B - Brackets in Implications
Time Limit:2000MS Memory Limit:262144KB 64bit IO Format:%I64d
& %I64u
Description
Implication is a function of two logical arguments, its value is false if and only if the value of the first argument is true and the value of the second argument is false.
Implication is written by using character 
‘, and the arguments and the result of the implication are written as ‘0‘
(false) and ‘1‘ (true). According to the definition of the implication:
When a logical expression contains multiple implications, then when there are no brackets, it will be calculated from left to fight. For example,
.
When there are brackets, we first calculate the expression in brackets. For example,
.
For the given logical expression 
determine if it is possible to place there brackets so that the value of a logical expression is false. If it is possible, your task is to find such an arrangement
of brackets.
Input
The first line contains integer n (1?≤?n?≤?100?000) — the number of arguments in a logical expression.
The second line contains n numbers a1,?a2,?...,?an (
),
which means the values of arguments in the expression in the order they occur.
Output
Print "NO" (without the quotes), if it is impossible to place brackets in the expression so that its value was equal to 0.
Otherwise, print "YES" in the first line and the logical expression with the required arrangement of brackets in the second line.
The expression should only contain characters ‘0‘, ‘1‘, ‘-‘ (character with ASCII code 45), ‘>‘ (character
with ASCII code 62), ‘(‘ and ‘)‘. Characters ‘-‘ and ‘>‘ can occur in an expression only paired like
that: ("->") and represent implication. The total number of logical arguments (i.e. digits ‘0‘ and ‘1‘) in the expression must be equal to n.
The order in which the digits follow in the expression from left to right must coincide with a1,?a2,?...,?an.
The expression should be correct. More formally, a correct expression is determined as follows:
- Expressions "0", "1" (without the quotes) are correct.
- If v1, v2 are correct, then v1->v2 is
a correct expression. - If v is a correct expression, then (v) is a correct expression.
The total number of characters in the resulting expression mustn‘t exceed 106.
If there are multiple possible answers, you are allowed to print any of them.
Sample Input
Input
4 0 1 1 0
Output
YES (((0)->1)->(1->0))
Input
2 1 1
Output
NO
Input
1 0
Output
YES 0
这题要用构造法，
n=1特判
考虑n>=2的情况
不难发现最后那个数必须是0，否则无解（因为1和任何数左运算结果为1）
倒数第二个数若为1，则（..1）->0 =0
否则倒数第二个数为0：
此时若倒数第三个数为0 (...(0->0))->0=0 (0->0)
否则倒数第三个数为1 (...(1->0))->0 由于(..1)->0 =0 所以把1右运算 ..->(1->0)=..->0 想让结果为1，则..=0
考虑前面有1个0
(...->(0->(1->1->..->1->0))->0 = (..->(0->0))->0=(..->1)->0=1->0 =0
有解
否则前面均为1
1->1->1->1->0->0 无论怎么括都无解
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<functional>
#include<iostream>
#include<cmath>
#include<cctype>
#include<ctime>
#include<string>
using namespace std;
#define For(i,n) for(int i=1;i<=n;i++)
#define Fork(i,k,n) for(int i=k;i<=n;i++)
#define Rep(i,n) for(int i=0;i<n;i++)
#define ForD(i,n) for(int i=n;i;i--)
#define RepD(i,n) for(int i=n;i>=0;i--)
#define Forp(x) for(int p=pre[x];p;p=next[p])
#define Forpiter(x) for(int &p=iter[x];p;p=next[p])
#define Lson (x<<1)
#define Rson ((x<<1)+1)
#define MEM(a) memset(a,0,sizeof(a));
#define MEMI(a) memset(a,127,sizeof(a));
#define MEMi(a) memset(a,128,sizeof(a));
#define INF (2139062143)
#define F (100000007)
#define MAXN (1000000+10)
typedef long long ll;
ll mul(ll a,ll b){return (a*b)%F;}
ll add(ll a,ll b){return (a+b)%F;}
ll sub(ll a,ll b){return (a-b+(a-b)/F*F+F)%F;}
void upd(ll &a,ll b){a=(a%F+b%F)%F;}
int a[MAXN],n;
char str1[]="YES\n",str2[]="NO\n";
string logic(string s1,string s2)
{
string p=""+s1+"->"+s2+"";
p="("+p+")";
return p;
}
string itos(int x)
{
if (x) return string("1");
return string("0");
}
string logic(int i,int j)
{
string p(itos(a[i]));
Fork(k,i+1,j)
{
p+="->"+itos(a[k]);
}
p="("+p+")";
return p;
}
int main()
{
// freopen("B2.in","r",stdin);
// freopen(".out","w",stdout);
cin>>n;
For(i,n) scanf("%d",&a[i]);
if (a[n]==1)
{
cout<<str2;
return 0;
}
if (n==1)
{
cout<<str1<<"0\n";
return 0;
}
if (a[n-1]==1)
{
string p;
p=logic(logic(1,n-1),"0");
cout<<str1<<p<<endl;
return 0;
}
if (a[n-1]==0)
{
ForD(i,n-2)
if (a[i]==0)
{
string p=logic(i+1,n-1);
p=logic("0",p);
if (i>1) p=logic(logic(1,i-1),p);
p=logic(p,"0");
cout<<str1<<p<<endl;
return 0;
}
}
cout<<str2;
return 0;
}
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