diff --git a/Finding 1-D collisions of a system of point masses.py b/Finding 1-D collisions of a system of point masses.py
new file mode 100644
index 0000000..ab1e571
--- /dev/null
+++ b/Finding 1-D collisions of a system of point masses.py	
@@ -0,0 +1,96 @@
+class Empty(Exception):
+    pass
+class HeapPriorityQueue():
+    #------------------------------ nonpublic behaviors ------------------------------
+    def _parent(self, j):
+        return (j-1) // 2 #returns the index of parent element of jth element in the heap
+    def _left(self, j): 
+        return 2*j+1 #returns the index of left element of jth element in the heap
+    def _right(self, j):
+        return 2*j+2 #returns the index of right element of jth element in the heap
+    def _has_left(self, j): #returns whether the jth element has a left element in the heap or not
+        return self._left(j) < len(self._data) # if index of left element of jth element is less than the length of list contaning heap elements then left element will exist and returns true otherwise false
+    def _has_right(self, j): #returns whether the jth element has a right element in the heap or not
+        return self._right(j) < len(self._data)  # if index of right element of jth element is less than the length of list contaning heap elements then right element will exist and returns true otherwise false
+    def _swap(self, i, j): #swaps the elements ith and jth index in the heap 
+        self._data[i], self._data[j] = self._data[j], self._data[i] #interchanging ith  and jth elements
+    def _upheap(self, j): #pushes an element from bottom to suitable position up inside the heap
+        parent = self._parent(j) #accessign the parent of jth element
+        if j > 0 and self._data[j] < self._data[parent]: #if parent is larger than jth element then jth element needs to be pushed up so we interchange jth element and its parent and recursively upheap it again
+            self._swap(j, parent)
+            self._upheap(parent) # recur at position of parent
+    def _downheap(self, j): #pushes an element from top to suitable position down the heap
+        if self._has_left(j): 
+            left = self._left(j)
+            small_child = left # initally assuming left child is smaller than right
+            if self._has_right(j):
+                right = self._right(j)
+                if self._data[right] < self._data[left]: #then checking the smaller among right and left child assigning the index of smaller value to the small_child variable
+                    small_child = right
+            if self._data[small_child] < self._data[j]: #if the jth element is greater than small_child(i.e. greater than both children) then we need to push it down so swap j with small_child index
+                self._swap(j, small_child)
+                self._downheap(small_child) # recur at position of small child
+#------------------------------ public behaviors ------------------------------
+    def __init__(self,l): 
+        self._data=l #initially taking a list l which needs to be converted into a binary heap later
+    def __len__(self):
+        return len(self._data) #returns lenth of the list containing elements of the binary heap
+    def is_empty(self): 
+        return len(self) == 0 #returns true if heap is empty
+    def enqueue(self,key): #function to insert an element inside the heap
+        self._data.append(key)
+        self._upheap(len(self._data)-1) #since it was appended at the last index so we upheap the last index of the list
+    def min(self): #rerurns the minimum element of the heap without removing it 
+        if self.is_empty():
+            raise Empty('Priority queue is empty.')
+        key = self._data[0] #1st element of the list is the least element 
+        return key
+    def remove_min(self): #returns the least element as well as removes it from the heap
+        if self.is_empty():
+            raise Empty('Priority queue is empty.')
+        self._swap(0,len(self._data)-1) #swapping the 1st and last element of the list
+        item=self._data.pop() #accessing the last element which is the smallest after swapping
+        self._downheap(0) #downheaping the 1st element which is the last element after swapping to suitale position so that next smallesst element of the heap comes at top again
+        return item #returning the smallest element 
+
+def listCollisions(M,x,v,m,T):
+    upcoming_coll=[-1]*len(M) #a list to store the times of upcoming collisions of any ith index
+    times=[] #a list to store the values of times at which collision can take place initially to be used to build the heap at t=0
+    ans=[] #final output list
+    time=0 #variable storing the value of time elapsed at the moment a collision has completed which keeps on updating on every collision
+    count=0 #variable storing the number of collisons that have took place
+    prev_coll=[0]*len(M) # list storing the times of just previous collision of any ith index collision
+    h=HeapPriorityQueue(times) # initiating heap using the initial time list
+    for i in range(len(v)- 1): #appending possible collision times in the times list initially
+        if v[i]-v[i+1]>0: #only in this case collison will be possible
+            times.append([(x[i+1]-x[i])/(v[i]-v[i+1]),i]) #storing time of collsion and the index as a list
+            upcoming_coll[i]=(x[i+1]-x[i])/(v[i]-v[i+1]) #updating the upcoming collision list
+    for i in range(len(times)-1,-1,-1): #fast buildheap method to convert the times list into heap
+        h._downheap(i)
+    while time<T and count<m and not(h.is_empty()): 
+        coll=h.remove_min() #extracting the collision  with least time i.e. one which will happen at first among all the possiblities inside the heap
+        i=coll[1] #index of collision
+        time=coll[0] #updating the time variable since the 0th index of heap element stores the time at which that collision will occur
+        if time==upcoming_coll[i]:       #for handling those cases when the time of collision of any ith index might have changed in between and the heap might be containing multiple collisions of a single index. So we continue only if the value of time(same as 0th index of collision list stored in heap) is same as the upcoming value of time of collision which keeps on updating so has the correct time at which collision of ith index will take place.
