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.
SOLUTION:
class Solution:
def equationsPossible(self, equations: List[str]) -> bool:
equalGraph = {}
inequalities = []
for eq in equations:
a = eq[0]
b = eq[-1]
opr = eq[1:-1]
if opr == "==":
equalGraph[a] = equalGraph.get(a, []) + [b]
equalGraph[b] = equalGraph.get(b, []) + [a]
else:
inequalities.append((a, b))
for a, b in inequalities:
paths = [a]
visited = {a}
while len(paths) > 0:
curr = paths.pop()
for j in equalGraph.get(curr, []):
if j not in visited:
visited.add(j)
paths.append(j)
if b in visited:
return False
return True
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