diff --git a/Problem1.cpp b/Problem1.cpp
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diff --git a/Problem1.java b/Problem1.java
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diff --git a/Problem2.cpp b/Problem2.cpp
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diff --git a/Problem2.java b/Problem2.java
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diff --git a/problem11.py b/problem11.py
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+#Here assuming one element is missing for sure.
+
+#version 1
+def missingNumber(arr):
+    low = 0
+    high = len(arr)-1
+    
+    while low <= high:
+      mid = low + (high-low)//2
+
+      if arr[mid] == mid+1:
+        low = mid+1
+      else:
+        high = mid-1
+    if low == len(arr):#if nothing is missing
+        return -1  
+    return low+1 #can be mid+1 as well
+
+#how to write the code if all elements are present and nothing is missing?
+
+if __name__ == "__main__":
+    arr = [1, 2, 3, 4, 5, 6, 8]
+    print(missingNumber(arr))
+
+#version 2
+def missingNumber(arr):
+    low = 0
+    high = len(arr)-1
+    
+    while low < high:
+      mid = low + (high-low)//2
+
+      if arr[mid] == mid+1:
+        low = mid+1
+      else:
+        high = mid
+    if arr[low] == low + 1:
+        return -1 #nothing is missing, low won't reach end as it exists before low == high
+    return low+1
+
+if __name__ == "__main__":
+    arr = [1, 2, 3, 4, 5, 6, 8]
+    print(missingNumber(arr))
+
+#Time Complexity O(logn)
+# Space Complexity: O(1)
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diff --git a/problem14.py b/problem14.py
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+++ b/problem14.py
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+from collections import defaultdict
+from typing import List
+
+class Solution:
+    def groupAnagrams(self, strs: List[str]) -> List[List[str]]:
+        if not strs:
+            return None
+
+        hashMap = defaultdict(list)
+        res = []
+
+        for str in strs:
+            #26 length array initialize
+            key = [0]*26
+
+            for char in str:
+                key[ord(char)-ord('a')] += 1
+
+            hashMap[tuple(key)].append(str)
+
+        for key,values in hashMap.items():
+            res.append(values)
+
+        return res
+    
+# Time Complexity: O(n*k + n)  = O(N*k)
+# Space Complexity: O(nK + n + nk) = O(n*k) worse case: hashMap has n keys of O(1) and values it stores all
+# the strings (nk)
+
+# n = number of strings
+# k = average length of each string
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diff --git a/problem15.py b/problem15.py
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+++ b/problem15.py
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+#can maintain mapping in LL and arry list also but for
+#O(1) search complexity, we need hashMap
+#we need s to t and t to s mapping to avoid breach of "No two characters may map to the same character". eg: egl and add , here g and l can map to d. To avoid this we need 2 hashmaps
+#we can't have a single map for s->t and t->s mapping because we won't know from which string the chars are coming from. Else we have to maintain a flag (in a tuple with key) with keys to show distinction but its as good as having two hashmaps. space complexity will be 2 * no. of keys, if we use 2 hashmaps or two keys within a single hashmap. 
+
+from collections import defaultdict
+
+class Solution:
+    def isIsomorphic(self, s: str, t: str) -> bool:
+        if len(s) != len(t):
+            return False
+
+        hashMap_s = defaultdict(str)
+        hashMap_t = defaultdict(str)
+
+        for i in range(len(s)):
+            if hashMap_s[s[i]]:
+                if hashMap_s[s[i]] != t[i]:
+                    return False #breach
+            else:
+                hashMap_s[s[i]] = t[i]
+            
+            if hashMap_t[t[i]]:
+                if hashMap_t[t[i]] != s[i]:
+                    return False #breach
+            else:
+                hashMap_t[t[i]] = s[i]
+
+        return True
+    
+# Time Complexity : O(N) length of string 
+# Space Complexity : O(1) as worse case it will store only 26 characters O(26) is 1.
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diff --git a/problem16.py b/problem16.py
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+++ b/problem16.py
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+class Solution:
+    def wordPattern(self, pattern: str, s: str) -> bool:
+        words = s.split() #O(N) N is the length of string
+
+        #M is the len of words or length of pattern
+
+        if len(pattern) != len(words):
+            return False
+
+        char_to_word = {} #O(M)
+        word_to_char = {} #O(M)
+
+        for ch, word in zip(pattern, words): #O(M)
+            if ch in char_to_word and char_to_word[ch] != word:
+                return False
+            
+            if word in word_to_char and word_to_char[word] != ch:
+                return False
+
+            char_to_word[ch] = word
+            word_to_char[word] = ch
+
+        return True
+    
+# Time Complexity: O(N) + O(M) which is O(N) 
+# Space Complexity: O(M) (list words) + O(M) + O(M)
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