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Author: CodewithAsh10

Long_division_method.py

@@ -0,0 +1,65 @@
+INFINITY_ = 99999999
+
+def sqrtByLongDivision(n, decimal_places=5):
+    if n < 0:
+        raise ValueError("Cannot compute square root of negative numbers.")
+    
+    # Preparing for long division
+    i = 0
+    a = []
+    
+    # Dividing the number into segments of two digits
+    while n > 0:
+        a.append(n % 100)  # Extracting two digits (a segment)
+        n //= 100          # Moving to the next two digits
+        i += 1
+
+    a.reverse()  # Reverse to start from the most significant segment
+
+    cur_quotient = 0.0
+    cur_divisor = 0.0
+    cur_dividend = 0.0
+    cur_remainder = 0.0
+
+    # Start long division from the first segment
+    for j in range(i):
+        # Include the next segment in the current dividend
+        cur_dividend = cur_dividend * 100 + a[j]
+        cur_remainder = INFINITY_
+
+        # Loop to find the largest udigit
+        for udigit in range(10):
+            # Check if the current divisor and udigit fit
+            if (cur_remainder >= cur_dividend - ((cur_divisor * 10 + udigit) * udigit) and 
+                cur_dividend - ((cur_divisor * 10 + udigit) * udigit) >= 0):
+                cur_remainder = cur_dividend - ((cur_divisor * 10 + udigit) * udigit)
+                quotient_units_digit = udigit
+
+        # Update the quotient and divisor
+        cur_quotient = cur_quotient * 10 + quotient_units_digit
+        cur_divisor = cur_quotient * 2
+        cur_dividend = cur_remainder
+
+    # Calculate decimal places
+    for _ in range(decimal_places):
+        cur_dividend *= 100  # Shift the remainder for decimal place calculation
+        cur_remainder = INFINITY_
+
+        for udigit in range(10):
+            if (cur_remainder >= cur_dividend - ((cur_divisor * 10 + udigit) * udigit) and 
+                cur_dividend - ((cur_divisor * 10 + udigit) * udigit) >= 0):
+                cur_remainder = cur_dividend - ((cur_divisor * 10 + udigit) * udigit)
+                quotient_units_digit = udigit
+
+        cur_quotient = cur_quotient * 10 + quotient_units_digit
+        cur_divisor = cur_quotient * 2
+        cur_dividend = cur_remainder
+
+    # Return the square root as a float
+    return cur_quotient / (10 ** decimal_places)
+
+# Driver code
+x = int(input("Enter the Number: "))
+print(sqrtByLongDivision(x))  # Output: square root of 11 as float
+
+