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 <= equations.length <= 500equations[i].length == 4equations[i][0] and equations[i][3] are lowercase lettersequations[i][1] is either '=' or '!'equations[i][2] is '='struct Solution;
struct UnionFind {
parent: Vec<usize>,
n: usize,
}
impl UnionFind {
fn new(n: usize) -> Self {
let parent = (0..n).collect();
UnionFind { parent, n }
}
fn find(&mut self, i: usize) -> usize {
let j = self.parent[i];
if i == j {
j
} else {
let k = self.find(j);
self.parent[i] = k;
k
}
}
fn union(&mut self, i: usize, j: usize) {
let i = self.find(i);
let j = self.find(j);
if i != j {
self.parent[i] = j;
self.n -= 1;
}
}
}
impl Solution {
fn equations_possible(equations: Vec<String>) -> bool {
let mut uf = UnionFind::new(26);
let mut pairs: Vec<(usize, usize)> = vec![];
for equation in equations {
let s: Vec<char> = equation.chars().collect();
let i = (s[0] as u8 - b'a') as usize;
let j = (s[3] as u8 - b'a') as usize;
if s[1] == '=' {
uf.union(i, j);
} else {
pairs.push((i, j));
}
}
for pair in pairs {
let i = pair.0;
let j = pair.1;
if uf.find(i) == uf.find(j) {
return false;
}
}
true
}
}
#[test]
fn test() {
let equations = vec_string!["a==b", "b!=a"];
let res = false;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["b==a", "a==b"];
let res = true;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["a==b", "b==c", "a==c"];
let res = true;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["a==b", "b!=c", "c==a"];
let res = false;
assert_eq!(Solution::equations_possible(equations), res);
let equations = vec_string!["c==c", "b==d", "x!=z"];
let res = true;
assert_eq!(Solution::equations_possible(equations), res);
}