Adds Longest Arithmetic Subsequence Implementation (#5501)

* Added LongestArthmeticSubsequence

---------

Co-authored-by: Piotr Idzik <65706193+vil02@users.noreply.github.com>

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

@@ -0,0 +1,42 @@
+package com.thealgorithms.dynamicprogramming;
+
+import java.util.HashMap;
+
+final class LongestArithmeticSubsequence {
+    private LongestArithmeticSubsequence() {
+    }
+
+    /**
+     * Returns the length of the longest arithmetic subsequence in the given array.
+     *
+     * A sequence seq is arithmetic if seq[i + 1] - seq[i] are all the same value
+     * (for 0 <= i < seq.length - 1).
+     *
+     * @param nums the input array of integers
+     * @return the length of the longest arithmetic subsequence
+     */
+    public static int getLongestArithmeticSubsequenceLength(int[] nums) {
+        if (nums == null) {
+            throw new IllegalArgumentException("Input array cannot be null");
+        }
+
+        if (nums.length <= 1) {
+            return nums.length;
+        }
+
+        HashMap<Integer, Integer>[] dp = new HashMap[nums.length];
+        int maxLength = 2;
+
+        // fill the dp array
+        for (int i = 0; i < nums.length; i++) {
+            dp[i] = new HashMap<>();
+            for (int j = 0; j < i; j++) {
+                final int diff = nums[i] - nums[j];
+                dp[i].put(diff, dp[j].getOrDefault(diff, 1) + 1);
+                maxLength = Math.max(maxLength, dp[i].get(diff));
+            }
+        }
+
+        return maxLength;
+    }
+}