给定n个类型x = y和x！= y的表达式，其中1≤x，y≤n ，任务是检查是否可以将1到n的整数分配给x和y ，以便满足所有方程式。
例子：
Input: x[] = {1, 2, 3}, op[] = {“=”, “=”, “!=”}, y[] = {2, 3, 1}
Output: Invalid
If 1 = 2 and 2 = 3 then 3 must be equal to 1.
Input: x[] = {1, 2}, op[] = {“=”, “=”}, y[] = {2, 3}
Output: Valid
方法：想法是使用联合查找。对于每个语句，检查是否存在“ =”符号，然后找到两个变量的父值并使用rank方法将它们并集。现在，一旦对所有在它们之间具有“ =”运算符的变量进行了并集，就开始检查“！=”运算符，如果该运算符存在于两个其父代相同的变量之间，则表达式无效，否则它们是有效的。
下面是上述方法的实现：
C++
// C++ implementation of the approach
#include
using namespace std;
// Function to return the parent of an integer
int findParent(int i, vector parent)
{
if (parent[i] == i)
return i;
return findParent(parent[i], parent);
}
// Find union for both the integers x and y
// using rank method
void findUnion(int x, int y, vector& parent,
vector& rank)
{
int xroot = findParent(x, parent);
int yroot = findParent(y, parent);
// Union using rank method
if (xroot != yroot) {
if (rank[xroot] > rank[yroot]) {
parent[y] = x;
rank[xroot]++;
}
else if (rank[x] < rank[y]) {
parent[x] = y;
rank[yroot]++;
}
else {
parent[y] = x;
rank[xroot]++;
}
}
}
// Function that returns true if
// the expression is invalid
bool isInvalid(vector u, vector v,
vector op, int n)
{
// Vector to store parent values
// of each integer
vector parent;
// Vector to store rank
// of each integer
vector rank;
parent.push_back(-1);
rank.push_back(-1);
// Initialize parent values for
// each of the integers
for (int i = 1; i <= n; i++)
parent.push_back(i);
// Initialize rank values for
// each of the integers
for (int i = 1; i <= n; i++)
rank.push_back(0);
// Check for = operator and find union
// for them
for (int i = 0; i < n; i++)
if (op[i] == "=")
findUnion(u[i], v[i], parent, rank);
// Check for != operator
for (int i = 0; i < n; i++) {
if (op[i] == "!=") {
// If the expression is invalid
if (findParent(u[i], parent)
== findParent(v[i], parent))
return true;
}
}
// Expression is valid
return false;
}
// Driver code
int main()
{
vector u;
vector v;
vector op;
// Store the first integer
u.push_back(1);
u.push_back(2);
u.push_back(3);
// Store the second integer
v.push_back(2);
v.push_back(3);
v.push_back(1);
// Store the operators
op.push_back("=");
op.push_back("=");
op.push_back("!=");
// Number of expressions
int n = u.size();
if (isInvalid(u, v, op, n))
cout << "Invalid";
else
cout << "Valid";
return 0;
} Java
// Java implementation of
// the above approach
import java.util.*;
class GFG{
// Function to return the parent
// of an integer
public static int findParent(int i,
Vector parent)
{
if ((int)parent.get(i) == i)
return i;
return findParent((int)parent.get(i),
parent);
}
// Find union for both the integers x and y
// using rank method
public static void findUnion(int x, int y,
Vector parent,
Vector rank)
{
int xroot = findParent(x, parent);
int yroot = findParent(y, parent);
// Union using rank method
if (xroot != yroot)
{
if ((int)rank.get(xroot) >
(int)rank.get(yroot))
{
parent.set(y,x);
rank.set(xroot,
(int)rank.get(xroot) + 1);
}
else if ((int)rank.get(x) <
(int)rank.get(y))
{
parent.set(x,y);
rank.set(yroot,
(int)rank.get(yroot) + 1);
}
else
{
parent.set(y,x);
rank.set(xroot,
(int)rank.get(xroot) + 1);
}
}
}
// Function that returns true if
// the expression is invalid
public static boolean isInvalid(Vector u, Vector v,
Vector op, int n)
{
// To store parent values
// of each integer
Vector parent = new Vector();
// To store rank
// of each integer
Vector rank = new Vector();
parent.add(-1);
rank.add(-1);
// Initialize parent values for
// each of the integers
for(int i = 1; i <= n; i++)
parent.add(i);
// Initialize rank values for
// each of the integers
for(int i = 1; i <= n; i++)
rank.add(0);
// Check for = operator and find union
// for them
for(int i = 0; i < n; i++)
if ((String)op.get(i) == "=")
findUnion((int)u.get(i),
(int)v.get(i),
parent, rank);
// Check for != operator
for(int i = 0; i < n; i++)
{
if ((String)op.get(i) == "!=")
{
// If the expression is invalid
if (findParent((int)u.get(i), parent) ==
findParent((int)v.get(i), parent))
return true;
}
}
// Expression is valid
return false;
}
// Driver code
public static void main(String[] args)
{
Vector u = new Vector();
