Teaching Kids Programming: Videos on Data Structures and Algorithms
Given function 
Compute the Square Root by using Binary Search Algorithm
Since the function is monotone increasing, we can use the binary search algorithm to find the value which is closest or equal to the square root.
The left boundary is zero. If the x is between 0 and 1, we can set the upperbound to 1 and if the x is greater than 1, we can set the upperbound to x and lowerbound to 1.
Within this range [0, upper], we can do the binary search and continue until the result difference is no more than e.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | def Sqrt(x, e = 1e-5): if x < 0: return None if x < 1: left, right = 0, 1 else: left, right = 1, x mid, cur = 0, 0 while abs(cur - x) > e: mid = (left + right) / 2 cur = mid * mid if cur > x: right = mid else: left = mid return mid |
def Sqrt(x, e = 1e-5):
if x < 0:
return None
if x < 1:
left, right = 0, 1
else:
left, right = 1, x
mid, cur = 0, 0
while abs(cur - x) > e:
mid = (left + right) / 2
cur = mid * mid
if cur > x:
right = mid
else:
left = mid
return mid1 2 | for i in range(10): print("Sqrt " + str(i) + " = " + str(Sqrt(i))) |
for i in range(10):
print("Sqrt " + str(i) + " = " + str(Sqrt(i)))1 2 3 4 5 6 7 8 9 10 | Sqrt 0 = 0 Sqrt 1 = 1 Sqrt 2 = 1.414215087890625 Sqrt 3 = 1.7320518493652344 Sqrt 4 = 2.0 Sqrt 5 = 2.2360658645629883 Sqrt 6 = 2.449490547180176 Sqrt 7 = 2.645751476287842 Sqrt 8 = 2.8284263610839844 Sqrt 9 = 3.0000014305114746 |
Sqrt 0 = 0 Sqrt 1 = 1 Sqrt 2 = 1.414215087890625 Sqrt 3 = 1.7320518493652344 Sqrt 4 = 2.0 Sqrt 5 = 2.2360658645629883 Sqrt 6 = 2.449490547180176 Sqrt 7 = 2.645751476287842 Sqrt 8 = 2.8284263610839844 Sqrt 9 = 3.0000014305114746
And the square root below 1:
1 2 3 4 5 6 | Sqrt(0.1234)**2 # 0.12340314779430628 Sqrt(0.9)**2 # 0.9000026455614716 # Sqrt(0.5)**2 0.500001078704372 |
Sqrt(0.1234)**2 # 0.12340314779430628 Sqrt(0.9)**2 # 0.9000026455614716 # Sqrt(0.5)**2 0.500001078704372
–EOF (The Ultimate Computing & Technology Blog) —
Last Post: List Calculator Algorithm
Next Post: Algorithms to Sum using Distinct Positive Factorial Numbers