feat: add binary search on answer template with example use case

Author: meenaksh06

searches/binary_search_on_answers.py

@@ -0,0 +1,66 @@
+from typing import Callable
+
+
+def binary_search_on_answer(
+    low: int, high: int, condition: Callable[[int], bool]
+) -> int:
+    """
+    Generic Binary Search on Answer template.
+
+    Finds the minimum value in the range [low, high] that satisfies the condition.
+
+    The condition function must be monotonic:
+    - False False False True True True
+
+    :param low: lower bound of search space
+    :param high: upper bound of search space
+    :param condition: function that returns True if mid is a valid answer
+
+    :return: smallest value that satisfies the condition
+
+    Examples:
+    >>> def condition(x): return x * x >= 16
+    >>> binary_search_on_answer(0, 10, condition)
+    4
+
+    >>> def condition(x): return x >= 7
+    >>> binary_search_on_answer(0, 10, condition)
+    7
+    """
+    answer = high
+
+    while low <= high:
+        mid = low + (high - low) // 2
+
+        if condition(mid):
+            answer = mid
+            high = mid - 1
+        else:
+            low = mid + 1
+
+    return answer
+
+
+# Example1: minimum capacity to ship
+
+def min_capacity_to_ship(weights: list[int], days: int) -> int:
+    """
+    Find minimum capacity to ship packages within given days.
+
+    >>> min_capacity_to_ship([1,2,3,4,5,6,7,8,9,10], 5)
+    15
+    """
+
+    def can_ship(capacity: int) -> bool:
+        days_used = 1
+        current = 0
+
+        for weight in weights:
+            if current + weight > capacity:
+                days_used += 1
+                current = 0
+            current += weight
+
+        return days_used <= days
+
+    return binary_search_on_answer(max(weights), sum(weights), can_ship)