Add Longest Consecutive Difference Path problem with solution

src/main/java/com/thealgorithms/dynamicprogramming/LongestConsecutiveDiffPath.java

@@ -0,0 +1,50 @@
+package com.thealgorithms.dynamicprogramming;
+
+import java.util.HashMap;
+
+/**
+ * Problem: Longest Consecutive Difference Path
+ *
+ * Given an integer array, find the length of the longest path such that
+ * the absolute difference between consecutive elements is exactly 1.
+ *
+ * Example:
+ * Input:  arr = [3, 4, 2, 1, 2, 3, 4, 5]
+ * Output: 5
+ * Explanation: The longest path is [1, 2, 3, 4, 5]
+ *
+ * Category: Dynamic Programming with Hashing
+ */
+public class LongestConsecutiveDiffPath {
+
+    /**
+     * Function to find the longest consecutive difference path length
+     * @param arr input integer array
+     * @return length of longest path
+     */
+    public static int longestPath(int[] arr) {
+        HashMap<Integer, Integer> map = new HashMap<>();
+        int maxLength = 0;
+
+        for (int num : arr) {
+            int len1 = map.getOrDefault(num - 1, 0);
+            int len2 = map.getOrDefault(num + 1, 0);
+            int currentLen = Math.max(len1, len2) + 1;
+            map.put(num, currentLen);
+            maxLength = Math.max(maxLength, currentLen);
+        }
+
+        return maxLength;
+    }
+
+    public static void main(String[] args) {
+        int[] arr = {3, 4, 2, 1, 2, 3, 4, 5};
+        System.out.println("Longest consecutive difference path length: " + longestPath(arr));
+
+        int[] arr2 = {1, 2, 3, 4, 2, 3, 4, 5, 6};
+        System.out.println("Longest consecutive difference path length: " + longestPath(arr2));
+
+        int[] arr3 = {10, 9, 8, 7, 6};
+        System.out.println("Longest consecutive difference path length: " + longestPath(arr3));
+    }
+}