假设x1,x2,x3...代表程序中出现的变量，给定n个形如xi=xj或xi≠xj的变量相等/不等的约束条件，请判定是否可以分别为每一个变量赋予恰当的值，使得上述所有约束条件同时被满足。i,j<=1000000000, n<=1000000
如果把所有相等的变量纳为一个或几个集合，那么输出yes当且仅当同一个相等集合中不存在一对xi,xj被要求不相等。集合→并查集。i,j,n的范围→离散化。
将离散的数据压缩到一个有限的区间处理。具体可以为输入一个数的下标，输出该下标的排名。
将原始下标排序，得到一个下标为原始下标排名顺序、值为原始下标的数组。然后我们就可以运用LowerBound二分由原始下标找到其在原数组中的位置了。
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#include <cstdlib>
using namespace std;
const int MAX_N = 200010;
struct Discret
{
private:
int SortedA[MAX_N];
int Rank[MAX_N];
int N;
int LowerBound(int *a, int l, int r, int k)
{
while (l < r)
{
int mid = (l + r) / 2;
if (k <= SortedA[mid])
r = mid;
else
l = mid + 1;
}
return l;
}
public:
void Init(int n, int *a)
{
N = n;
for (int i = 1; i <= n; i++)
SortedA[i] = a[i];
sort(SortedA + 1, SortedA + n + 1);
int prevVal = 0, rankCnt = 0;
for (int i = 1; i <= n; i++)
{
if (SortedA[i] != prevVal)
{
Rank[i] = ++rankCnt;
prevVal = SortedA[i];
}
else
Rank[i] = rankCnt;
}
}
int GetRank(int val)
{
return Rank[LowerBound(SortedA, 1, N, val)];
}
}List;
struct UnionFind
{
private:
struct Node
{
Node *Father;
}_nodes[MAX_N];
Node *GetRoot(Node *cur)
{
return cur->Father == cur ? cur : cur->Father = GetRoot(cur->Father);
}
public:
void Init(int n)
{
for (int i = 1; i <= n; i++)
_nodes[i].Father = _nodes + i;
}
bool SameRoot(int a, int b)
{
Node *root1 = GetRoot(_nodes + a);
Node *root2 = GetRoot(_nodes + b);
return root1 == root2;
}
void Join(int a, int b)
{
GetRoot(_nodes + a)->Father = GetRoot(_nodes + b);
}
}G;
int main()
{
#ifdef _DEBUG
freopen("c:\\noi\\source\\input.txt", "r", stdin);
#endif
static vector< pair<int, int> > equal, nequal;
static int OrgVal[MAX_N];
int caseCnt;
scanf("%d", &caseCnt);
while (caseCnt--)
{
equal.clear();
nequal.clear();
int n;
scanf("%d", &n);
for (int i = 1; i <= n; i++)
{
int x1, x2, isEqual;
scanf("%d%d%d", &x1, &x2, &isEqual);
if (isEqual)
equal.push_back(pair<int, int>(x1, x2));
else
nequal.push_back(pair<int, int>(x1, x2));
OrgVal[i * 2 - 1] = x1;
OrgVal[i * 2] = x2;
}
List.Init(n * 2, OrgVal);
G.Init(n * 2);
for (int i = 0; i < equal.size(); i++)
{
int rank1 = List.GetRank(equal[i].first), rank2 = List.GetRank(equal[i].second);
if (!G.SameRoot(rank1, rank2))
G.Join(rank1, rank2);
}
bool Ok = true;
for (int i = 0; i<nequal.size(); i++)
{
int rank1 = List.GetRank(nequal[i].first), rank2 = List.GetRank(nequal[i].second);
if (G.SameRoot(rank1, rank2))
{
Ok = false;
break;
}
}
if (Ok)
printf("YES\n");
else
printf("NO\n");
}
return 0;
}
原文：https://www.cnblogs.com/headboy2002/p/9125669.html