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399. Evaluate Division.cpp
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399. Evaluate Division.cpp
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//union find
//WA
//[["a","c"],["b","e"],["c","d"],["e","d"]]
//[2.0,3.0,0.5,5.0]
//[["a","b"]]
//in the "connect (a,b) and (b,c) to (a,c)" part, it fails when the path is too long
class DSU{
public:
map<string, string> parent;
DSU(set<string>& vertices){
for(string vertex : vertices){
parent[vertex] = vertex;
}
};
string find(string x){
if(parent[x] != x){
parent[x] = find(parent[x]);
}
return parent[x];
};
void unite(string x, string y){
parent[find(x)] = find(y);
};
};
class Solution {
public:
vector<double> calcEquation(vector<vector<string>>& equations, vector<double>& values, vector<vector<string>>& queries) {
set<string> vertices;
map<vector<string>, double> edges;
for(int i = 0; i < equations.size(); i++){
vector<string> equation = equations[i];
double value = values[i];
vertices.insert(equation[0]);
vertices.insert(equation[1]);
edges[equation] = value;
edges[{equation[1], equation[0]}] = 1/value;
}
//check how many connected components there are?
DSU dsu(vertices);
for(auto it = edges.begin(); it != edges.end(); it++){
vector<string> edge = it->first;
dsu.unite(edge[0], edge[1]);
}
//key: root of that group
map<string, set<string>> groups;
for(string vertex : vertices){
groups[dsu.find(vertex)].insert(vertex);
}
// for(auto it = groups.begin(); it != groups.end(); ++it){
// cout << it->first << " : ";
// for(auto it2 = it->second.begin(); it2 != it->second.end(); ++it2){
// cout << *it2 << " ";
// }
// cout << endl;
// }
//for each connect component, full connect their nodes
//we have (a,b) and (b,c), now connect them to (a,c)
for(auto it = groups.begin(); it != groups.end(); it++){
vector<string> oneGroup(it->second.begin(), it->second.end());
for(int i = 0; i < oneGroup.size(); i++){
for(int j = i; j < oneGroup.size(); j++){
string vi = oneGroup[i], vj = oneGroup[j];
if(i == j){
edges[{vi, vj}] = 1.0;
}else if(edges.find({vi, vj}) != edges.end()){
//they are connected directly
}else{
// cout << vi << " and " << vj << " are connected indirectly" << endl;
//they can be connected indirectly
//find vertex vk s.t. {vi,vk} and {vk,vj} exist
for(int k = 0; k < oneGroup.size(); k++){
string vk = oneGroup[k];
if(edges.find({vi, vk}) != edges.end() && edges.find({vj, vk}) != edges.end()){
edges[{vi,vj}] = edges[{vi,vk}] * edges[{vk, vj}];
edges[{vj,vi}] = edges[{vj,vk}] * edges[{vk, vi}];
break;
}
}
}
}
}
}
// for(auto it = edges.begin(); it != edges.end(); ++it){
// cout << it->first[0] << ", " << it->first[1] << endl;
// }
vector<double> ans;
for(vector<string>& query: queries){
string numerator = query[0];
string denominator = query[1];
if(edges.find({numerator, denominator}) != edges.end()){
ans.push_back(edges[{numerator, denominator}]);
}else{
ans.push_back(-1.0);
}
}
return ans;
}
};
//Floyd Warshall
//https://leetcode.com/problems/evaluate-division/discuss/88175/9-lines-%22Floydu2013Warshall%22-in-Python
//Runtime: 8 ms, faster than 9.29% of C++ online submissions for Evaluate Division.
//Memory Usage: 8.3 MB, less than 12.40% of C++ online submissions for Evaluate Division.
class Solution {
public:
vector<double> calcEquation(vector<vector<string>>& equations, vector<double>& values, vector<vector<string>>& queries) {
unordered_map<string, unordered_map<string, double>> quot;
int N = equations.size();
for(int i = 0; i < N; i++){
vector<string> equation = equations[i];
string num = equation[0], den = equation[1];
double value = values[i];
quot[num][num] = 1.0;
quot[den][den] = 1.0;
quot[num][den] = value;
quot[den][num] = 1.0/value;
}
for(auto it = quot.begin(); it != quot.end(); it++){
const string& k = it->first;
for(auto it2 = quot[k].begin(); it2 != quot[k].end(); it2++){
const string& i = it2->first;
for(auto it3 = quot[k].begin(); it3 != quot[k].end(); it3++){
const string& j = it3->first;
quot[i][j] = quot[i][k] * quot[k][j];
// adding this line gives WA!!!
//we don't need this line because i is not necessary <= j!
