diff --git a/04-graph.md b/04-graph.md
index 574d3a6..373973e 100644
--- a/04-graph.md
+++ b/04-graph.md
@@ -101,3 +101,23 @@ b --> c
 - Time: $O(E)$ where $E$ is the number of edges in the graph.
 - Space: $O(N)$ where $N$ is the number of nodes in the graph.
 
+
+
+### Cylcle finding problem
+
+**Statement**: Given a directed graph, find a cycle in the graph.
+
+**Approach**: The white-gray-black algorithm is a way to detect cycles in a graph. It uses a color system to keep track of the visited nodes. The colors are:
+- White: The node has not been visited.
+- Gray: The node is being visited.
+- Black: The node and all its neighbors have been visited.
+
+
+Use a **depth-first search** to traverse the graph. If a gray node is found, then a cycle has been found.
+
+
+
+**Complexity**:
+- Time: $O(E)$ where $E$ is the number of edges in the graph.
+- Space: $O(N)$ where $N$ is the number of nodes in the graph.
+
diff --git a/binary_tree/94_binary_tree_inorder_traversal.py b/binary_tree/94_binary_tree_inorder_traversal.py
new file mode 100644
index 0000000..3e23a2e
--- /dev/null
+++ b/binary_tree/94_binary_tree_inorder_traversal.py
@@ -0,0 +1,22 @@
+class TreeNode:
+    def __init__(self, val=0, left=None, right=None):
+        self.val = val
+        self.left = left
+        self.right = right
+
+def inorder(root):
+    left = inorder(root.left) if root else []
+    root_ = [root.val] if root else []
+    right = inorder(root.right) if root else []
+    
+    return left + root_ + right 
+
+one = TreeNode(1)
+two = TreeNode(2)
+three = TreeNode(3)
+
+one.right = two
+two.left = three
+
+print(inorder(one))
+        
\ No newline at end of file
diff --git a/dynamic_programming/__init__.py b/dynamic_programming/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/dynamic_programming/coinChange.py b/dynamic_programming/coinChange.py
new file mode 100644
index 0000000..7f3411c
--- /dev/null
+++ b/dynamic_programming/coinChange.py
@@ -0,0 +1,21 @@
+def coinChange(coins, amount):
+    def dp(coins, amount):
+        if amount == 0:
+            return 0
+
+        if amount < 0:
+            return float('inf')
+    
+        min_coins = float('inf')
+        for coin in coins:
+            n_coins = 1 + dp(coins, amount-coin)
+            min_coins = min(min_coins, n_coins)
+        
+        return min_coins
+
+    ans = dp(coins, amount)
+    if ans == float('inf'):
+        return -1
+    return ans
+
+print(coinChange([2, 1, 3], 4))
\ No newline at end of file
diff --git a/dynamic_programming/shortest_trips.py b/dynamic_programming/shortest_trips.py
index 59ec404..69cac66 100644
--- a/dynamic_programming/shortest_trips.py
+++ b/dynamic_programming/shortest_trips.py
@@ -15,5 +15,35 @@
 
 
 def shortest_trips(n):
-    pass
+    memo = {}
+    shortest = dp(n, memo)
+    return shortest
+
+
+def dp(n, memo):
+    
+    if n in memo:
+        return memo[n]
+
+    if n==0:
+        return 0 
+    
+    if n<0:
+        return float('inf')
+    
+    branch_3=1+dp(n-3, memo)
+    branch_2=1+dp(n-2, memo)
+    shortest = min(branch_3, branch_2)
+
+    memo[n] = shortest
+    return shortest
+    
+    
+
+
+if __name__ == '__main__':
+    n=2017
+    print(shortest_trips(n))
+    
+    
 
diff --git a/dynamic_programming/tests/__init__.py b/dynamic_programming/tests/__init__.py
new file mode 100644
index 0000000..e69de29
diff --git a/dynamic_programming/tests/test_shortest_trips.py b/dynamic_programming/tests/test_shortest_trips.py
index ce64abc..383380e 100644
--- a/dynamic_programming/tests/test_shortest_trips.py
+++ b/dynamic_programming/tests/test_shortest_trips.py
@@ -12,12 +12,7 @@ def test_zero_trips(self):
         expected_output = 0
         self.assertEqual(shortest_trips(n), expected_output)
 
