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Find the number of Islands Using Disjoint Set in C++
In this problem, we are given a 2D binary matrix. Our task is to find the number of islands Using DFS.
Island is a ground of 1 or more connected 1’s in the matrix.
Let’s take an example to understand the problem,
Input
bin[][] = {{ 1 0 0 0}
{0 1 0 1}
{0 0 0 0}
{0 0 1 0}}Output
3
Explanation
Islands are : bin00 - bin11 bin13 bin32
Solution Approach
To find the island from a binary matrix using a disjoint set data structure. To find island count, we will traverse the matrix and do union of all adjacent vertices by checking all 8 neighbours, if they are 1 take union of current index with its neighbour. Then do the second traversal of the matrix, and if at any index the value is 1, find its sent. If frequency is 0, increase to 1.
Example
Program to illustrate the working of our solution,
#include <bits/stdc++.h>
using namespace std;
class DisjointUnionSets{
vector<int> rank, parent;
int n;
public:
DisjointUnionSets(int n){
rank.resize(n);
parent.resize(n);
this->n = n;
makeSet();
}
void makeSet(){
for (int i = 0; i < n; i++)
parent[i] = i;
}
int find(int x){
if (parent[x] != x){
return find(parent[x]);
}
return x;
}
void Union(int x, int y){
int xRoot = find(x);
int yRoot = find(y);
if (xRoot == yRoot)
return;
if (rank[xRoot] < rank[yRoot])
parent[xRoot] = yRoot;
else if (rank[yRoot] < rank[xRoot])
parent[yRoot] = xRoot;
else {
parent[yRoot] = xRoot;
rank[xRoot] = rank[xRoot] + 1;
}
}
};
int findIslandCount(vector<vector<int>> mat){
int n = mat.size();
int m = mat[0].size();
DisjointUnionSets *dus = new DisjointUnionSets(n * m);
for (int j = 0; j < n; j++){
for (int k = 0; k < m; k++){
if (mat[j][k] == 0)
continue;
if (j + 1 < n && mat[j + 1][k] == 1)
dus->Union(j * (m) + k, (j + 1) * (m) + k);
if (j - 1 >= 0 && mat[j - 1][k] == 1)
dus->Union(j * (m) + k, (j - 1) * (m) + k);
if (k + 1 < m && mat[j][k + 1] == 1)
dus->Union(j * (m) + k, (j) * (m) + k + 1);
if (k - 1 >= 0 && mat[j][k - 1] == 1)
dus->Union(j * (m) + k, (j) * (m) + k - 1);
if (j + 1 < n && k + 1 < m && mat[j + 1][k + 1] == 1)
dus->Union(j * (m) + k, (j + 1) * (m) + k + 1);
if (j + 1 < n && k - 1 >= 0 && mat[j + 1][k - 1] == 1)
dus->Union(j * m + k, (j + 1) * (m) + k - 1);
if (j - 1 >= 0 && k + 1 < m && mat[j - 1][k + 1] == 1)
dus->Union(j * m + k, (j - 1) * m + k + 1);
if (j - 1 >= 0 && k - 1 >= 0 && mat[j - 1][k - 1] == 1)
dus->Union(j * m + k, (j - 1) * m + k - 1);
}
}
int *c = new int[n * m];
int islands = 0;
for (int j = 0; j < n; j++){
for (int k = 0; k < m; k++){
if (mat[j][k] == 1){
int x = dus->find(j * m + k);
if (c[x] == 0){
islands++;
c[x]++;
}
else
c[x]++;
}
}
}
return islands;
}
int main(void){
vector<vector<int>> mat = {
{1, 1, 0, 1, 0},
{0, 1, 0, 1, 1},
{1, 0, 0, 1, 1},
{0, 0, 0, 0, 0},
{1, 1, 1, 0, 1}
};
cout<<"The number of islands in binary matrix is : "<<findIslandCount(mat);
}Output
The number of islands in binary matrix is : 4
Updated on: 11-Feb-2022
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