feat(curriculum): add bisection method lab (#61253)

Co-authored-by: Hillary Nyakundi <63947040+larymak@users.noreply.github.com>

client/i18n/locales/english/intro.json

@@ -4420,8 +4420,10 @@
         ]
       },
       "lab-bisection-method": {
-        "title": "Build a Bisection Method",
-        "intro": [""]
+        "title": "Implement the Bisection Method",
+        "intro": [
+          "In this lab, you will implement the bisection method to find the square root of a number."
+        ]
       },
       "workshop-merge-sort": {
         "title": "Implement the Merge Sort Algorithm",

client/src/pages/learn/full-stack-developer/lab-bisection-method/index.md

@@ -0,0 +1,9 @@
+---
+title: Introduction to the Implement the Bisection Method
+block: lab-bisection-method
+superBlock: full-stack-developer
+---
+
+## Introduction to the Implement the Bisection Method
+
+In this lab, you will implement the bisection method to find the square root of a number.

curriculum/challenges/_meta/lab-bisection-method/meta.json

@@ -0,0 +1,11 @@
+{
+  "name": "Implement the Bisection Method",
+  "isUpcomingChange": true,
+  "dashedName": "lab-bisection-method",
+  "superBlock": "full-stack-developer",
+  "blockLayout": "link",
+  "blockType": "lab",
+  "helpCategory": "Python",
+  "challengeOrder": [{ "id": "686ccc2c8b967e17ab18d593", "title": "Implement the Bisection Method" }],
+  "usesMultifileEditor": true
+}

curriculum/challenges/english/25-front-end-development/lab-bisection-method/686ccc2c8b967e17ab18d593.md