+            if time<=T: # we continue only if the elapsed time till this collsion is less than or equal to T.
+                x[i]=x[i]+v[i]*(time-prev_coll[i]) #updating the position of ith particle using formula final position=intial position+velocity(difference between time of this collison and previous collsion) we the the difference of time because last time we updated the position when its collion took place so we need to update according to time difference till then only.
+                x[i+1]=x[i]  #during collsion position of both particles will be same
+                v1=v[i] #storing the value of v[i] to be used while updating v[i+1] because v[i] will be changed before v[i+1]
+                v[i]=(M[i]-M[i+1])*v[i]/(M[i]+M[i+1])+(2*M[i+1])*v[i+1]/(M[i]+M[i+1]) #using formula given in reference link of assignment
+                v[i+1]=(2*M[i])*v1/(M[i]+M[i+1])-(M[i]-M[i+1])*v[i+1]/(M[i]+M[i+1]) #using formula given in reference link of assignment
+                prev_coll[i]=time #updating the prev_coll list to be used when collision takes place next time
+                prev_coll[i+1]=time #updating the prev_coll list to be used when collision takes place next time
+                ans.append((round(time,4),i,round(x[i],4))) #appending the time,index,potion of collsion in the final ans list
+                count+=1 #incresing the count variable since collsion has took place
+                if i>=1: #checking if the collsion of (i-1)th and ith particle after collsion of ith and (i+1)th is possible or not
+                    if v[i-1]-v[i]>0: #if collision is possible
+                        h.enqueue([time+(x[i]-x[i-1]-v[i-1]*(time-prev_coll[i-1]))/(v[i-1]-v[i]),i-1]) #we enqueue the time and index of (i-1)th index collision into the heap
+                        upcoming_coll[i-1]=time+abs(x[i]-x[i-1]-v[i-1]*(time-prev_coll[i-1]))/(v[i-1]-v[i]) #and update the upcoming coll list as this collsion is not yet happened but can happen in future
+                if i<=len(v)-3: #checking the same thing for possibility of (i+1)th and (i+2)th particle collision
+                    if v[i+1]-v[i+2]>0:
+                        h.enqueue([time+(x[i+2]+v[i+2]*(time-prev_coll[i+2])-x[i+1])/(v[i+1]-v[i+2]),i+1])
+                        upcoming_coll[i+1]=time+(x[i+2]+v[i+2]*(time-prev_coll[i+2])-x[i+1])/(v[i+1]-v[i+2])
+        else: #if the time value stored in heap element and upcoming coll list do not match that means, time of this collsion was updated and hence collision at this time is not possible and this element was removed from the heap so we continue to the next iteration without making any changes to position or velocity or heap or final ans list
+            continue
+
+    return(ans) #returning the final ans list
\ No newline at end of file
diff --git a/Finding Maximum Capacity of a Network.py b/Finding Maximum Capacity of a Network.py
new file mode 100644
index 0000000..36fba29
--- /dev/null
+++ b/Finding Maximum Capacity of a Network.py	
@@ -0,0 +1,90 @@
+class Empty(Exception):
+    pass
+class HeapPriorityQueue(): #heap class for extarcting the max capcacity of packets
+    #------------------------------ nonpublic behaviors ------------------------------
+    def _parent(self, j):
+        return (j-1) // 2 #returns the index of parent element of jth element in the heap
+    def _left(self, j): 
+        return 2*j+1 #returns the index of left element of jth element in the heap
+    def _right(self, j):
+        return 2*j+2 #returns the index of right element of jth element in the heap
+    def _has_left(self, j): #returns whether the jth element has a left element in the heap or not
+        return self._left(j) < len(self._data) # if index of left element of jth element is less than the length of list contaning heap elements then left element will exist and returns true otherwise false
+    def _has_right(self, j): #returns whether the jth element has a right element in the heap or not
+        return self._right(j) < len(self._data)  # if index of right element of jth element is less than the length of list contaning heap elements then right element will exist and returns true otherwise false
+    def _swap(self, i, j): #swaps the elements ith and jth index in the heap 
+        self._data[i], self._data[j] = self._data[j], self._data[i] #interchanging ith  and jth elements
+    def _upheap(self, j): #pushes an element from bottom to suitable position up inside the heap
+        parent = self._parent(j) #accessign the parent of jth element
