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LeetCode/C++/alien-dictionary.cpp at master · Wei620/LeetCode · GitHub
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//
Time: O(n)
//
Space: O(|V|+|E|) = O(26 + 26^2) = O(1)
//
BFS solution.
class
Solution
{
public:
string
alienOrder
(vector<string>& words) {
unordered_set<
char
> nodes;
unordered_map<
char
, unordered_set<
char
>> in_degree, out_degree;
queue<
char
> zero_in_degree_queue;
for
(
const
auto
& word : words) {
for
(
const
auto
& c : word) {
nodes.
emplace
(c);
}
}
for
(
int
i =
1
; i < words.
size
(); ++i) {
findEdges
(words[i -
1
], words[i], &in_degree, &out_degree);
}
for
(
const
auto
& node : nodes) {
if
(in_degree.
find
(node) == in_degree.
end
()) {
zero_in_degree_queue.
emplace
(node);
}
}
//
BFS
string result;
while
(!zero_in_degree_queue.
empty
()) {
const
auto
& precedence = zero_in_degree_queue.
front
();
zero_in_degree_queue.
pop
();
result.
push_back
(precedence);
if
(out_degree.
find
(precedence) != out_degree.
end
()) {
for
(
const
auto
& c : out_degree[precedence]) {
in_degree[c].
erase
(precedence);
if
(in_degree[c].
empty
()) {
zero_in_degree_queue.
emplace
(c);
}
}
out_degree.
erase
(precedence);
}
}
if
(!out_degree.
empty
()) {
return
"
"
;
}
return
result;
}
private:
//
Construct the graph.
void
findEdges
(
const
string &word1,
const
string &word2,
unordered_map<
char
, unordered_set<
char
>> *in_degree,
unordered_map<
char
, unordered_set<
char
>> *out_degree) {
const
int
len =
min
(word1.
length
(), word2.
length
());
for
(
int
i =
0
; i < len; ++i) {
if
(word1[i] != word2[i]) {
(*in_degree)[word2[i]].
emplace
(word1[i]);
(*out_degree)[word1[i]].
emplace
(word2[i]);
break
;
}
}
}
};
//
DFS solution.
class
Solution2
{
public:
string
alienOrder
(vector<string>& words) {
//
Find ancestors of each node by DFS.
unordered_set<
char
> nodes;
unordered_map<
char
, vector<
char
>> ancestors;
for
(
int
i =
0
; i < words.
size
(); ++i) {
for
(
const
auto
& c : words[i]) {
nodes.
emplace
(c);
}
if
(i >
0
) {
findEdges
(words[i -
1
], words[i], &ancestors);
}
}
//
Output topological order by DFS.
string result;
unordered_map<
char
,
char
> visited;
for
(
const
auto
& node : nodes) {
if
(
topSortDFS
(node, node, &ancestors, &visited, &result)) {
return
"
"
;
}
}
return
result;
}
private:
//
Construct the graph.
void
findEdges
(
const
string &word1,
const
string &word2,
unordered_map<
char
, vector<
char
>> *ancestors) {
const
int
len =
min
(word1.
length
(), word2.
length
());
for
(
int
i =
0
; i < len; ++i) {
if
(word1[i] != word2[i]) {
(*ancestors)[word2[i]].
emplace_back
(word1[i]);
break
;
}
}
}
//
Topological sort, return whether there is a cycle.
bool
topSortDFS
(
const
char
& root,
const
char
& node,
unordered_map<
char
, vector<
char
>> *ancestors,
unordered_map<
char
,
char
> *visited,
string *result) {
if
(visited->
emplace
(
make_pair
(node, root)).
second
) {
for
(
auto
& ancestor: (*ancestors)[node]) {
if
(
topSortDFS
(root, ancestor, ancestors, visited, result)) {
return
true
;
}
}
result->
push_back
(node);
}
else
if
((*visited)[node] == root) {
//
Visited from the same root in the DFS path.
//
So it is cyclic.
return
true
;
}
return
false
;
}
};
//
DFS with adjacency matrix solution.
class
Solution3
{
public:
string
alienOrder
(vector<string>& words) {
string result;
vector<vector<
bool
>>
graph
(
26
, vector<
bool
>(
26
));
findDependency
(words, &graph);
findOrder
(&graph, &result);
return
result;
}
private:
void
findEdges
(
const
string &word1,
const
string &word2, vector<vector<
bool
>> *graph) {
const
int
len =
min
(word1.
length
(), word2.
length
());
for
(
int
i =
0
; i < len; ++i) {
if
(word1[i] != word2[i]) {
(*graph)[word1[i] -
'
a
'
][word2[i] -
'
a
'
] =
true
;
break
;
}
}
}
//
Construct the graph.
void
findDependency
(
const
vector<string>& words, vector<vector<
bool
>> *graph) {
for
(
const
auto
& c : words[
0
]) {
(*graph)[c -
'
a
'
][c -
'
a
'
] =
true
;
}
for
(
int
i =
1
; i < words.
size
(); ++i) {
for
(
const
auto
& c : words[i]) {
(*graph)[c -
'
a
'
] [c -
'
a
'
] =
true
;
}
findEdges
(words[i -
1
], words[i], graph);
}
}
//
Topological sort, return whether there is a cycle.
bool
topSortDFS
(string *result, vector<
bool
> *visited,
vector<vector<
bool
>> *graph,
const
int
root) {
if
((*visited)[root]) {
result->
clear
();
return
true
;
}
(*visited)[root] =
true
;
for
(
int
i =
0
; i <
26
; ++i) {
if
(i != root && (*graph)[root][i]) {
if
(
topSortDFS
(result, visited, graph, i)) {
return
true
;
}
}
}
(*graph)[root][root] =
false
;
result->
push_back
(root +
'
a
'
);
return
false
;
}
void
findOrder
(vector<vector<
bool
>> *graph, string *result) {
for
(
int
i =
0
; i <
26
; ++i) {
//
Find a root node.
bool
root_node = (*graph)[i][i];
if
((*graph)[i][i]) {
for
(
int
j =
0
; j <
26
; ++j) {
if
(j != i && (*graph)[j][i]) {
root_node =
false
;
break
;
}
}
}
if
(root_node) {
string reversed_order =
"
"
;
vector<
bool
>
visited
(
26
,
false
);
if
(
topSortDFS
(&reversed_order, &visited, graph, i)) {
result->
clear
();
return
;
}
else
{
result->
append
(reversed_order);
}
}
}
//
If there is any unvisited node, return "".
for
(
int
i =
0
; i <
26
; ++i) {
if
((*graph)[i][i]) {
result->
clear
();
return
;
}
}
//
The order should be reversed.
reverse
(result->
begin
(), result->
end
());
}
};
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