diff --git a/algorithm.xcodeproj/project.xcworkspace/xcuserdata/aseshshrestha.xcuserdatad/UserInterfaceState.xcuserstate b/algorithm.xcodeproj/project.xcworkspace/xcuserdata/aseshshrestha.xcuserdatad/UserInterfaceState.xcuserstate
index 8eab1fb..c92ef8f 100755
Binary files a/algorithm.xcodeproj/project.xcworkspace/xcuserdata/aseshshrestha.xcuserdatad/UserInterfaceState.xcuserstate and b/algorithm.xcodeproj/project.xcworkspace/xcuserdata/aseshshrestha.xcuserdatad/UserInterfaceState.xcuserstate differ
diff --git a/algorithm.xcodeproj/xcuserdata/aseshshrestha.xcuserdatad/xcdebugger/Breakpoints_v2.xcbkptlist b/algorithm.xcodeproj/xcuserdata/aseshshrestha.xcuserdatad/xcdebugger/Breakpoints_v2.xcbkptlist
index d6c93ed..218f386 100755
--- a/algorithm.xcodeproj/xcuserdata/aseshshrestha.xcuserdatad/xcdebugger/Breakpoints_v2.xcbkptlist
+++ b/algorithm.xcodeproj/xcuserdata/aseshshrestha.xcuserdatad/xcdebugger/Breakpoints_v2.xcbkptlist
@@ -14,8 +14,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "388"
-            endingLineNumber = "388"
+            startingLineNumber = "400"
+            endingLineNumber = "400"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -30,8 +30,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "354"
-            endingLineNumber = "354"
+            startingLineNumber = "366"
+            endingLineNumber = "366"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -46,8 +46,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "279"
-            endingLineNumber = "279"
+            startingLineNumber = "291"
+            endingLineNumber = "291"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -62,8 +62,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "247"
-            endingLineNumber = "247"
+            startingLineNumber = "259"
+            endingLineNumber = "259"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -126,8 +126,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "205"
-            endingLineNumber = "205"
+            startingLineNumber = "217"
+            endingLineNumber = "217"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -142,8 +142,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "168"
-            endingLineNumber = "168"
+            startingLineNumber = "180"
+            endingLineNumber = "180"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -158,8 +158,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "127"
-            endingLineNumber = "127"
+            startingLineNumber = "139"
+            endingLineNumber = "139"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -190,8 +190,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "116"
-            endingLineNumber = "116"
+            startingLineNumber = "128"
+            endingLineNumber = "128"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -206,8 +206,8 @@
             filePath = "algorithm/main.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "102"
-            endingLineNumber = "102"
+            startingLineNumber = "114"
+            endingLineNumber = "114"
             landmarkName = "main(argc, argv)"
             landmarkType = "9">
          </BreakpointContent>
@@ -270,8 +270,8 @@
             filePath = "algorithm/number.cpp"
             startingColumnNumber = "9223372036854775807"
             endingColumnNumber = "9223372036854775807"
-            startingLineNumber = "936"
-            endingLineNumber = "936"
+            startingLineNumber = "908"
+            endingLineNumber = "908"
             landmarkName = "reverse_integer(input)"
             landmarkType = "9">
          </BreakpointContent>
diff --git a/algorithm/main.cpp b/algorithm/main.cpp
index bb530fb..4377138 100755
--- a/algorithm/main.cpp
+++ b/algorithm/main.cpp
@@ -18,9 +18,21 @@
 
 int main(int argc, const char* argv[]) {
   
+  //  invoke_median_of_two_sorted_arrays();
+  
 //  invoke_four_number_sum();
   
-  invoke_reverse_integer();
+  invoke_jump_game_ii();
+  
+//  invoke_is_subsequence();
+  
+//  invoke_integer_to_roman();
+  
+//  invoke_jump_game();
+  
+//  invoke_best_time_to_buy_and_sell_stock_ii();
+  
+//  invoke_reverse_integer();
   
