Merge pull request AllAlgorithms#59 from bhuvanakundumani/master

abranhe · web-flow · commit c1deadcad58e · 2018-10-25T09:12:04.000-04:00
Added the magic square algorithm
diff --git a/math/magic_square.py b/math/magic_square.py
@@ -0,0 +1,42 @@
+
+
+
+"""A magic square is an N×N grid of numbers in which the entries in each row, column and main diagonal sum to the same number (equal to N(N2+1)/2)"""
+
+
+import numpy as np
+
+
+print("Hi! Welcome to the magic square algorithm")
+print("Please enter the number for which you would want a magic sqaure to be printed. Please enter an odd number")
+
+# The odd number for which the magic square is created is stored in the variable N
+
+N  = int(input())
+
+# create a matrix with values 0 using numpy. The datatype is int for the elements in the matrix
+magic_square = np.zeros((N,N), dtype=int)
+
+n = 1
+i, j = 0, N//2
+
+# n iterates from 1 to N**2. The loop exits when n is equal to N**2
+
+while n <= N**2:
+    # Start in the middle of the first row.
+    # (i = 0 and j = N//2 ) and the element at magic_square[i,j] is the middle in the first row.
+    # insert n = 1 to begin with at magic_square[i,j]
+    magic_square[i, j] = n
+    # increment n by 1
+    n += 1
+    # Move diagonally up and right, wrapping to the first column or last row if the move leads outside the grid
+
+    new_i, new_j = (i-1) % N, (j+1)% N
+
+    # if the cell is already filled with a number, move vertically down one space.
+    if magic_square[new_i, new_j]:
+        i += 1
+    else:
+        i, j = new_i, new_j
+
+print(magic_square)
diff --git a/math/pascals_triangle.py b/math/pascals_triangle.py
@@ -0,0 +1,26 @@
+
+"""
+Pascal's triangle is a triangular array of numbers in which those at the ends of the rows are 1 and each of the others is the sum of the nearest two numbers in the row above (the apex, 1, being at the top).
+    
+"""
+print("Welcome to Pascal's traingle:")
+
+
+n=int(input("Enter number of rows for the pascal's traingle: "))
+a=[]
+for i in range(n):
+    a.append([])
+    a[i].append(1)
+    for j in range(1,i):
+        a[i].append(a[i-1][j-1]+a[i-1][j])
+    if(n!=0):
+        a[i].append(1)
+		
+		
+# printing pascal's triangle
+print( " Your Pascal's traiange for the number {}".format(n))
+for i in range(n):
+    print("   "*(n-i),end=" ",sep=" ")
+    for j in range(0,i+1):
+        print('{0:6}'.format(a[i][j]),end=" ",sep=" ")
+    print()
