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Nearest 1 in a binary matrix in C++
Given a binary matrix, we need to find the minimum distance from each cell to the nearest cell that contains 1.
Let's see an example.
Input
0 0 1 1 1 0 0 0 0
Output
1 1 0 0 0 1 1 1 2
The minimum distance is the one that is minimum from current cell row - 1 cell row + current cell column - 1 cell column.
Algorithm
Initialise the matrix of desired size.
Initialise another matrix of same size to store distance.
Iterate over the entire matrix
.If the current cell value is 1, then set the distance to 0 as distance from 1 to 1 is 0
If the current cell value is 0
Iterate over the entire matrix again
If the cell is 1, then calculate the distance from the current cell.
Update the minimum distance.
.
Print the distance matrix.
Implementation
Following is the implementation of the above algorithm in C++
#include <bits/stdc++.h>
using namespace std;
vector<vector<int>> findNearest1Distance(vector<vector<int>>& matrix) {
int rows = matrix.size();
if (rows == 0) {
return matrix;
}
int cols = matrix[0].size();
vector<vector<int>> distance(rows, vector<int>(cols, INT_MAX));
for (int i = 0; i < rows; i++) {
for (int j = 0; j < cols; j++) {
if (matrix[i][j] == 1) {
distance[i][j] = 0;
}else if (matrix[i][j] == 0) {
for (int k = 0; k < rows; k++) {
for (int l = 0; l < cols; l++) {
if (matrix[k][l] == 1) {
distance[i][j] = min(distance[i][j], abs(k - i) + abs(l - j));
}
}
}
}
}
}
return distance;
}
int main() {
vector<vector<int>> matrix{
{0, 0, 1},
{1, 1, 0},
{0, 0, 0}
};
vector<vector<int>> result = findNearest1Distance(matrix);
for (int i = 0; i < 3; i++) {
for (int j = 0; j < 3; j++) {
cout << result[i][j] << " ";
}
cout << endl;
}
return 0;
}Output
If you run the above code, then you will get the following result.
1 1 0 0 0 1 1 1 2
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