01 Matrix in C++

Suppose we have a matrix consists of 0 and 1, we have to find the distance of the nearest 0 for each cell. Here the distance between two adjacent cells is 1.

So, if the input is like

then the output will be

To solve this, we will follow these steps −

• Define an array dir of size: 4 x 2 := {{1, 0}, { - 1, 0}, {0, - 1}, {0, 1}}

• n := row count, m := column count

• Define one matrix ret of order (n x m) and fill this with inf

• Define one queue q

• 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 not matrix[i, j] is non-zero, then −

      • ret[i, j] := 0

      • insert {i, j} into q

• for initialize lvl := 1, when not q is empty, update (increase lvl by 1), do −

  • sz := size of q

  • while sz is non-zero, decrease sz by 1 in each iteration, do −

    • Define one pair curr := front element of q

    • delete element from q

    • for initialize k := 0, when k < 4, update (increase k by 1), do −

      • nx := curr.first + dir[k, 0]

      • ny := curr.second + dir[k, 1]

      • if nx < 0 or nx >= n or ny < 0 or ny >= m or ret[nx, ny] < lvl, then −

        • ret[nx, ny] := lvl

      • insert {nx, ny} into q

• return ret

Example 

Let us see the following implementation to get better understanding −

 Live Demo

#include <bits/stdc++.h>
using namespace std;
void print_vector(vector<vector<auto> > v){
   cout << "[";
   for(int i = 0; i<v.size(); i++){
      cout << "[";
      for(int j = 0; j <v[i].size(); j++){
         cout << v[i][j] << ", ";
      }
      cout << "],";
   }
   cout << "]"<<endl;
}
int dir[4][2] = {{1, 0}, {-1, 0}, {0, -1}, {0, 1}};
class Solution {
public:
   vector<vector<int>> updateMatrix(vector<vector<int>>& matrix) {
   int n = matrix.size();
   int m = matrix[0].size();
   vector < vector <int> > ret(n, vector <int>(m, INT_MAX));
   queue < pair <int, int> > q;
   for(int i = 0; i < n; i++){
      for(int j = 0; j < m; j++){
         if(!matrix[i][j]){
            ret[i][j] = 0;
            q.push({i, j});
         }
      }
   }
   for(int lvl = 1; !q.empty(); lvl++){
      int sz = q.size();
      while(sz--){
         pair <int, int> curr = q.front();
         q.pop();
         for(int k = 0; k < 4; k++){
            int nx = curr.first + dir[k][0];
            int ny = curr.second + dir[k][1];
            if(nx < 0 || nx >= n || ny < 0 || ny >= m || ret[nx][ny] < lvl) continue;
               ret[nx][ny] = lvl;
               q.push({nx, ny});
            }
         }
      }
      return ret;
   }
};
main(){
   Solution ob;
   vector<vector<int>> v = {{0,0,0},{0,1,0},{1,1,1}};
   print_vector(ob.updateMatrix(v));
}

Input

{{0,0,0},{0,1,0},{1,1,1}}

Output

[[0, 0, 0, ],[0, 1, 0, ],[1, 2, 1, ],]