@@ -0,0 +1,355 @@
+---
+id: 686ccc2c8b967e17ab18d593
+title: Implement the Bisection Method
+challengeType: 27
+dashedName: implement-the-bisection-method
+---
+
+# --description--
+
+The bisection method, also known as the binary search method, uses a binary search to find the roots of a real-valued function. It works by narrowing down an interval where the square root lies until it converges to a value within a specified tolerance.
+
+For example, if the tolerance is `0.01`, the bisection method will keep halving the interval until the difference between the upper and lower bounds is less than or equal to `0.01`.
+
+In this lab, you will implement a function that uses the bisection method to find the square root of a number.
+
+**Objective:** Fulfill the user stories below and get all the tests to pass to complete the lab.
+
+**User stories**
+
+1. You should define a function named `square_root_bisection` with three parameters:
+    - The number for which you want to find the square root.
+    - The tolerance being the acceptable error margin for the result. You should set a default tolerance value.
+    - The maximum number of iterations to perform. You should set a default number of iterations.
+
+1. The `square_root_bisection` function should:
+    - Raise a `ValueError` with the message `Square root of negative number is not defined in real numbers` if the number passed to the function is negative.
+    - For numbers `0` and `1`, print the message: `The square root of [number] is [number]` and return the number itself as the square root.
+    - For any other positive number, print the approximate square root with the message: `The square root of [square_target] is approximately [root]` and return the computed root value.
+    - If no value meets the tolerance condition, print a failure message: `Failed to converge within the [maximum] iterations` and return `None`.
+
+**Note**: You cannot import any module for this lab.
+
+# --hints--
+
+You should not import any module.
+
+```js
+({ test: () => assert(runPython(`len(_Node(_code).find_imports()) == 0`)) })
+```
+
+You should have a function named `square_root_bisection`.
+
+```js
+({ test: () => assert(runPython(`_Node(_code).has_function("square_root_bisection")`)) })
+```
+
+Your `square_root_bisection` function should have three parameters.
+
+```js
+({ test: () => runPython(`
+    import inspect 
+    sig = inspect.signature(square_root_bisection)
+    assert len(sig.parameters) == 3
+`) })
+```
+
+You should set a default value for the tolerance and the maximum number of iterations.
+
+```js
+({ test: () => runPython(`
+try:
+  import inspect 
+  sig = inspect.signature(square_root_bisection)
+  assert len(sig.parameters) == 3
+  square_root_bisection(4)
+except TypeError:
+  assert False
+`) })
+```
+
+Your `square_root_bisection` function should raise a `ValueError` with the message `Square root of negative number is not defined in real numbers` when the number passed to the function is negative.
+
+```js
+({ test: () => runPython(`
+try:
+  square_root_bisection(-6)
+except ValueError as e:
+  assert str(e) == "Square root of negative number is not defined in real numbers"
+else:
+  assert False
+`) })
+```
+
+`square_root_bisection(0)` should return `0`.
+
+```js
+({ test: () => runPython(`assert square_root_bisection(0) == 0`) })
+```
+
+`square_root_bisection(0)` should print `The square root of 0 is 0`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+square_root_bisection(0)
+assert "The square root of 0 is 0" in _out
+`) })
+```
+
+`square_root_bisection(0.001, 1e-7, 50)` should return a number between `0.03162267660168379` and `0.031622876601683794`.
+
+```js
+({ test: () => runPython(`assert 0.03162267660168379 <= square_root_bisection(0.001, 1e-7, 50) <= 0.031622876601683794`) })
+```
+
+`square_root_bisection(0.001, 1e-7, 50)` should print `The square root of 0.001 is approximately X`, where `X` is a number between `0.03162267660168379` and `0.031622876601683794`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+
+_root = square_root_bisection(0.001, 1e-7, 50)
+
+assert 0.03162267660168379 <= _root <= 0.031622876601683794
+assert f"The square root of 0.001 is approximately {_root}" in _out
+`) })
+```
+
+`square_root_bisection(0.25, 1e-7, 50)` should return a number between `0.4999999` and `0.5000001`.
+
+```js
+({ test: () => runPython(`assert 0.4999999 <= square_root_bisection(0.25, 1e-7, 50) <= 0.5000001`) })
+```
+
+`square_root_bisection(0.25, 1e-7, 50)` should print `The square root of 0.25 is approximately X`, where `X` is a number between `0.4999999` and `0.5000001`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+
+_root = square_root_bisection(0.25, 1e-7, 50)
+
+assert 0.4999999 <= _root <= 0.5000001
+assert f"The square root of 0.25 is approximately {_root}" in _out
+`) })
+```
+
+`square_root_bisection(1)` should return `1`.
+
+```js
+({ test: () => runPython(`assert square_root_bisection(1) == 1`) })
+```
+
+`square_root_bisection(1)` should print `The square root of 1 is 1`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+square_root_bisection(1)
+assert "The square root of 1 is 1" in _out
+`) })
+```
+
+`square_root_bisection(81, 1e-3, 50)` should return a number between `8.999` and `9.001`.
+
+```js
+({ test: () => runPython(`assert 8.999 <= square_root_bisection(81, 1e-3, 50) <= 9.001`) })
+```
+
+`square_root_bisection(81, 1e-3, 50)` should print `The square root of 81 is approximately X`, where `X` is a number between `8.999` and `9.001`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+
+_root = square_root_bisection(81, 1e-3, 50)
+
+assert 8.999 <= _root <= 9.001
+assert f"The square root of 81 is approximately {_root}" in _out
+`) })
+```
+
+`square_root_bisection(225, 1e-3, 100)` should return a number between `14.999` and `15.001`.
+
+```js
+({ test: () => runPython(`assert 14.999 <= square_root_bisection(225, 1e-3, 100) <= 15.001`) })
+```
+
+`square_root_bisection(225, 1e-3, 100)` should print `The square root of 225 is approximately X`, where `X` is a number between `14.999` and `15.001`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+
+_root = square_root_bisection(225, 1e-3, 100)
+
+assert 14.999 <= _root <= 15.001
+assert f"The square root of 225 is approximately {_root}" in _out
+`) })
+```
+
+`square_root_bisection(225, 1e-5, 100)` should return a number between `14.99999` and `15.00001`.
+
+```js
+({ test: () => runPython(`assert 14.99999 <= square_root_bisection(225, 1e-5, 100) <= 15.00001`) })
+```
+
+`square_root_bisection(225, 1e-5, 100)` should print `The square root of 225 is approximately X`, where `X` is a number between `14.99999` and `15.00001`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+
+_root = square_root_bisection(225, 1e-5, 100)
+
+assert 14.99999 <= _root <= 15.00001
+assert f"The square root of 225 is approximately {_root}" in _out
+`) })
+```
+
+`square_root_bisection(225, 1e-7, 100)` should return a number between `14.9999999` and `15.0000001`.
+
+```js
+({ test: () => runPython(`assert 14.9999999 <= square_root_bisection(225, 1e-7, 100) <= 15.0000001`) })
+```
+
+`square_root_bisection(225, 1e-7, 100)` should print `The square root of 225 is approximately X`, where `X` is a number between `14.9999999` and `15.0000001`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+
+_root = square_root_bisection(225, 1e-7, 100)
+
+assert 14.9999999 <= _root <= 15.0000001
+assert f"The square root of 225 is approximately {_root}" in _out
+`) })
+```
+
+`square_root_bisection(225, 1e-7, 10)` should return `None`.
+
+```js
+({ test: () => runPython(`assert square_root_bisection(225, 1e-7, 10) is None`) })
+```
+
+`square_root_bisection(225, 1e-7, 10)` should print `Failed to converge within 10 iterations`.
+
+```js
+({ test: () => runPython(`
+built_in_print = print
+_out = []
+
+def custom_print(*args, **kwargs):
+  call_args = [arg for arg in args]
+  _out.extend(call_args)
+
+print = custom_print
+square_root_bisection(225, 1e-7, 10)
+assert "Failed to converge within 10 iterations" in _out
+`) })
+```
+
+# --seed--
+
+## --seed-contents--
+
+```py
+
+```
+
+# --solutions--
+
+```py
+def square_root_bisection(square_target, tolerance=1e-7, max_iterations=100):
+    if square_target < 0:
+        raise ValueError('Square root of negative number is not defined in real numbers')
+    if square_target == 1:
+        root = 1
+        print(f'The square root of {square_target} is 1')
+    elif square_target == 0:
+        root = 0
+        print(f'The square root of {square_target} is 0')
+
+    else:
+        low = square_target if square_target < 1 else 1
+        high = 1 if square_target < 1 else square_target
+        root = None
+
+        for _ in range(max_iterations):
+            mid = (low + high) / 2
+            square_mid = mid**2
+
+            if high - low <= tolerance:
+                root = mid
+                break
+
+            elif square_mid < square_target:
+                low = mid
+            else:
+                high = mid
+
+        if root is None:
+            print(f"Failed to converge within {max_iterations} iterations")
+
+        else:   
+            print(f'The square root of {square_target} is approximately {root}')
+
+    return root
+```