Merge 455749a9eb839eb836cfe63478eb43cf0f83340c into 338cbafe0d5b07d57f83060ea0f9ba3a6c1155e7

* Fix And Add power.py

To fix the inaccuracies and allow handling of negative exponents and bases, the key issue lies in how negative numbers are handled in the power calculation, especially when dividing.
## Example Output:
```python
>>> power(4, 6)
4096
>>> power(2, 3)
8
>>> power(-2, 3)
-8
>>> power(2, -3)
0.125
>>> power(-2, -3)
-0.125
```

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update power.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update power.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update power.py

* [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci

* Update power.py

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Maxim Smolskiy <mithridatus@mail.ru>

divide_and_conquer/power.py

@@ -1,4 +1,4 @@
-def actual_power(a: int, b: int):
+def actual_power(a: int, b: int) -> int:
     """
     Function using divide and conquer to calculate a^b.
     It only works for integer a,b.
@@ -19,10 +19,12 @@ def actual_power(a: int, b: int):
     """
     if b == 0:
         return 1
+    half = actual_power(a, b // 2)
+
     if (b % 2) == 0:
-        return actual_power(a, int(b / 2)) * actual_power(a, int(b / 2))
+        return half * half
     else:
-        return a * actual_power(a, int(b / 2)) * actual_power(a, int(b / 2))
+        return a * half * half
 
 
 def power(a: int, b: int) -> float:
@@ -43,9 +45,9 @@ def power(a: int, b: int) -> float:
     -0.125
     """
     if b < 0:
-        return 1 / actual_power(a, b)
+        return 1 / actual_power(a, -b)
     return actual_power(a, b)
 
 
 if __name__ == "__main__":
-    print(power(-2, -3))
+    print(power(-2, -3))  # output -0.125

dynamic_programming/brige_torch_problem.py

@@ -0,0 +1,30 @@
+person_pace = [1, 2, 5, 10, 12, 16]
+person_pace.sort()  # Sort the array for optimal pairing
+people = len(person_pace)
+
+# Base cases
+if people == 1:
+    print("Min Time to Cross is:", person_pace[0])
+elif people == 2:
+    print("Min Time to Cross is:", person_pace[1])
+else:
+    total_time = 0
+    while people > 3:
+        # Strategy 1: Send the two fastest first, then the fastest returns
+        option1 = person_pace[1] + person_pace[0] + person_pace[-1] + person_pace[1]
+        # Strategy 2: Send the two slowest, then the fastest returns
+        option2 = person_pace[-1] + person_pace[0] + person_pace[-2] + person_pace[0]
+
+        # Choose the minimum of the two strategies
+        total_time += min(option1, option2)
+
+        # Remove the two slowest people who have crossed
+        person_pace = person_pace[:-2]
+
+    # Handle the last 2 or 3 people
+    if len(person_pace) == 3:
+        total_time += person_pace[2] + person_pace[0] + person_pace[1]
+    elif len(person_pace) == 2:
+        total_time += person_pace[1]
+
+    print("Min Time to Cross is:", total_time)