 //  invoke_rotate_array();
   
diff --git a/algorithm/number.cpp b/algorithm/number.cpp
index f944ace..8254f8a 100755
--- a/algorithm/number.cpp
+++ b/algorithm/number.cpp
@@ -236,34 +236,6 @@ int missing_number() {
 	return missing_number - std::accumulate(input_array.begin(), input_array.end(), 0);
 }
 
-/*
- https://leetcode.com/problems/median-of-two-sorted-arrays/
- Input: nums1 = [1,3], nums2 = [2]
- Output: 2.00000
- */
-void median_of_two_sorted_arrays(const std::vector<int>& array_one, const std::vector<int>& array_two) {
-	auto array_one_count = array_one.size();
-	auto array_two_count = array_two.size();
-	
-	// Assign an array with the max number of items
-	auto max_array = array_one_count >= array_two_count ? array_one : array_two;
-	
-	std::vector<int> total(max_array.size());
-	
-	// Iterate through all the elements of the max array
-	/*
-	 1, 2 -> 3, 4
-	 */
-	for(int index = 0; index < max_array.size(); index++) {
-		
-	}
-}
-
-void invoke_median_of_two_sorted_arrays() {
-	std::vector<int> input_one{1, 3}, input_two{2};
-	median_of_two_sorted_arrays(input_one, input_two);
-}
-
 /*
  11. Container With Most Water
  https://leetcode.com/problems/container-with-most-water/
@@ -942,3 +914,183 @@ int reverse_integer(int input) {
 void invoke_reverse_integer() {
   std::cout<<reverse_integer(-123);
 }
+
+/*
+nums1 = [1,2], nums2 = [3,4]; Output: 2.50000
+nums1 = [[1,3,4,5], nums = [2,3,6,7]; Output: 3.50000
+*/
+double median_of_two_sorted_arrays(std::vector<int>& nums1, std::vector<int>& nums2) {
+  double output = 0.0;
+  return output;
+}
+void invoke_median_of_two_sorted_arrays() {
+  std::vector<int> nums1 = {1,2}, nums2 = {3,4};
+  std::cout<<median_of_two_sorted_arrays(nums1, nums2);
+}
+
+/*
+prices = [7,1,5,3,6,4]; Output = 5-1 + 6-3 => 7
+prices = [1,2,3,4,5]; Output = 5-1 => 4
+prices = [7,6,4,3,1]; Output = 0
+*/
+int best_time_to_buy_and_sell_stock_ii(std::vector<int>& prices) {
+  int output = 0;
+  for(int index = 1; index < prices.size(); ++index) {
+    auto diff = prices[index] - prices[index - 1];
+    if(diff > 0) {
+      output += diff;
+      continue;
+    }
+  }
+  return output;
+}
+void invoke_best_time_to_buy_and_sell_stock_ii() {
+  std::vector<int> prices = {7,1,5,3,6,4};
+  std::cout<<"Max profit: "<<best_time_to_buy_and_sell_stock_ii(prices);
+}
+
+/*
+nums: [3,2,1,0,4] => false
+ 
+nums: [2,3,1,1,4] => true
+0 1 2 3 4
+2 3 1 1 4 => 1 1$; 2 1 1$
+ 
+nums: [6,5,5,7,4] => true
+ 
+nums: [1 1 1 1 1]
+*/
+bool jump_game(std::vector<int>& nums) {
+  int last_index = nums.size() - 1;
+  for(int index = nums.size() - 2; index >= 0; --index) {
+    if(index + nums[index] >= last_index) {
