Java Chapter 13: Graphs

java/Graphs/BipartiteGraphValidation.java

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+public class BipartiteGraphValidation {
+    public boolean bipartiteGraphValidation(int[][] graph) {
+        int[] colors = new int[graph.length];
+        // Determine if each graph component is bipartite.
+        for (int i = 0; i < graph.length; i++) {
+            if (colors[i] == 0 && !dfs(i, 1, graph, colors)) {
+                return false;
+            }
+        }
+        return true;
+    }
+
+    private boolean dfs(int node, int color, int[][] graph, int[] colors) {
+        colors[node] = color;
+        for (int neighbor : graph[node]) {
+            // If the current neighbor has the same color as the current 
+            // node, the graph is not bipartite.
+            if (colors[neighbor] == color) {
+                return false;
+            }
+            // If the current neighbor is not colored, color it with the 
+            // other color and continue the DFS.
+            if (colors[neighbor] == 0 && !dfs(neighbor, -color, graph, colors)) {
+                return false;
+            }
+        }
+        return true;
+    }
+}

java/Graphs/ConnectTheDots.java

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+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.Collections;
+import java.util.List;
+
+class UnionFind {
+    int[] parent;
+    int[] size;
+
+    public UnionFind(int size) {
+        this.parent = new int[size];
+        this.size = new int[size];
+        for (int i = 0; i < size; i++) {
+            this.parent[i] = i;
+        }
+        Arrays.fill(this.size, 1);
+    }
+
+    public boolean union(int x, int y) {
+        int repX = find(x);
+        int repY = find(y);
+        if (repX != repY) {
+            if (this.size[repX] > this.size[repY]) {
+                this.parent[repY] = repX;
+                this.size[repX] += this.size[repY];
+            }
+            else {
+                this.parent[repX] = repY;
+                this.size[repY] += this.size[repX];
+            }
+            // Return True if both groups were merged.
+            return true;
+        }
+        // Return False if the points belong to the same group.
+        return false; 
+    }
+
+    public int find(int x) {
+        if (x == this.parent[x]) {
+            return x;
+        }
+        this.parent[x] = find(this.parent[x]);
+        return this.parent[x];
+    }
+}
+
+public class ConnectTheDots {
+    public int connectTheDots(int[][] points) {
+        int n = points.length;
+        // Create and populate a list of all possible edges.
+        List<int[]> edges = new ArrayList<>();
+        for (int i = 0; i < n; i++) {
+            for (int j = i + 1; j < n; j++) {
+                // Manhattan distance.
+                int cost = Math.abs(points[i][0] - points[j][0]) + Math.abs(points[i][1] - points[j][1]);
+                edges.add(new int[]{cost, i, j});
+            }
+        }
+        // Sort the edges by their cost in ascending order.
+        Collections.sort(edges, (a, b) -> Integer.compare(a[0], b[0]));
+        UnionFind uf = new UnionFind(n);
+        int totalCost, edgesAdded;
+        totalCost = edgesAdded = 0;
+        // Use Kruskal's algorithm to create the MST and identify its minimum cost.
+        for (int[] edge : edges) {
+            int cost = edge[0];
+            int p1 = edge[1];
+            int p2 = edge[2];
+            // If the points are not already connected (i.e. their representatives are
+            // not the same), connect them, and add the cost to the total cost.
+            if (uf.union(p1, p2)) {
+                totalCost += cost;
+                edgesAdded++;
+                // If n - 1 edges have been added to the MST, the MST is complete.
+                if (edgesAdded == n - 1) {
+                    return totalCost;
+                }
+            }
+        }
+        return 0;
+    }
+}