+        if j > 0 and self._data[j][1] > self._data[parent][1]: #if parent is samller than jth element then jth element needs to be pushed up so we interchange jth element and its parent and recursively upheap it again
+            self._swap(j, parent)
+            self._upheap(parent) # recur at position of parent
+    def _downheap(self, j): #pushes an element from top to suitable position down the heap
+        if self._has_left(j): 
+            left = self._left(j)
+            large_child = left # initally assuming left child is larger than right
+            if self._has_right(j):
+                right = self._right(j)
+                if self._data[right][1] > self._data[left][1]: #then checking the larger among right and left child assigning the index of larger value to the large_child variable
+                    large_child = right
+            if self._data[large_child][1] > self._data[j][1]: #if the jth element is samller than large_child then we need to push it down so swap j with large_child index
+                self._swap(j, large_child)
+                self._downheap(large_child) # recur at position of large child
+#------------------------------ public behaviors ------------------------------
+    def __init__(self,l): 
+        self._data=l #initially taking a list l which needs to be converted into a binary heap later
+    def __len__(self):
+        return len(self._data) #returns lenth of the list containing elements of the binary heap
+    def is_empty(self): 
+        return len(self) == 0 #returns true if heap is empty
+    def enqueue(self,key): #function to insert an element inside the heap
+        self._data.append(key)
+        self._upheap(len(self._data)-1) #since it was appended at the last index so we upheap the last index of the list
+    def max(self): #rerurns the maximum element of the heap without removing it 
+        if self.is_empty():
+            raise Empty('Priority queue is empty.')
+        key = self._data[0] #1st element of the list is the max element 
+        return key
+    def remove_max(self): #returns the maximum element as well as removes it from the heap
+        if self.is_empty():
+            raise Empty('Priority queue is empty.')
+        self._swap(0,len(self._data)-1) #swapping the 1st and last element of the list
+        item=self._data.pop() #accessing the last element which is the largest after swapping
+        self._downheap(0) #downheaping the 1st element which is the last element after swapping to suitale position so that next largest element of the heap comes at top again
+        return item #returning the largest element 
+def findMaxCapacity(n,l,a,b): #main function
+    if a==b:
+        return (float('inf'),[a])
+    l1=[] #adjacency list
+    for i in range(n):
+        l1.append([]) #empty lists for each vertex
+    for x in l:
+        l1[x[0]].append((x[1],x[2],x[0])) #appending the edges to both adjacency lists of two vertices
+        l1[x[1]].append((x[0],x[2],x[1]))
+    cap=float('inf') #initliasing the capacity of packet that needs to be returned with infinity
+    prev_list=[-1]*n #a list which stores the source vertices of all the edges that we came across to be used later while printing the final path
+    prev_list[a]=-2 #initialising the source vertex with -2
+    ans=[] #path list
+    h=HeapPriorityQueue(l1[a]) #creating heap list of the edges originating from the source vertex a 
+    for i in range(len(l1[a])-1,-1,-1): #fast buildheap method
+        h._downheap(i)
+    while True: #loop runs till we get the destination vertex(then we break it)
+        node=h.remove_max() # #extracting max capacity packets from the heap
+        cap=min(cap,node[1]) #updating the cap variable since it is the min of all the capacities along the best(larget capacity) path
+        if node[0]==b: #when we reach the destination vertex
+            prev_list[b]=node[2] #update the source of last edge to reach dest
+            break #exit from loop
+        elif prev_list[node[0]]!=-1: #if the vertex is already visited then nothings needs to be done
+            continue
+        else:
+            for i in l1[node[0]]: # if we get a new vertex other than dest vertex then we enquque the edges of that vertex in the heap
+                h.enqueue(i) 
+            prev_list[node[0]]=node[2] #update the sorce vertex of the edge
+    temp=prev_list[b] #temporary variable which stores the value of soruce vertices for tracking the path through which we reached the dest, initialising it with source of dest vertex
