Maximum Enemy Forts That Can Be Captured

Problem Description

You are given a 0-indexed integer array forts of length n representing the positions of several forts. forts[i] can be -1, 0, or 1 where:

• -1 represents there is no fort at the ith position.
• 0 indicates there is an enemy fort at the ith position.
• 1 indicates the fort at the ith position is under your command.

Now you have decided to move your army from one of your forts at position i to an empty position j such that:

• 0 <= i, j <= n - 1
• The army travels over enemy forts only. Formally, for all k where min(i,j) < k < max(i,j), forts[k] == 0.

While moving the army, all the enemy forts that come in the way are captured. Return the maximum number of enemy forts that can be captured. In case it is impossible to move your army, or you do not have any fort under your command, return 0.

Key Insights

• The problem requires identifying the maximum number of enemy forts (0s) that can be captured while moving from a friendly fort (1) to an empty position (-1).
• The solution involves iterating through the array and using two pointers to evaluate possible movements from each friendly fort.
• The movement can only occur over enemy forts, meaning we need to check the segments between friendly forts for enemy fort counts.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we will use a linear scan of the forts array. We will track the positions of friendly forts (where forts[i] == 1). For each friendly fort, we will check both directions (left and right) to count the number of enemy forts (where forts[j] == 0) that can be captured until we reach an empty position (where forts[k] == -1). We will maintain a maximum count of captured enemy forts during this process.

Code Solutions