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2307. Check for Contradictions in Equations

  • Time: $O(n^3)$
  • Space: $O(n^2)$
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class Solution {
 public:
  bool checkContradictions(vector<vector<string>>& equations,
                           vector<double>& values) {
    // Convert `string` to `int` for a better perfermance.
    unordered_map<string, int> strToInt;

    for (const vector<string>& equation : equations) {
      const string& u = equation[0];
      const string& v = equation[1];
      if (!strToInt.count(u))
        strToInt[u] = strToInt.size();
      if (!strToInt.count(v))
        strToInt[v] = strToInt.size();
    }

    vector<vector<pair<int, double>>> graph(strToInt.size());
    vector<double> seen(graph.size());

    for (int i = 0; i < equations.size(); ++i) {
      const int u = strToInt.at(equations[i][0]);
      const int v = strToInt.at(equations[i][1]);
      graph[u].emplace_back(v, values[i]);
      graph[v].emplace_back(u, 1 / values[i]);
    }

    for (int i = 0; i < graph.size(); ++i)
      if (!seen[i] && dfs(graph, i, seen, 1.0))
        return true;

    return false;
  }

 private:
  bool dfs(const vector<vector<pair<int, double>>>& graph, int u,
           vector<double>& seen, double val) {
    if (seen[u])
      return abs(val / seen[u] - 1) > 1e-5;

    seen[u] = val;
    for (const auto& [v, w] : graph[u])
      if (dfs(graph, v, seen, val / w))
        return true;

    return false;
  }
};

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class Solution {
  public boolean checkContradictions(List<List<String>> equations, double[] values) {
    // Convert `string` to `int` for a better perfermance.
    Map<String, Integer> strToInt = new HashMap<>();

    for (List<String> equation : equations) {
      strToInt.putIfAbsent(equation.get(0), strToInt.size());
      strToInt.putIfAbsent(equation.get(1), strToInt.size());
    }

    List<Pair<Integer, Double>>[] graph = new List[strToInt.size()];
    double[] seen = new double[graph.length];

    for (int i = 0; i < graph.length; ++i)
      graph[i] = new ArrayList<>();

    for (int i = 0; i < equations.size(); ++i) {
      final int u = strToInt.get(equations.get(i).get(0));
      final int v = strToInt.get(equations.get(i).get(1));
      graph[u].add(new Pair<>(v, values[i]));
      graph[v].add(new Pair<>(u, 1 / values[i]));
    }

    for (int i = 0; i < graph.length; ++i)
      if (seen[i] != 0.0 && dfs(graph, i, seen, 1.0))
        return true;

    return false;
  }

  private boolean dfs(List<Pair<Integer, Double>>[] graph, int u, double[] seen, double val) {
    if (seen[u] != 0.0)
      return Math.abs(val / seen[u] - 1) > 1e-5;

    seen[u] = val;
    for (Pair<Integer, Integer> pair : graph[u]) {
      final int v = pair.getKey();
      final double w = pair.getValue();
      if (dfs(graph, v, seen, val / w))
        return true;
    }

    return false;
  }
}

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class Solution:
  def checkContradictions(self, equations: List[List[str]], values: List[float]) -> bool:
    # Convert `string` to `int` for a better perfermance.
    strToInt = {}

    for u, v in equations:
      strToInt.setdefault(u, len(strToInt))
      strToInt.setdefault(v, len(strToInt))

    graph = [[] for _ in range(len(strToInt))]
    seen = [0.0] * len(graph)

    for i, ((A, B), value) in enumerate(zip(equations, values)):
      u = strToInt[A]
      v = strToInt[B]
      graph[u].append((v, value))
      graph[v].append((u, 1 / value))

    def dfs(u: int, val: float) -> bool:
      if seen[u]:
        return abs(val / seen[u] - 1) > 1e-5

      seen[u] = val
      return any(dfs(v, val / w) for v, w in graph[u])

    for i in range(len(graph)):
      if not seen[i] and dfs(i, 1.0):
        return True

    return False