+    ans.append(b) #appending the dest vertex in fianl path list
+    while prev_list[temp]!=-2: #backtracking the source vertices to get the path and stopping when reached the vertex a(since it's source was stored as -2)
+        ans.append(temp) #appending the path in ans list
+        temp=prev_list[temp] #updating temp
+    ans.append(temp) #appending a when loop stops
+    ans.reverse() #reversing to get the path from a-b
+    return (cap,ans) #returning cap and path
\ No newline at end of file
diff --git a/Finding Pattern in a Text.py b/Finding Pattern in a Text.py
new file mode 100644
index 0000000..04b96ab
--- /dev/null
+++ b/Finding Pattern in a Text.py	
@@ -0,0 +1,148 @@
+import random
+import math
+import string
+#To generate random prime less than N
+def randPrime(N):
+	primes = []
+	for q in range(2,N+1):
+		if(isPrime(q)):
+			primes.append(q)
+	return primes[random.randint(0,len(primes)-1)]
+
+# To check if a number is prime
+def isPrime(q):
+	if(q > 1):
+		for i in range(2, int(math.sqrt(q)) + 1):
+			if (q % i == 0):
+				return False
+		return True
+	else:
+		return False
+
+#pattern matching
+def randPatternMatch(eps,p,x):
+	N = findN(eps,len(p))
+	q = randPrime(N)
+	return modPatternMatch(q,p,x)
+
+#pattern matching with wildcard
+def randPatternMatchWildcard(eps,p,x):
+	N = findN(eps,len(p))
+	q = randPrime(N)
+	return modPatternMatchWildcard(q,p,x)
+
+# return appropriate N that satisfies the error bounds
+def findN(eps,m):
+	return int(2*math.log(26,2)*m*(math.log(m*math.log(26,2)/eps))/eps) 
+
+
+# Return sorted list of starting indices where p matches x
+def modPatternMatch(q,p,x):
+	ans=[] #final output list
+	m=len(p) #length of p
+	n=len(x) #length of p
+	prev=1 #initialisation of a varibale which stores the value of remainder by q of subsequent powers of 26 starting from 0 to m-1 
+	fpmodq=(string.ascii_uppercase.index(p[-1]))%q #initialisation of a varaible to the value of (26^0*last character of string p)modq which gets updated by adding the remainders of 26^k by q for k in range 0 to m-1 and finally gets the value of f(p)modq in reverse order
+	for i in range(2,m+1): 
+		fpmodq+=(prev*26*string.ascii_uppercase.index(p[-i]))%q #updating the prev variable and multiplying with the elements of string p then taking modq
+		prev=(26*prev)%q #updating prev by next power of 26
+	fpmodq=fpmodq%q #taking modq again in case fpmodq obtained above gets > q
+	prev=1 #again setting prev=1 to be used later
+	fxmodq=(string.ascii_uppercase.index(x[m-1]))%q # doing similar thing as fpmodq to find substring value of x named as fxmodq
+	for i in range(1,m): #loop working similar as fpmodq
+		fxmodq+=(prev*26*string.ascii_uppercase.index(x[m-1-i]))%q
+		prev=(26*prev)%q
+	rem=fxmodq #taking another variable rem which stores the sum of indivual remainder of 26^k*x[i] by q to be used later in case this sum is greater than q, because fxmodq will be again taken % with q in next line so the sum of remainders will not be available if this rem was not defined
+	fxmodq=fxmodq%q 
+	if fxmodq==fpmodq: #checking if initial subtring of x of length m matches with p or not, if yes then appending 0th index in the ans list
+		ans.append(0)
+	prev2=(prev*string.ascii_uppercase.index(x[0]))%q #another varibale which stores the value of 26^(m-1)*(first letter of subtring in x)%q to be used later which is updated in every substring, prev already has the value of 26^(m-1) modq after above loop
+	for i in range(m,n): #loop for traversing in the string x and checking for match with fpmodq
+		rem-=prev2 #when moved to next subtring then subtracting the value prev2 from previous rem since it is no longer the part of new subtring 
+		rem=(26*rem)%q #updating the rem since shifting to next subtring increases the power of 26 in each single element of subtring as compared to previous iteration
+		rem+=string.ascii_uppercase.index(x[i])%q  #adding the value of character next to the last character of previous subtring since it has 26^0 coeff so directly added value
+		fxmodq=rem%q #again taking remainder in case rem becomes >q
+		if fxmodq==fpmodq: #comparing values of substrings and p
+			ans.append(i-m+1) #appending proper index of x in the ans list
+		prev2=(prev*string.ascii_uppercase.index(x[i-m+1]))%q #updating prev2 with the value of first element of new substring using prev which has value (26^(m-1)) modq
+	return(ans)
+def modPatternMatchWildcard(q,p,x): #function to return pattern matching in case of wildcard element ?
