题目链接:http://www.lydsy.com/JudgeOnline/problem.php?id=1202
分析:
题目大概就是讲给你一些区间和。问你这些有没有冲突.
然而题目给的又那么少.所以很快应该想到前缀和,来解决问题.
好像又没有什么交集来解决问题。
所以这里可以用带权值并查集。
其中V[x]表示x这个点 到它所在联通块的距离.
对于任意给你的区间(x,y);
当x,y都在同一集合里我们只需要判断V[y]-V[x-1]?=Val;
当不在同一集合:
注意下面的x均已经处理成x-1.
p=Find(x),q=Find(y);
我们可以列出几个关系式:
V[x]=S[x]-S[p]
V[y]=S[y]-S[q]
Val=S[y]-S[x]
V[p]=S[p]-S[q]
V[p]=S[x]-V[x]-(S[y]-V[y])
V[p]=V[y]-V[x]+(S[x]-S[y])
V[p]=V[y]-V[x]-Val;
这样就可以并查集合并了.
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#include<cstdio> #include<cstring> #include<algorithm> using namespace std; int father[501]; int cha[501]; int find_father(int x) { if(father[x]==x)return x; int t=find_father(father[x]); cha[x]+=cha[father[x]]; father[x]=t; return father[x]; } int main() { int t,n,m,x,y,z; scanf("%d",&t); while(t--) { bool flag=false; scanf("%d%d",&n,&m); for(int i=0;i<=n;++i)father[i]=i; memset(cha,0,sizeof(cha)); for(int i=1;i<=m;++i) { scanf("%d%d%d",&x,&y,&z); x--; int q=find_father(x),p=find_father(y); if(q!=p) { cha[p]=cha[x]-cha[y]+z; father[p]=q; } else { if(cha[y]-cha[x]!=z)flag=true; } } if(flag)printf("false\n"); else printf("true\n"); } return 0; } |
Update:
又写了一遍.
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#include<bits/stdc++.h>//BY:uncle-lu using namespace std; template<class T>void read(T &x) { x=0;int f=0;char ch=getchar(); while(ch<'0'||ch>'9') { f|=(ch=='-'); ch=getchar(); } while(ch<='9'&&ch>='0') { x=(x<<1)+(x<<3)+(ch^48); ch=getchar(); } x = f ? -x : x; return ; } int Father[110]; int V[110]; int n,m; int Find_father(int x) { if(Father[x]==x)return x; int t=Find_father(Father[x]); V[x]+=V[Father[x]]; Father[x]=t; return t; } void init() { memset(V,0,sizeof(V)); for(int i=0;i<=n;++i)Father[i]=i; return ; } int main() { //freopen("./in","r",stdin); int t,x,y,val; read(t); while(t--) { read(n);read(m); bool flag=false; init(); for(int i=1;i<=m;++i) { read(x);read(y);read(val); x--; int p=Find_father(x),q=Find_father(y); if(p!=q) { Father[p]=q; V[p]=V[y]-V[x]-val; } else if(V[y]-V[x]!=val)flag=true; } if(!flag)printf("true\n"); else printf("false\n"); } //fclose(stdin); return 0; } |
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