Merge pull request #3 from codezoned/master

Update

Arrays-Sorting/src/Iterative_Merge_Sort/Iterative_Merge_Sort.py

@@ -0,0 +1,87 @@
+
+#made by SHASHANK CHAKRAWARTY
+#Time complexity of above iterative function is  Θ(nLogn)
+# Iterative Merge sort (Bottom Up)
+
+# Iterative mergesort function to
+# sort arr[0...n-1] 
+def mergeSort(a):
+
+    current_size = 1
+
+    # Outer loop for traversing Each 
+    # sub array of current_size
+    while current_size < len(a) - 1:
+
+        left = 0
+        # Inner loop for merge call 
+        # in a sub array
+        # Each complete Iteration sorts
+        # the iterating sub array
+        while left < len(a)-1:
+
+            # mid index = left index of 
+            # sub array + current sub 
+            # array size - 1
+            mid = left + current_size - 1
+
+            # (False result,True result)
+            # [Condition] Can use current_size
+            # if 2 * current_size < len(a)-1
+            # else len(a)-1
+            right = ((2 * current_size + left - 1,
+                    len(a) - 1)[2 * current_size 
+                          + left - 1 > len(a)-1])
+
+            # Merge call for each sub array
+            merge(a, left, mid, right)
+            left = left + current_size*2
+
+        # Increasing sub array size by
+        # multiple of 2
+        current_size = 2 * current_size
+
+# Merge Function
+def merge(a, l, m, r):
+#you create 2 sub arrays with length n1 and n2
+    n1 = m - l + 1
+    n2 = r - m
+#2 arrays are created
+    L = [0] * n1
+    R = [0] * n2
+#copy the elements into the left and right array for sorting
+    for i in range(0, n1):
+        L[i] = a[l + i]
+    for i in range(0, n2):
+        R[i] = a[m + i + 1]
+#here it sorts
+    i, j, k = 0, 0, l
+    while i < n1 and j < n2:
+        if L[i] > R[j]:
+            a[k] = R[j]
+            j += 1
+        else:
+            a[k] = L[i]
+            i += 1
+        k += 1
+#and you copy the elements into the arrays i.e Left and Right by comparing it with the size of the array which was declared previously 
+    while i < n1:
+        a[k] = L[i]
+        i += 1
+        k += 1
+
+    while j < n2:
+        a[k] = R[j]
+        j += 1
+        k += 1
+
+
+# Driver code you can change it accordingly
+a = [12, 11, 13, 5, 6, 7]
+print("Before Sorting ")
+print(a)
+
+mergeSort(a)
+
+print("After Sorting ")
+print(a)

Arrays-Sorting/src/Radix_Sort/Radix_Sort.py

@@ -0,0 +1,52 @@
+#Made By SHASHANK CHAKRAWARTY
+"""
+CONSIDER THE BELOW SATEMENT:
+Let there be d digits in input integers.
+Radix Sort takes O(d*(n+b)) time where b is the base for representing numbers, for example, for decimal system, b is 10.
+What is the value of d? If k is the maximum possible value, then d would be O(logb(k)).
+So overall time complexity is O((n+b) * logb(k)).
+"""
+
+
+#here is your method for RADIX SORT
+def radixsort(array):
+  RADIX = 10
+  maxLength = False
+  temp , placement = -1, 1
+
+  while not maxLength:
+    maxLength = True
+    # declare and initialize buckets
+    buckets = [list() for i in range( RADIX )]
+
+    # split array between lists
+    for i in array:
+      temp = int((i / placement) % RADIX)
+      buckets[temp].append(i)
+
+ # Do counting sort for every digit. Note that instead
+    # of passing digit number, exp is passed. exp is 10^i
+    # where i is current digit number
+
+      if maxLength and temp > 0:
+        maxLength = False
+
+    # empty lists into lst array
+    a = 0
+    for b in range( RADIX ):
+      buck = buckets[b]
+      for i in buck:
+        array[a] = i
+        a += 1
+
+    # move to next
+    placement *= RADIX
+
+#driver code you can change the values accordingly
+array = [ 170, 45, 75, 90, 802, 24, 2, 66]
+radixsort(array)
+
+print("Sorted elements are:")
+for i in range(len(array)):
+
+    print(array[i],end=' ')

