Maximize Distance.md

Maximize Distance.md

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+## Maximize Distance to Closest Person
+
+Given an array representing a row of seats where `seats[i] = 1` represents a person sitting in the `i`th seat, and `seats[i] = 0` represents that the `i`th seat is empty (0-indexed).
+
+### Problem Statement
+
+Alex wants to sit in the seat such that the distance between him and the closest person to him is maximized.
+
+### Solution
+
+To maximize the distance to the closest person in a row of seats, you can use the following Python function:
+
+```python
+def maxDistToClosest(seats):
+    max_distance = 0
+    prev_person_index = -1
+
+    for i, seat in enumerate(seats):
+        if seat == 1:
+            if prev_person_index == -1:
+                # If the first person is sitting at seat 0
+                max_distance = i
+            else:
+                # Calculate distance between two people
+                max_distance = max(max_distance, (i - prev_person_index) // 2)
+            prev_person_index = i
+
+    # Calculate distance from the last person to the last empty seat
+    max_distance = max(max_distance, len(seats) - 1 - prev_person_index)
+
+    return max_distance
+
+# Example usage:
+seats = [1, 0, 0, 0, 1, 0, 1]
+result = maxDistToClosest(seats)
+print(result)  # Output: 2
+```
+This code iterates through the seats, **keeping track of the previous person's index** and **calculating the maximum distance between two people** or between a person and an empty seat. **It returns the maximum distance to the closest person**.
+