+      last_index = index;
+    }
+  }
+
+  return last_index <= 0;
+}
+void invoke_jump_game() {
+  std::vector<int> nums = {2,3,1,1,4};
+  std::cout<<std::boolalpha<<jump_game(nums);
+}
+
+/*
+ 1 3     *
+[2,3,1,1,4] => 2
+/\
+1 2
+| |
+3 1
+ 0 1 2 3 4 5 6
+[2,3,1,2,1,1,4] => 3
+/\
+1 2
+| |
+3 1
+|
+1
+|\
+1 2
+ 
+[1,2] => 1
+
+[1,2,3] => 2
+|
+1
+|\
+1 2
+   \
+    1*
+ 
+[1,1,1,1,2,4] = 5
+         |\
+         1 2
+*/
+int jump_game_ii(std::vector<int>& nums) {
+  int min_jumps = 0;
+  
+  return min_jumps;
+}
+void invoke_jump_game_ii() {
+  std::vector<int> nums = {2,3,1,2,1,1,4};
+  std::cout<<jump_game_ii(nums)<<std::endl;
+}
+
+/*
+Hashmap:
+1: I
+5: V
+10: X
+50: L
+100: C
+500: D
+1000: M
+ 
+3749 => MMMDCCXLIX
+3000: MMM: 1000 + 1000 + 1000
+700:  DCC: 500 + 100 + 100
+40:   XL:  50 - 10
+9:    IX:  10 - 1
+ 
+3749 % 10 = 9 = IX
+3749 % 10 = 374 => 374 % 10 = 4 * 10 = 40 = XL
+37   % 10 = 7   => 7 * 100 = 700 = DCC
+3    % 10 = 3   => 3 * 1000 = 3000 = MMM
+*/
+std::string integer_to_roman(int number) {
+  std::string output;
+  
+  std::vector<std::string> symbol = {"M","CM","D","CD","C","XC","L","XL","X","IX","V","IV","I"};
+  std::vector<int> symbol_value = {1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1};
+  
+  for(int index = 0; number != 0; ++index) {
+    while(number >= symbol_value[index]) {
+      number -= symbol_value[index];
+      output += symbol[index];
+    }
+  }
+  
+  return output;
+  
+//  static std::unordered_map<int, std::string_view> roman_map = {
+//    {1, "I"},
+//    {5, "V"},
+//    {9,  "IX"},
+//    {10, "X"},
+//    {40, "XL"},
+//    {50, "L"},
+//    {100, "C"},
+//    {500, "D"},
+//    {700, "DCC"},
+//    {1000, "M"},
+//    {3000, "MMM"},
+//  };
+//
+//  std::vector<std::string_view> temp_output;
+//  
+//  int multiplicant = 0;
+//  
+//  do {
+//    auto last_number = number % 10;
+//    number /= 10;
+//    
+//    multiplicant *= 10;
+//    if(multiplicant == 0) {
+//      multiplicant = 1;
+//    }
+//    
+//    std::cout<<last_number * multiplicant<<" => "<<roman_map[last_number * multiplicant]<<std::endl;
+//    temp_output.push_back(roman_map[last_number * multiplicant]);
+//    
+//  } while(number != 0);
+//
+//  for(int index = temp_output.size() - 1; index >= 0; --index) {
+//    output.append(temp_output[index]);
+//  }
+//  return output;
+}
+void invoke_integer_to_roman() {
+  std::cout<<integer_to_roman(3749)<<std::endl;
+}
+
diff --git a/algorithm/number.hpp b/algorithm/number.hpp
index 25d0be5..61bd509 100755
--- a/algorithm/number.hpp
+++ b/algorithm/number.hpp
@@ -33,11 +33,6 @@ CSingleLinkedList<int> invoke_reverse_linked_list(CSingleLinkedList<int> input_l
 