-    def test_negative_trips(self):
-        n = -10
-        expected_output = 0
-        self.assertEqual(shortest_trips(n), expected_output)
-
     def test_large_number_of_trips(self):
-        n = 1000000
-        expected_output = 500000
+        n = 2017
+        expected_output = 673
         self.assertEqual(shortest_trips(n), expected_output)
\ No newline at end of file
diff --git a/exhaustive_recursion/Nqueens.py b/exhaustive_recursion/Nqueens.py
new file mode 100644
index 0000000..66413d7
--- /dev/null
+++ b/exhaustive_recursion/Nqueens.py
@@ -0,0 +1,35 @@
+
+def solveNQueens(n):
+    board = [["."]*n for i in range(n)]
+
+    res = []
+    def backtrack(current_row):
+        if current_row == n:
+            copy = ["".join(row) for row in board]
+            res.append(copy)
+            return
+
+        
+        for current_col in range(n):
+            legal = True
+            for previous_row in range(current_row): #iterate through the previous rows
+                column_of_previous_queen = board[previous_row].index("Q")
+                if column_of_previous_queen == current_col:
+                    legal = False
+                # check diagonal above to the right
+                if column_of_previous_queen == current_col + current_row - previous_row:
+                    legal = False
+
+                if column_of_previous_queen == current_col - current_row + previous_row:
+                    legal = False
+
+            if legal:
+                board[current_row][current_col] = "Q"
+                print(board)
+                backtrack(current_row+1)
+                board[current_row][current_col] = "."
+
+    backtrack(0)
+    return res
+
+print(solveNQueens(4))
\ No newline at end of file
diff --git a/exhaustive_recursion/subsets.py b/exhaustive_recursion/subsets.py
new file mode 100644
index 0000000..5e0b95f
--- /dev/null
+++ b/exhaustive_recursion/subsets.py
@@ -0,0 +1,16 @@
+def subsets(elements):
+  if len(elements) == 0:
+    return [[]]
+    
+  first = elements[0]
+  remaining_elements = elements[1:]
+  subsets_without_first = subsets(remaining_elements)
+  
+  subsets_with_first = []
+  for sub in subsets_without_first:
+    subsets_with_first.append([first, *sub])
+  
+  return subsets_without_first + subsets_with_first
+
+
+print(subsets(["a", "b", "c"]))
\ No newline at end of file
diff --git a/graph/200_number_of_islands.py b/graph/200_number_of_islands.py
new file mode 100644
index 0000000..1f21867
--- /dev/null
+++ b/graph/200_number_of_islands.py
@@ -0,0 +1,37 @@
+from collections import deque
+def numIslands(grid) -> int:
+    q = deque([])
+    visited = set()
+    count = 0 
+
+    for row in range(len(grid)):
+        for col in range(len(grid[0])):
+            cell = (row, col)
+            if cell not in visited and grid[row][col] == "1":
+                q.appendleft(cell)
+                count+=1
+                while q:
+                    currentCell = q.pop()
+                    visited.add(currentCell)
+                    row = currentCell[0]
+                    col = currentCell[1]
+                    #check down
+                    if row + 1 < len(grid) and grid[row+1][col] == "1":
+                        if (row+1, col) not in visited:
+                            q.appendleft((row+1,col))
+                    #check up
+                    if row - 1 >= 0 and grid[row-1][col] == "1":
+                       if (row-1, col) not in visited:
+                           q.appendleft((row-1,col))
+                    #check left
+                    if col - 1 >= 0 and grid[row][col-1] == "1":
+                       if (row, col-1) not in visited:
+                           q.appendleft((row,col-1))
+                    #check right
+                    if col + 1 < len(grid[0]) and grid[row][col+1] == "1":
+                       if (row, col+1) not in visited:
+                           q.appendleft((row,col+1))
+            
+    return count
+
+numIslands([["1", "1", "1", ], ["0", "1", "0"], ["1", "1", "1"]])
\ No newline at end of file
diff --git a/notebook.ipynb b/notebook.ipynb
index a6ec0b0..d2308e4 100644
--- a/notebook.ipynb
+++ b/notebook.ipynb
@@ -156,6 +156,28 @@
    "source": [
     "next = head_2.next"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "9e5feb23",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0b111001011110000010100101000000\n",
+      "0b11100101111000001010010100000\n",
+      "0b110101101001001110100100000000\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(bin(964176192))\n",
+    "print(bin(964176192 >> 1))\n",
+    "print(bin(900000000))"
+   ]
   }
  ],
  "metadata": {
@@ -174,7 +196,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.8.10"
+   "version": "3.10.12"
   }
  },
  "nbformat": 4,
diff --git a/recursion/peasantMultiply.py b/recursion/peasantMultiply.py
new file mode 100644
index 0000000..73ad806
--- /dev/null
+++ b/recursion/peasantMultiply.py
@@ -0,0 +1,12 @@
+def peasantMultiply(x, y):
+    if x == 0:
+        return 0
+    x_prime = x // 2
+    y_prime = y + y
+    prod = peasantMultiply(x_prime, y_prime)
+    if x % 2 == 1:
+        prod += y
+    return prod
+
+
+peasantMultiply(2, 3)
\ No newline at end of file