Question
In a 2D grid of 0s and 1s, we change at most one 0 to a 1.
After, what is the size of the largest island? (An island is a 4-directionally connected group of 1s).
Example 1:
Input: [[1, 0], [0, 1]]
Output: 3
Explanation: Change one 0 to 1 and connect two 1s, then we get an island with area = 3.
Example 2:
Input: [[1, 1], [1, 0]]
Output: 4
Explanation: Change the 0 to 1 and make the island bigger, only one island with area = 4.
Example 3:
Input: [[1, 1], [1, 1]]
Output: 4
Explanation: Can't change any 0 to 1, only one island with area = 4.
Solution
TODO
Code
class Solution {
public int largestIsland(int[][] grid) {
if(grid.length == 0 || grid[0].length == 0) return 0;
Map<Integer, Integer> areaMap = new HashMap<>();
int maxArea = 0;
int flag = -1;
List<int[]> zeroList = new ArrayList<>();
for(int i=0; i<grid.length; i++) {
for(int j=0; j<grid[0].length; j++) {
if(grid[i][j] == 1) {
int area = dfs(grid, i, j, flag);
maxArea = Math.max(maxArea, area);
areaMap.put(flag, area);
flag--;
}
else if((grid[i][j] == 0)){
zeroList.add(new int[]{i, j});
}
}
}
for(int[] point: zeroList) {
int i=point[0];
int j=point[1];
int area = 1;
Set<Integer> set = new HashSet<>();
set.add(getFlag(grid, i-1, j));
set.add(getFlag(grid, i+1, j));
set.add(getFlag(grid, i, j-1));
set.add(getFlag(grid, i, j+1));
for(int f: set) area += areaMap.getOrDefault(f, 0);
maxArea = Math.max(maxArea, area);
}
return maxArea;
}
private int dfs(int[][] grid, int i, int j, int flag) {
if(i<0 || i>=grid.length || j<0 || j>=grid[0].length) return 0;
if(grid[i][j] != 1) return 0;
int area = 1;
grid[i][j] = flag;
area += dfs(grid, i+1, j, flag);
area += dfs(grid, i-1, j, flag);
area += dfs(grid, i, j+1, flag);
area += dfs(grid, i, j-1, flag);
return area;
}
private int getFlag(int[][] grid, int i, int j) {
if(i<0 || i>=grid.length || j<0 || j>=grid[0].length) return 0;
if(grid[i][j] == 0) return 0;
return grid[i][j];
}
}
Performance
O(m^n)