java/Graphs/CountIslands.java

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+public class CountIslands {
+    public int countIslands(int[][] matrix) {
+        if (matrix == null || matrix.length == 0 || matrix[0] == null || matrix[0].length == 0) {
+            return 0;
+        }
+        int count = 0;
+        for (int r = 0; r < matrix.length; r++) {
+            for (int c = 0; c < matrix[0].length; c++) {
+                // If a land cell is found, perform DFS to explore the full 
+                // island, and include this island in our count.
+                if (matrix[r][c] == 1) {
+                    dfs(r, c, matrix);
+                    count++;
+                }
+            }
+        }
+        return count;
+    }
+
+    private void dfs(int r, int c, int[][] matrix) {
+        // Mark the current land cell as visited.
+        matrix[r][c] = -1;
+        // Define direction vectors for up, down, left, and right.
+        int[][] dirs = new int[][]{{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
+        // Recursively call DFS on each neighboring land cell to continue 
+        // exploring this island.
+        for (int[] d : dirs) {
+            int nextR = r + d[0];
+            int nextC = c + d[1];
+            if (isWithinBounds(nextR, nextC, matrix) && matrix[nextR][nextC] == 1) {
+                dfs(nextR, nextC, matrix);
+            }
+        }
+    }
+
+    private boolean isWithinBounds(int r, int c, int[][] matrix) {
+        return 0 <= r && r < matrix.length && 0 <= c && c < matrix[0].length;
+    }
+}

java/Graphs/GraphDeepCopy.java

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+import java.util.HashMap;
+import java.util.Map;
+
+import DS.GraphNode;
+
+/*
+    // Definition of GraphNode:
+    class GraphNode {
+        public int val;
+        public List<GraphNode> neighbors;
+        public MultiLevelListNode(int val) {
+            this.val = val;
+            this.neighbors = new ArrayList<>();
+        }
+    }
+ */
+
+public class GraphDeepCopy {
+    public GraphNode graphDeepCopy(GraphNode node) {
+        if (node == null) {
+            return null;
+        }
+        Map<GraphNode, GraphNode> cloneMap = new HashMap<>();
+        return dfs(node, cloneMap);
+    }
+
+    private GraphNode dfs(GraphNode node, Map<GraphNode, GraphNode> cloneMap) {
+        // If this node was already cloned, then return this previously  
+        // cloned node.
+        if (cloneMap.containsKey(node)) {
+            return cloneMap.get(node);
+        }
+        // Clone the current node.
+        GraphNode clonedNode = new GraphNode(node.val);
+        // Store the current clone to ensure it doesn't need to be created 
+        // again in future DFS calls.
+        cloneMap.put(node, clonedNode);
+        // Iterate through the neighbors of the current node to connect  
+        // their clones to the current cloned node.
+        for (GraphNode neighbor : node.neighbors) {
+            GraphNode clonedNeighbor = dfs(neighbor, cloneMap);
+            clonedNode.neighbors.add(clonedNeighbor);
+        }
+        return clonedNode;
+    }
+}

java/Graphs/LongestIncreasingPath.java

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+public class LongestIncreasingPath {
+    public int longestIncreasingPath(int[][] matrix) {
+        if (matrix == null || matrix.length == 0 || matrix[0] == null || matrix[0].length == 0) {
+            return 0;
+        }
+        int res = 0;
+        int m = matrix.length;
+        int n = matrix[0].length;
+        int[][] memo = new int[m][n];
+        // Find the longest increasing path starting at each cell. The
+        // maximum of these is equal to the overall longest increasing
+        // path.
+        for (int r = 0; r < m; r++) {
+            for (int c = 0; c < n; c++) {
+                res = Math.max(res, dfs(r, c, matrix, memo));
+            }
+        }
+        return res;
+    }
+
+    private int dfs(int r, int c, int[][] matrix, int[][] memo) {
+        if (memo[r][c] != 0) {
+            return memo[r][c];
+        }
+        int maxPath = 1;
+        int[][] dirs = new int[][]{{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
+        // The longest path starting at the current cell is equal to the
+        // longest path of its larger neighboring cells, plus 1.
+        for (int[] d : dirs) {
+            int nextR = r + d[0];
+            int nextC = c + d[1];
+            if (isWithinBounds(nextR, nextC, matrix) && matrix[nextR][nextC] > matrix[r][c]) {
+                maxPath = Math.max(maxPath, 1 + dfs(nextR, nextC, matrix, memo));
+            }
+        }
+        memo[r][c] = maxPath;
+        return maxPath;
+    }
+
+    private boolean isWithinBounds(int r, int c, int[][] matrix) {
+        return 0 <= r && r < matrix.length && 0 <= c && c < matrix[0].length;
+    }
+}

