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Program to find minimum number of groups in communication towers in C++?
Suppose we have a 2D binary matrix where 1 represents a communication tower, and 0 represents an empty cell. The towers can communicate in the following ways: 1. If tower A, and tower B are either on the same row or column, they can communicate with each other. 2. If tower A can talk with tower B and B can talk with C, then A can talk to C (transitive property). We have to find the total number of tower groups there are (here a group is a list of towers that can talk with each other).
So, if the input is like
| 1 | 1 | 0 |
| 0 | 0 | 1 |
| 1 | 0 | 1 |
To solve this, we will follow these steps:
Define a function dfs(), this will take one 2D array matrix, i, j, n, m,
matrix[i, j] := 2
for initialize k := 1, when k < n, update (increase k by 1), do:
p := (i + k) mod n
q := j
if matrix[p, q] is same as 1, then:
dfs(matrix, p, q, n, m)
for initialize k := 1, when k < m, update (increase k by 1), do:
p := i
q = (j + k)
if matrix[p, q] is same as 1, then:
dfs(matrix, p, q, n, m)
From the main method do the following:
n := size of matrix
ans := 0
for initialize i := 0, when i < n, update (increase i by 1), do:
for initialize j := 0, when j < m, update (increase j by 1), do:
if matrix[i, j] is same as 1, then:
(increase ans by 1)
dfs(matrix, i, j, n, m)
return ans
Let us see the following implementation to get better understanding:
Example
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
void dfs(vector<vector<int>>& matrix, int i, int j, int& n, int& m) {
matrix[i][j] = 2;
for (int k = 1; k < n; k++) {
int p = (i + k) % n, q = j;
if (matrix[p][q] == 1) dfs(matrix, p, q, n, m);
}
for (int k = 1; k < m; k++) {
int p = i, q = (j + k) % m;
if (matrix[p][q] == 1) dfs(matrix, p, q, n, m);
}
}
int solve(vector<vector<int>>& matrix) {
int n = matrix.size(), m = matrix[0].size();
int ans = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
if (matrix[i][j] == 1) {
ans++;
dfs(matrix, i, j, n, m);
}
}
}
return ans;
}
};
int solve(vector<vector<int>>& matrix) {
return (new Solution())->solve(matrix);
}
main(){
vector<vector<int>> v = {
{1,1,0},
{0,0,1},
{1,0,1}
};
cout << solve(v);
}Input
{{1,1,0},
{0,0,1},
{1,0,1}};Output
1
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