Create newton_forward_interpolation.py (TheAlgorithms#333)

* Create newton_forward_interpolation.py

This code is for calculating newton forward difference interpolation for fixed difference.

* Add doctests and reformat with black

Author: jainanmol123

arithmetic_analysis/newton_forward_interpolation.py

@@ -0,0 +1,55 @@
+# https://www.geeksforgeeks.org/newton-forward-backward-interpolation/
+
+import math
+
+# for calculating u value
+def ucal(u, p):
+    """
+    >>> ucal(1, 2)
+    0
+    >>> ucal(1.1, 2)
+    0.11000000000000011
+    >>> ucal(1.2, 2)
+    0.23999999999999994
+    """
+    temp = u
+    for i in range(1, p):
+        temp = temp * (u - i)
+    return temp
+
+
+def main():
+    n = int(input("enter the numbers of values"))
+    y = []
+    for i in range(n):
+        y.append([])
+    for i in range(n):
+        for j in range(n):
+            y[i].append(j)
+            y[i][j] = 0
+
+    print("enter the values of parameters in a list")
+    x = list(map(int, input().split()))
+
+    print("enter the values of corresponding parameters")
+    for i in range(n):
+        y[i][0] = float(input())
+
+    value = int(input("enter the value to interpolate"))
+    u = (value - x[0]) / (x[1] - x[0])
+
+    # for calculating forward difference table
+
+    for i in range(1, n):
+        for j in range(n - i):
+            y[j][i] = y[j + 1][i - 1] - y[j][i - 1]
+
+    summ = y[0][0]
+    for i in range(1, n):
+        summ += (ucal(u, i) * y[0][i]) / math.factorial(i)
+
+    print("the value at {} is {}".format(value, summ))
+
+
+if __name__ == "__main__":
+    main()