Arrays-Sorting/src/merge_sort/merge_sort.py

@@ -0,0 +1,57 @@
+#made by SHASHANK CHAKRAWARTY
+#The code demostrates step by step process of the merge sort how it splites, dividesin tothe 2 halves and then after getting sorted in the steps it gets merged
+
+#Merge Sort is a Divide and Conquer algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves.
+'''
+1)Time Complexity: Can be represented by Recurrance relation Time Complexity:T(n) = 2T(n/2) + \Theta(n)
+2)Time complexity of Merge Sort is \Theta(nLogn) in all 3 cases (worst, average and best) as merge sort always divides the array in two halves.
+3)Auxiliary Space: O(n)
+4)Algorithmic Paradigm: Divide and Conquer
+5)Sorting In Place: No in a typical implementation
+6)Stable: Yes
+'''
+
+def mergeSort(alist):
+    print("Splitting ",alist)
+    if len(alist)>1:
+#the array gets divided into the halves
+
+        mid = len(alist)//2
+
+#here the subarrays are created
+
+        lefthalf = alist[:mid]
+        righthalf = alist[mid:]
+
+#function calling occurs
+        mergeSort(lefthalf)
+        mergeSort(righthalf)
+
+        i=0
+        j=0
+        k=0
+        while i < len(lefthalf) and j < len(righthalf):
+            if lefthalf[i] < righthalf[j]:
+                alist[k]=lefthalf[i] #copy the value to the newly created array in the lefthalf
+                i=i+1
+            else:
+                alist[k]=righthalf[j] #copy the value to the newly created array in the righthalf
+                j=j+1
+            k=k+1
+#the process of merging goes from here
+        while i < len(lefthalf):  
+            alist[k]=lefthalf[i]
+            i=i+1
+            k=k+1
+
+        while j < len(righthalf):
+            alist[k]=righthalf[j]
+            j=j+1
+            k=k+1
+    print("Merging ",alist)
+#The DRIVER CODE,YOU CAN CHANGE THE VALUE ACCORDINGLY
+
+
+alist = [54,26,93,17,77,31,44,55,20]
+mergeSort(alist)
+print(alist)

Arrays-searching/src/fibonacci_search/Fibonacci_Search.py

@@ -0,0 +1,79 @@
+#Made by SHASHANK CHAKRAWARTY
+# Python3 program for Fibonacci search.
+'''
+Works for sorted arrays
+A Divide and Conquer Algorithm.
+Has Log n time complexity.
+
+1)Fibonacci Search divides given array in unequal parts
+
+'''
+
+#Given a sorted array arr[] of size n and an element x to be searched in it. Return index of x if it is present in array else return -1.
+
+def fibMonaccianSearch(arr, x, n):
+
+    # Initialize fibonacci numbers 
+
+    var2 = 0 # (m-2)'th Fibonacci No.
+    var1 = 1 # (m-1)'th Fibonacci No.
+    res = var2 + var1 # m'th Fibonacci
+
+
+    # fibM is going to store the smallest 
+    # Fibonacci Number greater than or equal to n 
+
+    while (res < n):
+        var2 = var1
+        var1 = res
+        res = var2 + var1
+
+    # Marks the eliminated range from front
+    offset = -1;
+
+    # while there are elements to be inspected.
+    # Note that we compare arr[var2] with x.
+    # When fibM becomes 1, var2 becomes 0 
+
+
+    while (res > 1):
+
+        # Check if var2 is a valid location
+        i = min(offset+var2, n-1)
+
+        # If x is greater than the value at 
+        # index var2, cut the subarray array 
+        # from offset to i 
+        if (arr[i] < x):
+            res = var1
+            var1 = var2
+            var2 = res - var1
+            offset = i
+
+         # If x is greater than the value at 
+        # index var2, cut the subarray 
+        # after i+1
+        elif (arr[i] > x):
+            res = var2
+            var1 = var1 - var2
+            var2 = res - var1
+
+        # element found. return index 
+        else :
+            return i
+
+    # comparing the last element with x */
+    if(var1 and arr[offset+1] == x):
+        return offset+1;
+
+    # element not found. return -1 
+    return -1
+
+# Driver Code, you can change the values accordingly
+arr = [10, 22, 35, 40, 45, 50,
+       80, 82, 85, 90, 100]
+n = len(arr)
+x = 85
+print("Found at index:",
+      fibMonaccianSearch(arr, x, n))
+