+	ans=[] #output list
+	ind=0 #another variable to store the value of index(taking from last element of string) of the wildcard character ?
+	m=len(p) 
+	n=len(x)
+	prev=1 #same working as above function
+	fpmodq=0 #same use as above function
+	wildcard_mul=1 #a variable to store the value of 26^k mod q of the wildcard character '?' to be used later
+	wildcard_mul_2=1 #a variable to store the value of 26^(k-1) mod q of the wildcard character '?' to be used later
+	for i in range(1,m+1): #loop traversing in reverse order in p
+		if i<=m-1: #to avoid list index out of range in next step
+			if p[-1]!='?' and p[-i-1]=='?': # storing the value of (power of 26 of the next chacter to ? in p)modq when the last character is not ?(because then it has no next character in p)
+				wildcard_mul_2=prev 
+		if p[-i]!='?': #when the character is not '?' then adding indivual remainders of characters*prev by q in fpmodq
+			fpmodq+=(prev*string.ascii_uppercase.index(p[-i]))%q
+		else:
+			ind=i #assigning tthe index of ? to ind 
+			wildcard_mul=prev #assigning the value of wildcard_mul as the (power of 26 at position of ?)mod q
+		prev=(26*prev)%q #updating prev similar to above function
+	fpmodq=fpmodq%q 
+	prev=1 # resetting prev to be used later
+	fxmodq=0 # same use as above function
+	val1=0 # new variable to store the value of 26^k*(character present at the place of ? in substring of x as compared to p)modq to be used later which gets updated in each substring
+	val2=0 # new variable to store the value of 26^(k-1)*(next character of character present at the place of ? in substring of x as compared to p)modq to be used later which gets updated in each substring
+	for i in range(m): #iterating in first subtring of x of length m in reverse order
+		if i!=ind-1: #if the character is not at the place of ? as compared to p then updating fxmodq
+			fxmodq+=(prev*string.ascii_uppercase.index(x[m-1-i]))%q
+		else: #wehn we reache the index of ? in subtring
+			if i!=m-1: #if ? is not the first character of subtring
+				val1=(wildcard_mul*string.ascii_uppercase.index(x[m-1-i]))%q # assigning the value of val1 using the wildcard_mul defined earlier
+			elif i==m-1:
+				val1=-1 #setting val1 as -1 when ? is the first character since this case needs to be addressed separately
+			if i!=0: #if ? is not the last element of substring
+				val2=((wildcard_mul_2)*string.ascii_uppercase.index(x[m-i]))%q #assigning the value of val2
+			elif i==0:
+				val2=-1
+		if i!=m-1: #in the last interation prev need not be updated since it has already got the value of 26^(m-1) modq
+			prev=(26*prev)%q #updating prev
+	rem=fxmodq #same use as above function
+	fxmodq=fxmodq%q
+	if fxmodq==fpmodq:
+		ans.append(0)
+	
+	prev2=(prev*string.ascii_uppercase.index(x[0]))%q #same use as above function
+	for i in range(m,n): #iterating in x 
+		if val1!=-1:
+			rem-=prev2 #subtracting prev2 if ? was not the first character of p because in that case prev2 was not counted in rem in previous substring so need not be subtracted here
+		if val1!=-1:
+			rem+=val1 # adding val1(because it was excluded from rem in repvious iteration) to rem if ? was not the first element of p since it is not more a part of new subtring so need not be added
+		if val2!=-1: # if ? is the last element of p then it has no next character so nothing to be done if val2==-1
+			rem-=val2 #subtracting the value of val2 from rem because in previous substring it was next to the index of ? in substring as compared to p and in this iteration it comes at the index of of ? so need to be excluded
+		rem=(26*rem)%q
+		if val2!=-1: # adding the value of last character in new subtring if last character of p was not ? because then the next character of last character of previous subtring will now be at the index of ? so need not be added
+			rem+=string.ascii_uppercase.index(x[i])%q  
+		if val1!=-1: #updating val1
+			val1=(wildcard_mul*string.ascii_uppercase.index(x[i-ind+1]))%q
+		if val2!=-1: #updating val2
+			val2=((wildcard_mul_2)*string.ascii_uppercase.index(x[i-ind+2]))%q
+		fxmodq=rem%q
+		if fxmodq==fpmodq: #comapring and appending
+			ans.append(i-m+1)
+		prev2=(prev*string.ascii_uppercase.index(x[i-m+1]))%q #updating prev
+	return(ans) #returning ans list
+n = 1000
+e = 0.1
+wrong_e = 0
+for i in range(10):
+	c,w =0,0
+	for i in range(n):
+		if randPatternMatch(e, 'IRIS', 'IAPPLEBOIRISHAIRISBH') == [8,14]:
+			c += 1
+		else:
+			w += 1
+	if w/n > e:
+		wrong_e += 1
+	print (c,w)
+	print ('error:', w/n)
+# print (c,w)
+# print ('error:', w/n)
+print (wrong_e)
\ No newline at end of file
diff --git a/Finding Restaurants Nearby.py b/Finding Restaurants Nearby.py
new file mode 100644
index 0000000..e98d980
--- /dev/null
+++ b/Finding Restaurants Nearby.py	
@@ -0,0 +1,161 @@
+class treeNode(object): #node class with desired properties to use later
+    def __init__(self,value):
+        self.range=None #to store the range of x coordinate in the tree
+        self.value=None #to return the value stored at a node
+        self.l=None #to assign the left child
