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Problem solution · Java

Number of Distinct Islands II

Number of Distinct Islands II: a Java solution using depth-first search. Learn the idea, check the complexity, and read the full code, with credit to walkccc LeetCode Solutions.

Technique
Depth-first search
Source
walkccc LeetCode Solutions
Length
80 lines
Start with the idea.

Try the problem first. If you get stuck, read the approach below, then write your own solution. The full code is at the bottom.

Approach

Depth-first search

For Number of Distinct Islands II, the implementation follows one branch at a time, making it suitable for components, trees, backtracking, or dependency exploration.

  1. Define the state carried into one recursive or stack frame.
  2. Mark or choose the current state before exploring children.
  3. Combine child results or undo the choice when the branch finishes.

Code notes

  • 80 lines of Java from the credited upstream file 711.java.
  • The implementation visibly relies on sequence storage, hash lookup, ordered lookup.
  • 7 loop blocks detected, together with recursive traversal.

Complexity

Count unique states for graph traversal; for backtracking, count the branching factor and maximum depth.

Check the problem constraints before deciding whether this complexity will pass.

Source

Code and credit

This code comes from walkccc LeetCode Solutions by P.-Y. Chen (walkccc) and is used under the MIT licence.

Open problem ↗Original source ↗
Full codeNumber of Distinct Islands II · JavaJava
Use this to learn the idea, then write your own version.
class Solution {  public int numDistinctIslands2(int[][] grid) {    final int m = grid.length;    final int n = grid[0].length;    // all the islands with different shapes    Set<List<Pair<Integer, Integer>>> islands = new HashSet<>();    boolean[][] seen = new boolean[m][n];     for (int i = 0; i < m; ++i)      for (int j = 0; j < n; ++j) {        List<Pair<Integer, Integer>> island = new ArrayList<>();        dfs(grid, i, j, seen, island);        if (!island.isEmpty())          islands.add(normalize(island));      }     return islands.size();  }   private void dfs(int[][] grid, int i, int j, boolean[][] seen,                   List<Pair<Integer, Integer>> island) {    if (i < 0 || i == grid.length || j < 0 || j == grid[0].length)      return;    if (grid[i][j] == 0 || seen[i][j])      return;     seen[i][j] = true;    island.add(new Pair<>(i, j));     dfs(grid, i + 1, j, seen, island);    dfs(grid, i - 1, j, seen, island);    dfs(grid, i, j + 1, seen, island);    dfs(grid, i, j - 1, seen, island);  }   private List<Pair<Integer, Integer>> normalize(List<Pair<Integer, Integer>> island) {    // points[i] := 8 different rotations/reflections of an island    Pair<Integer, Integer>[][] points = new Pair[8][island.size()];     for (int k = 0; k < island.size(); ++k) {      final int i = island.get(k).getKey();      final int j = island.get(k).getValue();      points[0][k] = new Pair<>(i, j);      points[1][k] = new Pair<>(i, -j);      points[2][k] = new Pair<>(-i, j);      points[3][k] = new Pair<>(-i, -j);      points[4][k] = new Pair<>(j, i);      points[5][k] = new Pair<>(j, -i);      points[6][k] = new Pair<>(-j, i);      points[7][k] = new Pair<>(-j, -i);    }     for (Pair<Integer, Integer>[] point : points)      Arrays.sort(point, Comparator.comparingInt(Pair<Integer, Integer>::getKey)                             .thenComparingInt(Pair<Integer, Integer>::getValue));     // Normalize each p by substracting p[1..7] with p[0].    for (Pair<Integer, Integer>[] p : points) {      for (int i = 1; i < island.size(); ++i)        p[i] = new Pair<>(p[i].getKey() - p[0].getKey(), p[i].getValue() - p[0].getValue());      p[0] = new Pair<>(0, 0);    }     Arrays.sort(points, new Comparator<Pair<Integer, Integer>[]>() {      @Override      public int compare(Pair<Integer, Integer>[] a, Pair<Integer, Integer>[] b) {        for (int i = 0; i < a.length; ++i) {          if (a[i].getKey() != b[i].getKey())            return a[i].getKey() - b[i].getKey();          if (a[i].getValue() != b[i].getValue())            return a[i].getValue() - b[i].getValue();        }        return 0;      }    });     return Arrays.asList(points[0]);  }}

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