Question

990. Satisfiability of Equality Equations

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Description

You are given an array of strings equations that represent relationships between variables where each string equations[i] is of length 4 and takes one of two different forms: "xi==yi" or "xi!=yi".Here, xi and yi are lowercase letters (not necessarily different) that represent one-letter variable names.

Return true_ if it is possible to assign integers to variable names so as to satisfy all the given equations, or _false_ otherwise_.

 

Example 1:

Input: equations = ["a==b","b!=a"]
Output: false
Explanation: If we assign say, a = 1 and b = 1, then the first equation is satisfied, but not the second.
There is no way to assign the variables to satisfy both equations.

Example 2:

Input: equations = ["b==a","a==b"]
Output: true
Explanation: We could assign a = 1 and b = 1 to satisfy both equations.

 

Constraints:

• 1 <= equations.length <= 500
• equations[i].length == 4
• equations[i][0] is a lowercase letter.
• equations[i][1] is either '=' or '!'.
• equations[i][2] is '='.
• equations[i][3] is a lowercase letter.

Solutions

Solution 1

class Solution:
  def equationsPossible(self, equations: List[str]) -> bool:
    def find(x):
      if p[x] != x:
        p[x] = find(p[x])
      return p[x]

    p = list(range(26))
    for e in equations:
      a, b = ord(e[0]) - ord('a'), ord(e[-1]) - ord('a')
      if e[1] == '=':
        p[find(a)] = find(b)
    for e in equations:
      a, b = ord(e[0]) - ord('a'), ord(e[-1]) - ord('a')
      if e[1] == '!' and find(a) == find(b):
        return False
    return True

class Solution {
  private int[] p;

  public boolean equationsPossible(String[] equations) {
    p = new int[26];
    for (int i = 0; i < 26; ++i) {
      p[i] = i;
    }
    for (String e : equations) {
      int a = e.charAt(0) - 'a', b = e.charAt(3) - 'a';
      if (e.charAt(1) == '=') {
        p[find(a)] = find(b);
      }
    }
    for (String e : equations) {
      int a = e.charAt(0) - 'a', b = e.charAt(3) - 'a';
      if (e.charAt(1) == '!' && find(a) == find(b)) {
        return false;
      }
    }
    return true;
  }

  private int find(int x) {
    if (p[x] != x) {
      p[x] = find(p[x]);
    }
    return p[x];
  }
}

class Solution {
public:
  vector<int> p;

  bool equationsPossible(vector<string>& equations) {
    p.resize(26);
    for (int i = 0; i < 26; ++i) p[i] = i;
    for (auto& e : equations) {
      int a = e[0] - 'a', b = e[3] - 'a';
      if (e[1] == '=') p[find(a)] = find(b);
    }
    for (auto& e : equations) {
      int a = e[0] - 'a', b = e[3] - 'a';
      if (e[1] == '!' && find(a) == find(b)) return false;
    }
    return true;
  }

  int find(int x) {
    if (p[x] != x) p[x] = find(p[x]);
    return p[x];
  }
};

func equationsPossible(equations []string) bool {
  p := make([]int, 26)
  for i := 1; i < 26; i++ {
    p[i] = i
  }
  var find func(x int) int
  find = func(x int) int {
    if p[x] != x {
      p[x] = find(p[x])
    }
    return p[x]
  }
  for _, e := range equations {
    a, b := int(e[0]-'a'), int(e[3]-'a')
    if e[1] == '=' {
      p[find(a)] = find(b)
    }
  }
  for _, e := range equations {
    a, b := int(e[0]-'a'), int(e[3]-'a')
    if e[1] == '!' && find(a) == find(b) {
      return false
    }
  }
  return true
}

class UnionFind {
  private parent: number[];

  constructor() {
    this.parent = Array.from({ length: 26 }).map((_, i) => i);
  }

  find(index: number) {
    if (this.parent[index] === index) {
      return index;
    }
    this.parent[index] = this.find(this.parent[index]);
    return this.parent[index];
  }

  union(index1: number, index2: number) {
    this.parent[this.find(index1)] = this.find(index2);
  }
}

function equationsPossible(equations: string[]): boolean {
  const uf = new UnionFind();
  for (const [a, s, _, b] of equations) {
    if (s === '=') {
      const index1 = a.charCodeAt(0) - 'a'.charCodeAt(0);
      const index2 = b.charCodeAt(0) - 'a'.charCodeAt(0);
      uf.union(index1, index2);
    }
  }
  for (const [a, s, _, b] of equations) {
    if (s === '!') {
      const index1 = a.charCodeAt(0) - 'a'.charCodeAt(0);
      const index2 = b.charCodeAt(0) - 'a'.charCodeAt(0);
      if (uf.find(index1) === uf.find(index2)) {
        return false;
      }
    }
  }
  return true;
}