+        self.r=None #to assign the right child
+
+    def mergesort(self,node): #mergesroting function to solt the list atores at node
+        arr=node.value #return the list stored at node
+        if len(arr)>1:
+            mid=len(arr)//2 
+            L=arr[:mid] #left half
+            l1=treeNode(L) #new node storing left half of the list
+            l1.value=L #assigning the value of node
+            R=arr[mid:] #right half
+            r1=treeNode(R) #new node storing right half of the list
+            r1.value=R #assigning the value of node
+            node.l=l1.mergesort(l1) #assigning the left of the node as the sorted list of left half of the list
+            node.r=r1.mergesort(r1) #assigning the left of the node as the sorted list of left half of the list
+            node.value=merge(node.l.value,node.r.value) #merging the two sorted lists of left and right half and assigning the value of node to it
+            if len(node.l.value)==1: #assigning the range of left of node when its length is 1 i.e. it is the leaf node , also the base case for assigning ranges of nodes
+                node.l.range=node.l.value[0].range #already range was stored during the creation of these leaf nodes 
+            if len(node.r.value)==1:
+                node.r.range=node.r.value[0].range
+            node.range=(node.l.range[0],node.r.range[1]) #for assigning ranges of other nodes as the lower limit of range of left node to the higher limit of range of right node
+            i=j=k=0
+            while i<len(L) and j< len(R):
+                if L[i].value[0][1]<=R[j].value[0][1]: #comparing the two lists and changing the value of that index in arr accordingly
+                    arr[k]=L[i]
+                    i+=1
+                else:
+                    arr[k]=R[j]
+                    j+=1
+                k+=1
+            while i<len(L): #for remaining elements in the bigger list after comparison
+                arr[k]=L[i]
+                i+=1
+                k+=1
+            while j<len(R): #for remaining elements in the bigger list after comparison
+                arr[k]=R[j]
+                j+=1
+                k+=1
+        
+        node.value=arr #creating new node to store the 
+        return node #returns the node containing the y sorted list
+
+def merge(l1,l2): #for merging two sorted lists
+    l=[]
+    n1=len(l1)
+    n2=len(l2)
+    i=0
+    j=0
+    while i<n1 and j<n2:
+        if l1[i].value[0][1]<=l2[j].value[0][1]: #comparing the two lists and appending the value in teh final list accordingly
+            l.append(l1[i])
+            i+=1
+        else:
+            l.append(l2[j])
+            j+=1
+    while i<n1:
+        l.append(l1[i]) #for remaining elements in the bigger list after comparison
+        i+=1
+    while j<n2:
+        l.append(l2[j]) #for remaining elements in the bigger list after comparison
+        j+=1
+    return l
+
+def search(arr, x,o): #for the searching the index of just higher and just lower y coordinate than x(it is also a y coordinate) where o=1 is for jsut higher and o=-1 for just lower using binary search
+    if arr[0].value[0][1]>=x and o==1: #if the lowest element of arr is greater than x then all elements will be greater than x so just higher will be at index 0
+        return 0
+    elif arr[-1].value[0][1]<=x and o==-1: #if the lowest element of arr is greater than x then all elements will be greater than x so just higher will be at index 0
+        return len(arr)-1
+    if arr[-1].value[0][1]<x and o==1: #if largest element of list is lower than x then none of the elements will be larger than x so return -1
+        return -1
+    elif arr[0].value[0][1]>x and o==-1: #if smallest element of list is larger than x then none of the elements will be smaller than x so return -1
+        return -1
+    else:
+        if o==1: #searching the just higher element
+            low = 0 #common binary search code
+            high = len(arr) - 1
+            mid = 0
+            while low <= high:
+                mid = (high + low) // 2
+                if arr[mid].value[0][1] < x: 
+                    if mid<len(arr)-1 and o==-1:
+                        if arr[mid+1].value[0][1]>x:
+                            return mid
+                    low = mid + 1
+                elif arr[mid].value[0][1] >= x: #if mid element is greater than x and the previous element is less than x that means mid is the jsut higher element than x
+                    if mid>0 and o==1:
+                        if arr[mid-1].value[0][1]<x:
+                            return mid
+                    high = mid - 1
+            return -1
+        else: #searching the just lower element
+            low = 0
+            high = len(arr) - 1
+            mid = 0
+            while low <= high:
+
+                mid = (high + low) // 2
+                if arr[mid].value[0][1] <= x: #if mid element is less than x and the previous element is higher than x that means mid is the jsut lower element than x
