399.Evaluate Division

Description

Equations are given in the formatA / B = k, whereAandBare variables represented as strings, andkis a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return-1.0.

Example:
Givena / b = 2.0, b / c = 3.0.
queries are:a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? .
return[6.0, 0.5, -1.0, 1.0, -1.0 ].

The input is:vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries, whereequations.size() == values.size(), and the values are positive. This represents the equations. Returnvector<double>.

According to the example above:

equations = [ ["a", "b"], ["b", "c"] ],
values = [2.0, 3.0],
queries = [ ["a", "c"], ["b", "a"], ["a", "e"], ["a", "a"], ["x", "x"] ].

The input is always valid. You may assume that evaluating the queries will result in no division by zero and there is no contradiction.

Discussion

method 1 & 2

bfs & dfs + hash map

code

// BFS
class Solution {
public:
    vector<double> calcEquation(vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries) {
        vector<double> rst;
        if(0 == equations.size() || 0 == queries.size() || equations.size() != values.size())
            return rst;

        unordered_multimap<string, tuple<string, string, double>> tracker;
        //unordered_map<pair<string, string>, double> tracker_2;
        for(int loop = 0; loop < equations.size(); ++loop) {
            tracker.insert(make_pair(equations[loop].first, make_tuple(equations[loop].first, equations[loop].second, values[loop])));
            //tracker_2.insert(equations[loop], values[loop]);
            if(values[loop] != 0) {
                tracker.insert(make_pair(equations[loop].second, make_tuple(equations[loop].second, equations[loop].first, 1 / values[loop])));
                //tracker_2.insert(make_pair(equation[loop].second, equation[loop].first), 1/values[loop]);
            }
        }

        for(auto query : queries) {
            double tmp = 0;
            if(true == findQuery(tracker, query, tmp)) {
                rst.push_back(tmp);
            }
            else {
                rst.push_back(-1);
            }
        }

        return rst;
    }
private:
    bool findQuery(unordered_multimap<string, tuple<string, string, double>> &tracker, pair<string, string>& query, double &tmp) {
        bool found = false;
        queue<tuple<string, string, double>> q;
        auto range = tracker.equal_range(query.first);

        //cout << "find: " << query.first << ", " << query.second << endl;

        for(auto iter = range.first; iter != range.second; ++iter) {
            if(iter == range.first && query.first == query.second) {
                tmp = 1;
                found = true;
                break;
            }

            if(get<1>(iter->second) == query.second) {
                tmp = get<2>(iter->second);
                found = true;
                break;
            }

            else {
                q.push(iter->second);
            }
        }
        //cout << "test" << endl; 
        while(!q.empty() && false == found) {
            auto next = q.front();
            q.pop();
            //cout << "map char:" << get<1>(next) << endl;
            range = tracker.equal_range(get<1>(next));
            for(auto iter = range.first; iter != range.second; ++iter) {
                //cout << "pair:" << get<0>(next) << ", " << get<1>(next) << ">" << get<0>(iter->second) << "," << get<1>(iter->second) << "," << get<2>(iter->second) << endl;
                if(get<0>(next) == get<1>(iter->second))
                    continue;
                double value = get<2>(next) * get<2>(iter->second);
                if(get<1>(iter->second) == query.second) {
                    //cout << "break?" << endl;
                    tmp = value;
                    found = true;
                    break;
                }
                else {
                    q.push(make_tuple(get<0>(iter->second), get<1>(iter->second), value));
                    // cannot update tracker, since iterator is under used.
                    /*
                    tracker.insert(make_pair(get<0>(next), make_tuple(get<0>(next), get<1>(iter->second), value)));
                    if(value != 0) {
                        tracker.insert(make_pair(get<1>(next), make_tuple(get<1>(next), get<0>(iter->second), 1 / value)));
                    }
                    */
                }
            }
            //cout << "test2" << endl; 
        }

        return found;
    }
};

method 3

union find (copy from leetcode discussion)

class Solution {
public:
    vector<double> calcEquation(vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries) {
        unordered_map<string, Node*> map;
        vector<double> res;
        for (int i = 0; i < equations.size(); i ++) {
            string s1 = equations[i].first, s2 = equations[i].second;
            if (map.count(s1) == 0 && map.count(s2) == 0) {
                map[s1] = new Node();
                map[s2] = new Node();
                map[s1] -> value = values[i];
                map[s2] -> value = 1;
                map[s1] -> parent = map[s2];
            } else if (map.count(s1) == 0) {
                map[s1] = new Node();
                map[s1] -> value = map[s2] -> value * values[i];
                map[s1] -> parent = map[s2];
            } else if (map.count(s2) == 0) {
                map[s2] = new Node();
                map[s2] -> value = map[s1] -> value / values[i];
                map[s2] -> parent = map[s1];
            } else {
                unionNodes(map[s1], map[s2], values[i], map);
            }
        }

        for (auto query : queries) {
            if (map.count(query.first) == 0 || map.count(query.second) == 0 || findParent(map[query.first]) != findParent(map[query.second]))
                res.push_back(-1);
            else
                res.push_back(map[query.first] -> value / map[query.second] -> value);
        }
        return res;
    }

private:
    struct Node {
        Node* parent;
        double value = 0.0;
        Node()  {parent = this;}
    };

    void unionNodes(Node* node1, Node* node2, double num, unordered_map<string, Node*>& map) {
        Node* parent1 = findParent(node1), *parent2 = findParent(node2);
        double ratio = node2 -> value * num / node1 -> value;
        for (auto it = map.begin(); it != map.end(); it ++)
            if (findParent(it -> second) == parent1)
                it -> second -> value *= ratio;
        parent1 -> parent = parent2;
    }

    Node* findParent(Node* node) {
        if (node -> parent == node)
            return node;
        node -> parent = findParent(node -> parent);
        return node -> parent;
    }
};