diff --git a/DIRECTORY.md b/DIRECTORY.md
index 150e4e61ea06..6511a2c50c83 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -241,6 +241,7 @@
     * [Kth Largest Element](data_structures/arrays/kth_largest_element.py)
     * [Median Two Array](data_structures/arrays/median_two_array.py)
     * [Monotonic Array](data_structures/arrays/monotonic_array.py)
+    * [Next Greater Element](data_structures/arrays/next_greater_element.py)
     * [Pairs With Given Sum](data_structures/arrays/pairs_with_given_sum.py)
     * [Permutations](data_structures/arrays/permutations.py)
     * [Prefix Sum](data_structures/arrays/prefix_sum.py)
@@ -986,6 +987,7 @@
   * [Doppler Frequency](physics/doppler_frequency.py)
   * [Escape Velocity](physics/escape_velocity.py)
   * [Grahams Law](physics/grahams_law.py)
+  * [Hamiltonian](physics/hamiltonian.py)
   * [Horizontal Projectile Motion](physics/horizontal_projectile_motion.py)
   * [Hubble Parameter](physics/hubble_parameter.py)
   * [Ideal Gas Law](physics/ideal_gas_law.py)
diff --git a/data_structures/arrays/next_greater_element.py b/data_structures/arrays/next_greater_element.py
new file mode 100644
index 000000000000..4532aa219322
--- /dev/null
+++ b/data_structures/arrays/next_greater_element.py
@@ -0,0 +1,21 @@
+# Program to find the Next Greater Element (NGE) for each element in the array
+
+arr = [4, 5, 2, 25, 7, 8]
+n = len(arr)
+
+print("Original array:", arr)
+
+# List to store results, default is -1 for elements with no greater element
+nge = [-1] * n
+
+# Outer loop for each element
+for i in range(n):
+    # Inner loop to find the next greater element
+    for j in range(i + 1, n):
+        if arr[j] > arr[i]:
+            nge[i] = arr[j]
+            break  # Stop once the next greater is found
+
+# Print result
+for i in range(n):
+    print(f"Next Greater Element for {arr[i]} is {nge[i]}")