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1568. Minimum Number of Days to Disconnect Island.cpp
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1568. Minimum Number of Days to Disconnect Island.cpp
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//https://leetcode.com/problems/minimum-number-of-days-to-disconnect-island/discuss/819303/Python-you-need-at-most-2-days
//Runtime: 476 ms, faster than 18.56% of C++ online submissions for Minimum Number of Days to Disconnect Island.
//Memory Usage: 31.9 MB, less than 16.52% of C++ online submissions for Minimum Number of Days to Disconnect Island.
//time: O(m^2*n^2)
class Solution {
public:
int m, n;
vector<vector<int>> dirs;
vector<vector<bool>> visited;
int getConns(vector<vector<int>>& grid){
int conns = 0;
visited = vector<vector<bool>>(m, vector<bool>(n, false));
for(int i = 0; i < m; ++i){
for(int j = 0; j < n; ++j){
if(!grid[i][j] || visited[i][j]) continue;
++conns;
queue<pair<int, int>> q;
q.push({i, j});
visited[i][j] = true;
while(!q.empty()){
pair<int, int> p = q.front(); q.pop();
for(vector<int>& dir : dirs){
int ni = p.first + dir[0];
int nj = p.second + dir[1];
if(ni < 0 || ni >= m || nj < 0 || nj >= n ||
!grid[ni][nj] || visited[ni][nj])
continue;
visited[ni][nj] = true;
q.push({ni,nj});
}
}
}
}
return conns;
}
int minDays(vector<vector<int>>& grid) {
m = grid.size();
n = grid[0].size();
dirs = {{0,1}, {0,-1}, {1,0}, {-1,0}};
int conns = getConns(grid);
// cout << "conns: " << conns << endl;
if(conns == 0 || conns >= 2) return 0;
for(int i = 0; i < m; ++i){
for(int j = 0; j < n; ++j){
if(!grid[i][j]) continue;
grid[i][j] = 0;
conns = getConns(grid);
// cout << "conns: " << conns << endl;
/*
[[0,0,0],[0,1,0],[0,0,0]]
is also needed to be disconnected,
i.e. to destroy the island
*/
if(conns == 0 || conns >= 2)
return 1;
grid[i][j] = 1;
}
}
return 2;
}
};
//Tarjan’s algorithm for finding articulation points
//https://leetcode.com/problems/minimum-number-of-days-to-disconnect-island/discuss/819643/Java-Tarjan-4ms-with-explain
//https://www.geeksforgeeks.org/articulation-points-or-cut-vertices-in-a-graph/
//Runtime: 24 ms, faster than 97.01% of C++ online submissions for Minimum Number of Days to Disconnect Island.
//Memory Usage: 11.5 MB, less than 72.15% of C++ online submissions for Minimum Number of Days to Disconnect Island.
class Solution {
public:
int m, n;
vector<vector<int>> dirs;
vector<vector<int>> graph;
int getConns(vector<vector<int>>& grid){
int conns = 0;
vector<vector<bool>> visited(m, vector<bool>(n, false));
for(int i = 0; i < m; ++i){
for(int j = 0; j < n; ++j){
if(!grid[i][j] || visited[i][j]) continue;
++conns;
queue<pair<int, int>> q;
q.push({i, j});
visited[i][j] = true;
while(!q.empty()){
pair<int, int> p = q.front(); q.pop();
for(vector<int>& dir : dirs){
int ni = p.first + dir[0];
int nj = p.second + dir[1];
if(ni < 0 || ni >= m || nj < 0 || nj >= n ||
!grid[ni][nj] || visited[ni][nj])
continue;
visited[ni][nj] = true;
q.push({ni,nj});
}
}
}
}
return conns;
}
bool APUtil(int u, int& time, vector<bool>& visited, vector<int>& disc,
vector<int>& low, vector<int>& parent){
int child_count = 0;
visited[u] = true;
++time;
disc[u] = low[u] = time;
// cout << "visit: " << u/n << ", " << u%n << " at " << time << endl;
for(int& v : graph[u]){
if(!visited[v]){
++child_count;
parent[v] = u;
bool res = APUtil(v, time, visited, disc, low, parent);
if(res) return true;
/*
if the subtree rooted at v has
a back edge connected to somewhere higher than u,
then low[u] will be updated
*/
low[u] = min(low[u], low[v]);
if(parent[u] == -1 && child_count > 1)
return true;
/*
u: not root nor leaf,
and one of its children's subtree doesn't have backedge
*/
if(parent[u] != -1 && low[v] >= disc[u])
return true;
}else if(v != parent[u]){
//?
low[u] = min(low[u], disc[v]);
}
}
return false;
}
bool AP(){
vector<bool> visited(m*n, false);
vector<int> disc(m*n, 0);
vector<int> low(m*n, 0);
vector<int> parent(m*n, -1);
int time = 0;
for(int i = 0; i < m*n; ++i){
if(graph[i].empty() || visited[i]) continue;
// cout << "root: " << i/n << ", " << i%n << " has " << graph[i].size() << " children" << endl;
bool res = APUtil(i, time, visited, disc, low, parent);
if(res) return true;
}
for(int i = 0; i < m*n; ++i){
if(graph[i].empty()) continue;
// cout << i/n << ", " << i%n << " , disc: " << disc[i] << ", low: " << low[i] << ", parent: " << parent[i]/n << ", " << parent[i]%n << endl;
}
return false;
};
int getid(int i, int j){
//*n, not *m !!
return i*n + j;
};
int minDays(vector<vector<int>>& grid) {
m = grid.size();
n = grid[0].size();
dirs = {{0,1}, {0,-1}, {1,0}, {-1,0}};
int conns = getConns(grid);
// cout << "conns: " << conns << endl;
if(conns == 0 || conns >= 2) return 0;
int sum = 0;
for(int i = 0; i < m; ++i){
for(int j = 0; j < n; ++j){
sum += grid[i][j];
}
}
if(sum <= 2) return sum;
graph = vector<vector<int>>(m*n);
// cout << "m: " << m << ", n: " << n << endl;
for(int i = 0; i < m; ++i){
for(int j = 0; j < n; ++j){
if(!grid[i][j]) continue;
int cid = getid(i, j);
// cout << "(" << i << ", " << j << "): ";
for(vector<int>& dir : dirs){
int ni = i + dir[0];
int nj = j + dir[1];
if(ni < 0 || ni >= m || nj < 0 || nj >= n || !grid[ni][nj])
continue;
int nid = getid(ni, nj);
graph[cid].push_back(nid);
// cout << "(" << ni << ", " << nj << "), ";
// graph[nid].push_back(cid); //duplicate
}
// cout << endl;
}
}
//can find articulation point, so only need one cut
if(AP()) return 1;
return 2;
}
};