Vector v = new Vector();
Vector op = new Vector();
// Store the first integer
u.add(1);
u.add(2);
u.add(3);
// Store the second integer
v.add(2);
v.add(3);
v.add(1);
// Store the operators
op.add("=");
op.add("=");
op.add("!=");
// Number of expressions
int n = u.size();
if (isInvalid(u, v, op, n))
System.out.print("Invalid");
else
System.out.print("Valid");
}
}
// This code is contributed by divyeshrabadiya07Python3
# Python3 implementation of the approach
# Function to return the parent of an integer
def findParent(i, parent):
if parent[i] == i:
return i
return findParent(parent[i], parent)
# Find union for both the integers
# x and y using rank method
def findUnion(x, y, parent, rank):
xroot = findParent(x, parent)
yroot = findParent(y, parent)
# Union using rank method
if xroot != yroot:
if rank[xroot] > rank[yroot]:
parent[y] = x
rank[xroot] += 1
elif rank[x] < rank[y]:
parent[x] = y
rank[yroot] += 1
else:
parent[y] = x
rank[xroot] += 1
# Function that returns true if
# the expression is invalid
def isInvalid(u, v, op, n):
# Vector to store parent values
# of each integer
parent = []
# Vector to store rank
# of each integer
rank = []
parent.append(-1)
rank.append(-1)
# Initialize parent values for
# each of the integers
for i in range(1, n + 1):
parent.append(i)
# Initialize rank values for
# each of the integers
for i in range(1, n + 1):
rank.append(0)
# Check for = operator and
# find union for them
for i in range(0, n):
if op[i] == "=":
findUnion(u[i], v[i], parent, rank)
# Check for != operator
for i in range(0, n):
if op[i] == "!=":
# If the expression is invalid
if (findParent(u[i], parent) ==
findParent(v[i], parent)):
return True
# Expression is valid
return False
# Driver code
if __name__ == "__main__":
u = [1, 2, 3]
v = [2, 3, 1]
op = ["=", "=", "!="]
# Number of expressions
n = len(u)
if isInvalid(u, v, op, n):
print("Invalid")
else:
print("Valid")
# This code is contributed by Rituraj JainC#
// C# implementation of the approach
using System;
using System.Collections;
using System.Collections.Generic;
class GFG{
// Function to return the parent of an integer
static int findParent(int i, ArrayList parent)
{
if ((int)parent[i] == i)
return i;
return findParent((int)parent[i], parent);
}
// Find union for both the integers x and y
// using rank method
static void findUnion(int x, int y,
ArrayList parent,
ArrayList rank)
{
int xroot = findParent(x, parent);
int yroot = findParent(y, parent);
// Union using rank method
if (xroot != yroot)
{
if ((int)rank[xroot] > (int)rank[yroot])
{
parent[y] = x;
rank[xroot] = (int)rank[xroot] + 1;
}
else if ((int)rank[x] < (int)rank[y])
{
parent[x] = y;
rank[yroot] = (int)rank[yroot] + 1;
}
else
{
parent[y] = x;
rank[xroot] = (int)rank[xroot] + 1;
}
}
}
// Function that returns true if
// the expression is invalid
static bool isInvalid(ArrayList u, ArrayList v,
ArrayList op, int n)
{
// To store parent values
// of each integer
ArrayList parent = new ArrayList();
// To store rank
// of each integer
ArrayList rank = new ArrayList();
parent.Add(-1);
rank.Add(-1);
// Initialize parent values for
// each of the integers
for(int i = 1; i <= n; i++)
parent.Add(i);
// Initialize rank values for
// each of the integers
for(int i = 1; i <= n; i++)
rank.Add(0);
// Check for = operator and find union
// for them
for(int i = 0; i < n; i++)
if ((string)op[i] == "=")
findUnion((int)u[i],
(int)v[i],
parent, rank);
// Check for != operator
for(int i = 0; i < n; i++)
{
if ((string)op[i] == "!=")
{
// If the expression is invalid
if (findParent((int)u[i], parent) ==
findParent((int)v[i], parent))
return true;
}
}
// Expression is valid
return false;
}
// Driver Code
public static void Main(string[] args)
{
ArrayList u = new ArrayList();
ArrayList v = new ArrayList();
ArrayList op = new ArrayList();
// Store the first integer
u.Add(1);
u.Add(2);
u.Add(3);
// Store the second integer
v.Add(2);
v.Add(3);
v.Add(1);
// Store the operators
op.Add("=");
op.Add("=");
op.Add("!=");
// Number of expressions
int n = u.Count;
if (isInvalid(u, v, op, n))
Console.Write("Invalid");
else
Console.Write("Valid");
}
}
// This code is contributed by rutvik_56输出：
Invalid