java/Graphs/MatrixInfection.java

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+import java.util.LinkedList;
+import java.util.Queue;
+
+public class MatrixInfection {
+    public int matrixInfection(int[][] matrix) {
+        int[][] dirs = new int[][]{{-1, 0}, {1, 0}, {0, -1}, {0, 1}};
+        Queue<int[]> queue = new LinkedList<>();
+        int ones, seconds;
+        ones = seconds = 0;
+        // Count the total number of uninfected cells and add each infected 
+        // cell to the queue to represent level 0 of the level-order  
+        // traversal.
+        for (int r = 0; r < matrix.length; r++) {
+            for (int c = 0; c < matrix[0].length; c++) {
+                if (matrix[r][c] == 1) {
+                    ones += 1;
+                } else if (matrix[r][c] == 2) {
+                    queue.offer(new int[]{r, c});
+                }
+            }
+        }
+        // Use level-order traversal to determine how long it takes to 
+        // infect the uninfected cells.
+        while (!queue.isEmpty() && ones > 0) {
+            // 1 second passes with each level of the matrix that's explored.
+            seconds++;
+            int size = queue.size();
+            for (int i = 0; i < size; i++) {
+                int[] pos = queue.poll();
+                int r = pos[0];
+                int c = pos[1];
+                // Infect any neighboring 1s and add them to the queue to be 
+                // processed in the next level.
+                for (int[] d : dirs) {
+                    int nextR = r + d[0];
+                    int nextC = c + d[1];
+                    if (isWithinBounds(nextR, nextC, matrix) && matrix[nextR][nextC] == 1) {
+                        matrix[nextR][nextC] = 2;
+                        ones--;
+                        queue.offer(new int[]{nextR, nextC});
+                    }
+                }
+            }
+        }
+        // If there are still uninfected cells left, return -1. Otherwise, 
+        // return the time passed.
+        return ones == 0 ? seconds : -1;
+    }
+
+    private boolean isWithinBounds(int r, int c, int[][] matrix) {
+        return 0 <= r && r < matrix.length && 0 <= c && c < matrix[0].length;
+    }
+}

java/Graphs/MergingCommunities.java

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+import java.util.Arrays;
+
+class UnionFind {
+    int[] parent;
+    int[] size;
+
+    public UnionFind(int size) {
+        this.parent = new int[size];
+        this.size = new int[size];
+        for (int i = 0; i < size; i++) {
+            this.parent[i] = i;
+        }
+        Arrays.fill(this.size, 1);
+    }
+
+    public void union(int x, int y) {
+        int repX = find(x);
+        int repY = find(y);
+        if (repX != repY) {
+            // If 'repX' represents a larger community, connect
+            // 'repY 's community to it.
+            if (this.size[repX] > this.size[repY]) {
+                this.parent[repY] = repX;
+                this.size[repX] += this.size[repY];
+            }
+            // Otherwise, connect 'rep_x's community to 'rep_y'.
+            else {
+                this.parent[repX] = repY;
+                this.size[repY] += this.size[repX];
+            }
+        }
+    }
+
+    public int find(int x) {
+        if (x == this.parent[x]) {
+            return x;
+        }
+        // Path compression.
+        this.parent[x] = find(this.parent[x]);
+        return this.parent[x];
+    }
+
+    public int getSize(int x) {
+        return this.size[find(x)];
+    }
+}
+
+public class MergingCommunities {
+    UnionFind uf;
+
+    public MergingCommunities(int n) {
+        this.uf = new UnionFind(n);
+    }
+
+    public void connect(int x, int y) {
+        this.uf.union(x, y);
+    }
+
+    public int getCommunitySize(int x) {
+        return this.uf.getSize(x);
+    }
+}