Java 8 solution:

static int flatlandSpaceStations(int n, int[] c) {
        // Sort space station location in ascending order
        Arrays.sort(c);
        
        // Set max distance intially as the distance between city 0 to the first space station
        int maxDistance = c[0];
        
        // Calculate the max distance of the city between two space station
        for(int i = 1; i <c.length; i++){
            maxDistance = Math.max(maxDistance, (c[i] - c[i-1])/2);
        }
        
        // Calculate the distance between the last n city to the last space station
        maxDistance = Math.max(maxDistance, (n-1) - c[c.length-1]);
        
        return maxDistance;
    }

I tried the below solution which seemed to pass all the test cases. This solution sorts the input array and has a time complexity of O(nlog(n)). The algorithm used is somewhat related to the two-pointer algorithm.

static int flatlandSpaceStations(int n, int[] c) {

    if(c.length == n)
        return 0;

    int maxDist = Integer.MIN_VALUE;

    if(c.length == 1){
        for(int i=0; i < n; i++){
            maxDist = Math.max(calculateDistance(i, c[0]), maxDist);
        }    
    }else{
        int left = 0;
        int right = 1;
        int leftDist = 0;
        int rightDist = 0;
        Arrays.sort(c);
        for(int i=0; i < n; i++){
            leftDist = calculateDistance(i, c[left]);
            rightDist = calculateDistance(i, c[right]);

            if(leftDist > rightDist){
                maxDist = Math.max(rightDist, maxDist);
                if(right < c.length -1){
                    left++;
                    right++;    
                }

            }else{
                maxDist = Math.max(leftDist, maxDist);
            }
        }
    }

    return maxDist;


}

Is the custom comparator too much? Maybe. But it's funnier that way.

int flatlandSpaceStations(int n, vector<int> c) {
    int longuest = 0;
    
    for(int i = 0; i<n; i++ ){
        
        if(find(c.begin(), c.end(), i)==c.end()){
            int closest = *min_element(c.begin(),c.end(),
                            [&](int a, int b){
                                return abs(a - i) < abs(b - i);
                            });
            
            longuest = abs(closest-i)>longuest? abs(closest-i) : longuest;
        }
        
    }
    
    return longuest;
}

JAVA

static int flatlandSpaceStations(int n, int[] c) {

    ArrayList<Integer> arrayList = new ArrayList<>();
    for(int i=0;i<n;i++){
        int k=0;
        int res = Integer.MAX_VALUE;
        while(k<c.length){
            int res1 = c[k]-i;
            if(res1<0){
                res1 = 0-res1;
            }
            if(res>res1){
                res = res1;
            }
            k++;
        }
        arrayList.add(res);
    }
    int max = 0;
    for(int i =0;i<arrayList.size();i++){
        if(arrayList.get(i)>max){
            max = arrayList.get(i);
        }
    }
    return max;
}