+                    if mid<len(arr)-1 and o==-1:
+                        if arr[mid+1].value[0][1]>x: 
+                            return mid
+                    low = mid + 1
+                elif arr[mid].value[0][1] > x:
+                    if mid>0 and o==1:
+                        if arr[mid-1].value[0][1]<x:
+                            return mid
+                    high = mid - 1
+            return -1
+
+class PointDatabase(object): #main class
+    def __init__(self,pointlist):
+        if len(pointlist)==0: 
+            self._data=[]
+        else:
+            self._root=None #root node
+            self._data=pointlist 
+            self._data=sorted(self._data) #sorting the input pointlist w.r.t x coordinates
+            li=[]
+            for i in self._data:
+                a=treeNode([i]) #storing each point inside a list as a node
+                a.value=[i] #assigning its value
+                a.range=(i[0],i[0]) #assigning the range of single elements inside the list to be used later while merging them adn assignig its value
+                li.append(a)
+            self._data=li #updating self._data
+            self.build() #calling the build function to build the data structure storing all the points
+    def build(self): #build function to build the data structure storing all the points
+        a=treeNode(self._data) #creating another node for the base list
+        a.value=self._data #assigning value
+        self._root=a.mergesort(a) #assigning the node containing sorted list of the base list as the value of root node
+    def searchNearby(self,q,d): #nearby searching function
+        if len(self._data)==0:
+            return []
+        if d==0: #if d is 0 then return empty list because no point can be at exact d distance away from q
+            return []
+        x1=q[0]-d #lower limit of allowed x values
+        x2=q[0]+d #upper limit of allowed x values
+        y1=q[1]-d #lower limit of allowed y values
+        y2=q[1]+d #upper limit of allowed y values
+        ans=[] #final output list
+        def search_2(node,x1,x2,y1,y2,ans): # helper function to recursively search nodes in the data structure for fiding the nodes with appropriate range of x
+            if node.range[0]>x2 or node.range[1]<x1: #the allowed intervals is outside the range of x in node so exit from the function
+                return 
+            elif node.range[0]>=x1 and node.range[1]<=x2: # the range of x is completely indide the allowed range so search for suitable y and append in ans
+                i=search(node.value, y1, 1) #searching the index of element just higher than y1
+                j=search(node.value, y2, -1) #searching the index of element just lower than y2
+                if i!=-1 and j!=-1 and i<=j: #if i and j have suitable values
+                    for k in range(i,j+1):
+                        ans.append(node.value[k].value[0]) #apppending the correct points in the final list
+                return 
+            
+            else:
+                if node.l!=None :
+                    search_2(node.l, x1, x2, y1, y2, ans) #recursively searching on the left child node
+                if node.r!=None :
+                    search_2(node.r, x1, x2, y1, y2, ans) #recursively searching on the right child node
+        search_2(self._root, x1, x2, y1, y2, ans) #calling the function on root node
+        return ans #returning the final ans
\ No newline at end of file
diff --git a/Finding position of drones.py b/Finding position of drones.py
new file mode 100644
index 0000000..fd86509
--- /dev/null
+++ b/Finding position of drones.py	
@@ -0,0 +1,108 @@
+#Declaration: I have used the linkedstack class from the reference book 'Data structures an algorithm in python' by Roberto tamassia and it was also given in the class slides of linked list topic whereas I have commented it's working as per my own understanding
+import time
+a=time.time()
+class Empty(Exception):
+    pass
+class LinkedStack:
+    class _Node: #non public class for storing a singly linked node
+        __slots__=['_element', '_next'] 
+        def __init__(self,element,next):
+            self._element=element # referencing the user's element
+            self._next=next # referencing the user's next node
+    def __init__(self): #initilasing an empty stack
+        self._head=None  #referncing to the head node
+        self._size=0 # #initilasing the size of stack to zero
+    def __len__(self): #function to find length of stack
+        return self._size #returns the size of the stacks which keeps on updating after push and pop
+    def is_empty(self): #returns whether the stack is empty or not
+        return self._size==0 #returns true if size of stack is zero else false
+    def top(self): #returns top element of the stack
+        if self.is_empty(): #raises error if the stack is empty
+            raise Empty('Stack is Empty')
+        return self._head._element #returns the head element 
+    def push(self,e): #pushes the element e to the stack