Image_Processing/src/Binary_Image.m

@@ -0,0 +1,43 @@
+%Binary Image by Master-Fury
+
+clear all;
+
+%Setting up the directory
+fpath1=fullfile('C:\Users\Manish (Master)\Desktop\images');  % Add your directory   
+addpath(fpath1);
+basefile=sprintf('*.png');                                   % Add format of image
+all_images=fullfile(fpath1,basefile);
+fnames=dir(all_images);
+
+
+% READING OF IMAGE 
+for i = 1:length(fnames)
+    all_images = fullfile(fnames(i).folder, fnames(i).name);
+    I = imread(all_images);  % Image reading using imread
+    figure
+    imshow(I)                  % To see original image
+    title('Original Image');
+    % The original image contains colors RGB (in matlab it stores in the format RBG)
+    % Conversion of image into gray-scale image can be done by removing any one color from image. 
+
+    Gray_Scale=I(:,:,2);           % Green color removed. 
+    figure
+    imshow(Gray_Scale)
+    title('Grey-Scale Version of Image')
+
+    % Conversion of GRAY-SCALE to BINARY IMAGE
+    Binary_Image = imbinarize(Gray_Scale,'adaptive','ForegroundPolarity','dark','Sensitivity',0.4); 
+    % You can use different methods like instead of adaptive you can use global(by default).
+    % Foreground Polarity can be dark or bright (refer documentaion for more info)
+    % Sensitivity can be from 0 to 1 , by default it is 0.5
+    figure
+    imshow(Binary_Image)
+    title('Binary Version of Image')
+end
+% SPECIAL NOTE
+% There is major difference between gray-scale image and binary image. The
+% differnce is - binary images consists only 0 & 1 (refer workspace) matrix
+% 1 represents white and 0 represents black. 
+% A binary image is a digital image that has only two possible values for each pixel.
+% In the case of gray scale image, 
+% for example 8-bit gray scale image (2^8=256) pixel value may vary between 0 to 256.

general_problems/armstrong.py → Mathematical_Algorithms/src/Armstrong_Number.py

@@ -1,5 +1,4 @@
-#by: shashank
-#armstrong number 
+# ARMSTRONG NUMBER BY SHASHANK
 
 num=int(input('Enter a Number:'))
 Sum=0
@@ -8,13 +7,13 @@
     digit=temp%10
     Sum+=digit**3
     temp//=10
-   # print(digit,temp,Sum)
+
 
 if (num == Sum):
-    print('armstrong')
+    print('Hurray! It is a Armstrong Number')
 
 else:
-    print('not armstrong')
+    print('Sorry! Try again, Its not a Armstrong Number')
 
 
 

Mathematical_Algorithms/src/GCD_Using_Euclid's_Algorithm_For_Array.py

@@ -0,0 +1,24 @@
+#GCD of an Array Using Euclidean Algo By Master-Fury
+
+def array_gcd(m,n):
+    if m<n:
+        (m,n)=(n,m)
+    if(m%n)==0:
+        return(n)
+    else:
+        return (gcd(n,m%n))
+
+#DRIVER CODE
+
+n= [2,4,6,8,16]               #Enter Your Numbers Here
+result=array_gcd(n[0],n[1])
+for i in range(2,len(n)):
+    result=array_gcd(result,n[i])
+print("GCD of given numbers is ",result)
+
+##DESCRIPTION
+##I have used Euclidean Algorithm to find GCD of two numbers which is a recursive method,
+##also I have made this for an array of numbers.
+##You can try also different methods like naive GCD and other.
+
+

Mathematical_Algorithms/src/Sieve_of_Eratosthenes.py

@@ -0,0 +1,27 @@
+#Sieve of Eratosthenes by Master-Fury
+
+def SieveOfEratosthenes(n):
+
+    prime = [True for i in range(n+1)]
+    p=2                                       
+    while (p * p <= n):
+        if(prime[p]== True):
+            for i in range (p*2,n+1,p):
+                prime[i]= False
+        p+=1
+    for p in range (2,n):
+        if prime[p]:
+            print (p)
+
+#DRIVER CODE
+n=10                         #ENTER THE NUMBER HERE!!
+print ("The following are the prime numbers smaller than or equal to ",n)
+SieveOfEratosthenes(n)
+
+
+##Description
+##Given a number n, print all primes smaller than or equal to n.
+##It is also given that n is a small number.
+##The sieve of Eratosthenes is one of the most efficient ways to find all
+##primes smaller than n when n is smaller than 10 million
+##Time complexity : O(sqrt(n)loglog(n))