// quot[j][i] = quot[j][k] * quot[k][i];
}
}
}
vector<double> ans;
for(vector<string>& query : queries){
string num = query[0], den = query[1];
if(quot[num].find(den) == quot[num].end()){
ans.push_back(-1.0);
}else{
ans.push_back(quot[num][den]);
}
}
return ans;
}
};
//DFS
//https://leetcode.com/problems/evaluate-division/discuss/171649/1ms-DFS-with-Explanations
//Runtime: 0 ms, faster than 100.00% of C++ online submissions for Evaluate Division.
//Memory Usage: 8.5 MB, less than 7.50% of C++ online submissions for Evaluate Division.
class Solution {
public:
double dfs(string start, string end, unordered_map<string, unordered_map<string, double>>& graph, unordered_set<string>& visited){
if(graph.find(start) == graph.end()){
return -1;
}
if(graph[start].find(end) != graph[start].end()){
return graph[start][end];
}
for(const auto& nei : graph[start]){
if(find(visited.begin(), visited.end(), nei.first) != visited.end())
continue;
visited.insert(nei.first);
double res;
if((res = dfs(nei.first, end, graph, visited)) != -1){
//optimization: runtime 4ms -> 0ms
return graph[start][end] = graph[start][nei.first] * res;
}
}
return -1;
}
vector<double> calcEquation(vector<vector<string>>& equations, vector<double>& values, vector<vector<string>>& queries) {
unordered_map<string, unordered_map<string, double>> quot;
int N = equations.size();
for(int i = 0; i < N; i++){
const vector<string>& equation = equations[i];
const string& num = equation[0], den = equation[1];
const double& value = values[i];
quot[num][num] = 1.0;
quot[den][den] = 1.0;
quot[num][den] = value;
quot[den][num] = 1.0/value;
}
vector<double> ans;
unordered_set<string> visited;
for(const vector<string>& query : queries){
const string& num = query[0], den = query[1];
visited = {num};
ans.push_back(dfs(num, den, quot, visited));
}
return ans;
}
};
//BFS
//https://leetcode.com/problems/evaluate-division/discuss/88275/Python-fast-BFS-solution-with-detailed-explantion
//Runtime: 4 ms, faster than 58.89% of C++ online submissions for Evaluate Division.
//Memory Usage: 8.5 MB, less than 8.40% of C++ online submissions for Evaluate Division.
class Solution {
public:
double dfs(string start, string end, unordered_map<string, unordered_map<string, double>>& graph, unordered_set<string>& visited){
if(graph.find(start) == graph.end()){
return -1;
}
if(graph[start].find(end) != graph[start].end()){
return graph[start][end];
}
for(const auto& nei : graph[start]){
if(find(visited.begin(), visited.end(), nei.first) != visited.end())
continue;
visited.insert(nei.first);
double res;
if((res = dfs(nei.first, end, graph, visited)) != -1){
//optimization: runtime 4ms -> 0ms
return graph[start][end] = graph[start][nei.first] * res;
}
}
return -1;
}
vector<double> calcEquation(vector<vector<string>>& equations, vector<double>& values, vector<vector<string>>& queries) {
unordered_map<string, unordered_map<string, double>> quot;
int N = equations.size();
for(int i = 0; i < N; i++){
const vector<string>& equation = equations[i];
const string& num = equation[0], den = equation[1];
const double& value = values[i];
quot[num][num] = 1.0;
quot[den][den] = 1.0;
quot[num][den] = value;
quot[den][num] = 1.0/value;
}
vector<double> ans;
unordered_set<string> visited;
for(const vector<string>& query : queries){
const string& num = query[0], den = query[1];
double prod;
//cout << num << " - " << den << endl;
if(quot.find(num) == quot.end() || quot.find(den) == quot.end()){
//cout << "cannot find " << num << " or " << den << endl;
prod = -1.0;
}else if(quot[num].find(den) != quot[num].end()){
//cout << num << " - " << den << " already exist" << endl;
prod = quot[num][den];
}else{
//cout << "do BFS" << endl;
prod = -1.0;
//do BFS
//(node, current product)
queue<pair<string, double>> q;
q.push({num, 1.0});
visited = {num};
while(!q.empty()){
//cannot use pair<string, double>& here!!
pair<string, double> cur = q.front(); q.pop();
if(cur.first == den){
prod = cur.second;
break;
}
for(const pair<string, double>& nei : quot[cur.first]){
if(visited.find(nei.first) != visited.end())
continue;
visited.insert(nei.first);
/*
quot represents for the weight of edges,
not accumulative product,
so following line is wrong!
quot[cur.first][nei.first] = cur.second * nei.second;
*/
q.push({nei.first, cur.second * nei.second});
}
}
}
//cout << prod << endl;
ans.push_back(prod);
}
return ans;
}
};