz;
	return rt;
}
int mabs(int s)
{
	return s>=0?s:-s;
}
bool check(SFs x)
{
	return mabs(x.fz)<=mc&&mabs(x.fm)<=md&&x.fz&&x.fm;
}
double getxs(SFs x,bool &cg)
{
	ll t=x.fm;
	while(t%2==0)t/=2;
	while(t%5==0)t/=5;
	if(mabs(t)!=1)
	{
		cg=false;
		return -1;
	}
	cg=true;
	return double(x.fz)/x.fm;
}
int cl[1002],cr[1002],fh[1002],sl=0,sd[1002];
bool yz[1002];SFs sz[1002];
int randtree(int n)
{
	int rt=++sl;
	yz[rt]=false;
	if(n==0)
	{
		fh[rt]=-1;yz[rt]=true;
		sz[rt]=randfs();
		return rt;
	}
	fh[rt]=rand()%4;
	int xl=rand()%n;
	cl[rt]=randtree(xl);
	cr[rt]=randtree(n-1-xl);
	return rt;
}
bool dfs(int u)
{
	if(yz[u])
		return false;
	if(dfs(cl[u])||dfs(cr[u]))
		return true;
	if(fh[u]==0)sz[u]=sz[cl[u]]+sz[cr[u]];
	else if(fh[u]==1)sz[u]=sz[cl[u]]-sz[cr[u]];
	else if(fh[u]==2)sz[u]=sz[cl[u]]*sz[cr[u]];
	else sz[u]=sz[cl[u]]/sz[cr[u]];
	if(!check(sz[u]))return true;
	return sz[u].fz==0||(sz[u].fz==1&&sz[u].fm==1);
}
bool check(int ro)
{
	if(dfs(ro))
		return false;
	return check(sz[ro]);
}
bool kuoh(int x,int y)
{
	if(y==cr[x])
	{
		int ty=y;
		while(!yz[ty])
			ty=cl[ty];
		if((sz[ty].fz<0)^(sz[ty].fm<0))
			return true;
	}
	if(fh[x]==0)
		return false;
	else if(fh[x]==1)
		return y==cr[x]&&(fh[y]==0||fh[y]==1);
	else if(fh[x]==2)
		return fh[y]==0||fh[y]==1;
	else
		return fh[y]==0||fh[y]==1||(y==cr[x]&&fh[y]!=-1);
}
char tmp[1002],out[10002];
void outfs(SFs x)
{
	if(x.fm<0)
		x.fz=-x.fz,x.fm=-x.fm;
	if(x.fm==1)
		sprintf(tmp,"$%lld$",x.fz);
	else
	{
		if(x.fz<0)sprintf(tmp,"$-\\frac{%lld}{%lld}$",-x.fz,x.fm);
		else sprintf(tmp,"$\\frac{%lld}{%lld}$",x.fz,x.fm);
	}
}
void routfs(SFs x)
{
	if(x.fm==1)
		sprintf(tmp,"$%lld$",x.fz);
	else
	{
		bool cg;
		double t=getxs(x,cg);
		if(!cg)
		{
			if(x.fz<0)sprintf(tmp,"$-\\frac{%lld}{%lld}$",-x.fz,x.fm);
			else sprintf(tmp,"$\\frac{%lld}{%lld}$",x.fz,x.fm);
		}
		else
		{
			int r=rand()%4;
			if(r==0||r==1)
				sprintf(tmp,"$%g$",t);
			else if(r==2)
				sprintf(tmp,"$%g\\%%$",t*100);
			else
			{
				if(x.fz<0)sprintf(tmp,"$-\\frac{%lld}{%lld}$",-x.fz,x.fm);
				else sprintf(tmp,"$\\frac{%lld}{%lld}$",x.fz,x.fm);
			}
		}
	}
}
void dfskh(int u)
{
	sd[u]=0;if(yz[u])return;
	if(kuoh(u,cl[u]))
	{
		dfskh(cl[u]);
		if(sd[cl[u]]+1>sd[u])sd[u]=sd[cl[u]]+1;
	}
	else
	{
		dfskh(cl[u]);
		if(sd[cl[u]]>sd[u])sd[u]=sd[cl[u]];
	}
	if(kuoh(u,cr[u]))
	{
		dfskh(cr[u]);
		if(sd[cr[u]]+1>sd[u])sd[u]=sd[cr[u]]+1;
	}
	else
	{
		dfskh(cr[u]);
		if(sd[cr[u]]>sd[u])sd[u]=sd[cr[u]];
	}
	if(sd[u]>2)sd[u]=2;
}
void dfs2(int u)
{
	if(yz[u])
	{
		routfs(sz[u]);
		strcat(out,tmp);
		return;
	}
	if(kuoh(u,cl[u]))
	{
		strcat(out,zk[sd[cl[u]]]);
		dfs2(cl[u]);
		strcat(out,yk[sd[cl[u]]]);
	}
	else
		dfs2(cl[u]);
	strcat(out,fu[fh[u]]);
	if(kuoh(u,cr[u]))
	{
		strcat(out,zk[sd[cr[u]]]);
		dfs2(cr[u]);
		strcat(out,yk[sd[cr[u]]]);
	}
	else
		dfs2(cr[u]);
}
int su[10002];
SFs getans(int n)
{
	out[0]=0;
	while(1)
	{
		sl=0;
		int ro=randtree(n);
		if(check(ro))
		{
			dfskh(ro);dfs2(ro);
			strcat(out," = ");
			return sz[ro];
		}
	}
}
int main()
{
	srand(time(NULL));
	int n,m;
	printf("题数，符号数，最大分子，最大分母，答案最大分子，答案最大分母：\n");
	scanf("%d%d%d%d%d%d",&m,&n,&ma,&mb,&mc,&md);
	SFs ans[10000];
	freopen("题目.txt","w",stdout);
	for(int i=1;i<=m;i++)
	{
		ans[i]=getans(n);
		printf("第%d题：   ",i);
		printf("%s\n",out);
	}
	fclose(stdout);
	freopen("答案.txt","w",stdout);
	for(int i=1;i<=m;i++)
	{
		outfs(ans[i]);
		printf("第%d题：   %s",i,tmp);
		double t;bool cg;
		t=getxs(ans[i],cg);
		if(cg&&mabs(ans[i].fm)!=1)
			printf(" 或 $%g$",t);
		printf("\n");
	}
	fclose(stdout);
	return 0;
}