Satisfiability of Equality Equations

Description

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

Return true if and only if it is possible to assign integers to variable names so as to satisfy all the given equations.

 

Example 1:

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

Example 3:

Input: ["a==b","b==c","a==c"]
Output: true

Example 4:

Input: ["a==b","b!=c","c==a"]
Output: false

Example 5:

Input: ["c==c","b==d","x!=z"]
Output: true

 

Note:

1. 1 <= equations.length <= 500
2. equations[i].length == 4
3. equations[i][0] and equations[i][3] are lowercase letters
4. equations[i][1] is either '=' or '!'
5. equations[i][2] is '='

Solution(javascript)

/** Union Find
 * @param {string[]} equations
 * @return {boolean}
 */
const equationsPossible = function (equations) {
  const parent = {}
  const size = {}
  const notEquals = []
  const root = (item) => {
    while (parent[item] && item !== parent[item]) {
      parent[item] = parent[parent[item]]
      item = parent[item]
    }
    return item
  }
  const union = (a, b) => {
    const rootA = root(a)
    const rootB = root(b)
    if (rootA === rootB) {
      return
    }
    if (size[rootA] < size[rootB]) {
      parent[rootA] = rootB
      size[rootB] += size[rootA]
    } else {
      parent[rootB] = rootA
      size[rootA] += size[rootB]
    }
  }

  equations.forEach((item) => {
    const var1 = item[0]
    const var2 = item[3]
    parent[var1] = parent[var1] || var1
    parent[var2] = parent[var2] || var2
    size[var1] = size[var1] || 1
    size[var2] = size[var2] || 1
    if (item[1] === '!') {
      notEquals.push([var1, var2])
    } else {
      union(var1, var2)
    }
  })
  return notEquals.every(([a, b]) => root(a) !== root(b))
}