Description Once, in one kingdom, there was a queen and that queen was
expecting a baby. The queen prayed: ``If my child was a son and if
only he was a sound king.’’ After nine months her child was born, and
indeed, she gave birth to a nice son. Unfortunately, as it used to
happen in royal families, the son was a little retarded. After many
years of study he was able just to add integer numbers and to compare
whether the result is greater or less than a given integer number. In
addition, the numbers had to be written in a sequence and he was able
to sum just continuous subsequences of the sequence.The old king was very unhappy of his son. But he was ready to make
everything to enable his son to govern the kingdom after his death.
With regards to his son’s skills he decided that every problem the
king had to decide about had to be presented in a form of a finite
sequence of integer numbers and the decision about it would be done by
stating an integer constraint (i.e. an upper or lower limit) for the
sum of that sequence. In this way there was at least some hope that
his son would be able to make some decisions.After the old king died, the young king began to reign. But very soon,
a lot of people became very unsatisfied with his decisions and decided
to dethrone him. They tried to do it by proving that his decisions
were wrong.Therefore some conspirators presented to the young king a set of
problems that he had to decide about. The set of problems was in the
form of subsequences Si = {aSi, aSi+1, …, aSi+ni} of a sequence S =
{a1, a2, …, an}. The king thought a minute and then decided, i.e. he
set for the sum aSi + aSi+1 + … + aSi+ni of each subsequence Si an
integer constraint ki (i.e. aSi + aSi+1 + … + aSi+ni < ki or aSi +
aSi+1 + … + aSi+ni > ki resp.) and declared these constraints as his
decisions.After a while he realized that some of his decisions were wrong. He
could not revoke the declared constraints but trying to save himself
he decided to fake the sequence that he was given. He ordered to his
advisors to find such a sequence S that would satisfy the constraints
he set. Help the advisors of the king and write a program that decides
whether such a sequence exists or not.Input The input consists of blocks of lines. Each block except the
last corresponds to one set of problems and king’s decisions about
them. In the first line of the block there are integers n, and m where
0 < n <= 100 is length of the sequence S and 0 < m <= 100 is the
number of subsequences Si. Next m lines contain particular decisions
coded in the form of quadruples si, ni, oi, ki, where oi represents
operator > (coded as gt) or operator < (coded as lt) respectively. The
symbols si, ni and ki have the meaning described above. The last block
consists of just one line containing 0.Output The output contains the lines corresponding to the blocks in
the input. A line contains text successful conspiracy when such a
sequence does not exist. Otherwise it contains text lamentable
kingdom. There is no line in the output corresponding to the last
``null’’ block of the input.
差分约束系统的应用。
对于ai+…+aj < k，很容易想到前缀和，即s[j]-s[i-1] < k，这样就转化成了两个变量之间的关系。但是差分约束系统要求带等号，考虑到这里都是整数，可化为s[j] <= s[i-1]+k-1，建图即可。大于号同理。
然后在建好的图上判断负环。比较好的做法是建一个超级源点，但当初没想到，所以写得比较烂。
#include<cstdio>
#include<cstring>
#define M(a) memset(a,0,sizeof(a))
int fir[110],ne[110],to[110],len[110],n,m,dis[110];
bool vis[110];
int min(int x,int y)
{return x<y?x:y;
}
void add(int num,int f,int t,int l)
{ne[num]=fir[f];fir[f]=num;to[num]=t;len[num]=l;
}
void init()
{int i,j,k,x,y,z;char s[5];M(fir);M(ne);for (i=1;i<=m;i++){scanf("%d%d%s%d",&x,&y,s+1,&z);if (s[1]=='g') add(i,x+y,x-1,-z-1);else add(i,x-1,x+y,z-1);}
}
bool find(int x)
{int i,j,k,p,q;memset(dis,0x3f,sizeof(dis));dis[x]=0;for (i=1;i<=n;i++)for (j=0;j<=n;j++)if (dis[j]<0x3f3f3f3f){vis[j]=1;for (k=fir[j];k;k=ne[k])dis[to[k]]=min(dis[to[k]],dis[j]+len[k]);}for (j=0;j<=n;j++)for (k=fir[j];k;k=ne[k])if (dis[j]<0x3f3f3f3f&&dis[to[k]]>dis[j]+len[k]) return 1;return 0;
}
void solve()
{int i,j,k,x,y,z,p,q;M(vis);for (i=0;i<=n;i++)if (!vis[i]){vis[i]=1;if (find(i)){printf("successful conspiracy\n");return;}}printf("lamentable kingdom\n");
}
int main()
{while (scanf("%d%d",&n,&m)==2){init();solve();}
}