+        self._head = self._Node(e,self._head) # updates the head of the stack by creating another element storing value of e and next value as the intial head
+        self._size+=1 #incrementing the size of stack
+    def pop(self): #removes the top element from the stack
+        if self.is_empty(): #raises error if the stack is empty
+            raise Empty('Stack is Empty')
+        answer=self._head._element #head element value stored before updating
+        self._head=self._head._next #updating the head as the next element of head
+        self._size-=1 #decreasing the size of stack
+        return answer #rerurning the stored value of answer
+    def __str__(self): #returns the stack in string format
+        arr='' #initialising the array as an empty string
+        start=self._head #starting with the head element
+        for i in range(self._size):
+            arr+=str(start._element)+', ' #adding the value of element at the variable start and , to the string 
+            start=start._next #updating the start variable to the next element of the list
+        return '<' +arr+']' #retuning the string with applying brackets 
+
+def findPositionandDistance(P):
+    x=0 # variable for updating the coordinates of x 
+    y=0 # variable for updating the coordinates of y
+    z=0 # variable for updating the coordinates of z
+    d=0 # variable for updating the value of distance d 
+    num=[] #list for storing the digits in the string to be used later for multiplying with the multiplier
+    ans=[] #final output list
+    multiplier=1 #variable for storing the number with which x/y/z must be added whenever there is +/- X/Y/Z in the input string depending on how many open brackets and multipliers are present before the +/ operation
+    prev_mult=LinkedStack() #stack for storing the latest factor by which the multiplier was multplied so that the top element of stack can be used to again divide the multiplier when there is a ) in the string.
+
+    for i in range(len(P)): #applying loop to access each element of the input string
+        if P[i]=='+' or P[i]=='-' : #these operations are included whenever X/Y/Z is found in the string later so can skip them initially to reduce time complexity
+            continue
+
+        elif P[i]=='X':
+            if P[i-1]=='+': #checking the operation preceding the variable and accordingly updating the coordinates of that variable
+                x+=multiplier
+                d+=multiplier
+                continue
+            else: #the other possibility will definitely be a - operation
+                x-=multiplier
+                d+=multiplier
+                continue
+
+        elif P[i]=='Y':
+            if P[i-1]=='+': #checking the operation preceding the variable and accordingly updating the coordinates of that variable
+                y+=multiplier
+                d+=multiplier
+                continue
+            else: #the other possibility will definitely be a - operation
+                y-=multiplier
+                d+=multiplier
+                continue
+            
+        elif P[i]=='Z':
+            if P[i-1]=='+': #checking the operation preceding the variable and accordingly updating the coordinates of that variable
+                z+=multiplier
+                d+=multiplier
+                continue
+            else: #the other possibility will definitely be a - operation
+                z-=multiplier
+                d+=multiplier
+                continue
+
+        elif P[i].isdigit(): # whenever we find digits in the string then we keep on appending them in the num list until we find a '(' which means that the string of digits has ended
+            num.append(P[i])
+            continue
+            # solve(s,num)
+        elif P[i]=='(': # the ( means that the string of digits preceding it has ended hence we convert the num list into integer and update the multiplier by mutiplying with that integer so that opeartions inside the ( are performed with the suitable multiplier
+            multiplier*=int(''.join(num)) 
+            prev_mult.push(int(''.join(num))) #pushing the latest factor of multiplier in the prev_mult stack
+            num=[] # again updating the num list to empty so that it can be used again later
+            continue
+
+        elif P[i]==')': 
+
+            multiplier//=prev_mult.top() #whenever we find a ) then update the multiplier by dividing with it's latest factor it was multiplier earlier by using the top element of stack prev_mult
+            prev_mult.pop() #removing the previous factor of multiplier so that next factor comes on top of stack to be used when we find the next ) for dividing the multiplier
+            continue
+
+    ans.append(x) #after all elements of the string are operated then we finally append the values of x,y,z,d to the final output list ans
+    ans.append(y)
+    ans.append(z)
+    ans.append(d)
+    return(ans) #returning ans
+print(findPositionandDistance('2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(2(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