 int missing_number();
 
-/*
- */
-void median_of_two_sorted_arrays(const std::vector<int>& array_one, const std::vector<int>& array_two);
-void invoke_median_of_two_sorted_arrays();
-
 int container_with_most_water(const std::vector<int>& container_height);
 void invoke_container_with_most_water();
 
@@ -226,4 +221,27 @@ void invoke_rotate_array();
 */
 void invoke_reverse_integer();
 
+/*
+4. Median of Two Sorted Arrays: https://leetcode.com/problems/median-of-two-sorted-arrays/description/
+ https://www.algoexpert.io/questions/median-of-two-sorted-arrays
+*/
+void invoke_median_of_two_sorted_arrays();
+
+/*
+ 122. Best Time to Buy and Sell Stock II https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii
+*/
+void invoke_best_time_to_buy_and_sell_stock_ii();
+
+/*
+ 55. Jump Game https://leetcode.com/problems/jump-game
+*/
+void invoke_jump_game();
+
+void invoke_jump_game_ii();
+
+/*
+12. Integer to Roman https://leetcode.com/problems/integer-to-roman
+*/
+void invoke_integer_to_roman();
+
 #endif /* NUMBER_HPP */
diff --git a/algorithm/string.cpp b/algorithm/string.cpp
index 2145ab0..a503b20 100755
--- a/algorithm/string.cpp
+++ b/algorithm/string.cpp
@@ -243,6 +243,7 @@ bool is_anagram(const std::string& first_word, const std::string& second_word) {
   return false;
 }
 
+// R: O(nm) S: O(min(n,m))
 int levenshtein_distance(const std::string &first_word, const std::string& second_word) {
   // Space: O(mn)
   std::vector<std::vector<int>> edit_distance_table(first_word.size() + 1);
@@ -287,17 +288,14 @@ int levenshtein_distance(const std::string &first_word, const std::string& secon
 
   return edit_distance_table[first_word.size()][second_word.size()];
 }
-
-// R: O(nm) S: O(min(n,m))
 void invoke_levenshtein_distance() {
   std::cout<<"The number of edit operations required: "<<levenshtein_distance("abcdefghij", "1234567890")<<std::endl;
 }
 
+// T: O(wh), S(wh)
 int river_sizes(std::vector<std::vector<int>>& input_matrix) {
   return 0;
 }
-
-// T: O(wh), S(wh)
 void invoke_river_sizes() {
   // Output: 2, 2, 5, 1, 2
   std::vector<std::vector<int>> matrix = {
@@ -319,3 +317,50 @@ void valid_ip_address(const std::string& ip_addresses) {
 void invoke_valid_ip_address() {
   valid_ip_address("1921680");
 }
+
+bool valid_palindrome(std::string s) {
+  int backward_index = s.size() - 1;
+  for(int forward_index = 0; forward_index < backward_index;) {
+    if(!isalnum(s[forward_index])) {
+      ++forward_index;
+      continue;
+    }
+    if(!isalnum(s[backward_index])) {
+      --backward_index;
+      continue;
+    }
+
+    if(std::tolower(s[forward_index]) != std::tolower(s[backward_index])) {
+      return false;
+    }
+    --backward_index;
+    ++forward_index;
+  }
+  return true;
+}
+void invoke_valid_palindrome() {
+  std::cout<<std::boolalpha<<valid_palindrome("A man, a plan, a canal: Panama")<<std::endl;
+}
+
+/*
+a: abc
+b: ahbgdc
+ 
+a: axc
+b: ahbgdc
+*/
+bool is_subsequence(std::string str1, std::string str2) {
+  int first_index = 0;
+  for(int second_index = 0; second_index < str2.size() && first_index < str1.size(); ++second_index) {
+    if(str1[first_index] == str2[second_index]) {
+      ++first_index;
+      if(first_index == str1.size()) {
+        return true;
+      }
+    }
+  }
+  return false;
+}
+void invoke_is_subsequence() {
+  std::cout<<std::boolalpha<<is_subsequence("axc", "ahbgdc");
+}
diff --git a/algorithm/string.hpp b/algorithm/string.hpp
index 2236ea0..aedd888 100755
--- a/algorithm/string.hpp
+++ b/algorithm/string.hpp
@@ -29,4 +29,8 @@ void invoke_levenshtein_distance();
 
 void invoke_valid_ip_address();
 
+void invoke_valid_palindrome();
+
+void invoke_is_subsequence();
+
 #endif /* string_hpp */