Find maximum deviation of all substrings

Question

Given a string, find the maximum deviation among all substrings. The maximum deviation is defined as the difference between the maximum frequency of a character and the minimum frequency of a character.

For example, in abcaba , a has a frequency of 3; b has a frequency of 2; c has a frequency of 1. so a has the maximum frequency, which is 3, whereas c has a minimum frequency of 1. Therefore the deviation of this string is 3 - 1 = 2 . And we also need to find all other deviations for each of the substrings for abacaba , the maximum among them is the answer.

I couldn't think of a better way rather than the obvious brute force approach. Thanks in advance!

Answer 1

For finding all substrings you have to consider O(n ² ). See this post for more details. You can just optimize it by stop point where substring lengths be smaller than current maximum deviation.

maxDeviation = 0;
n = strlen(str);
for i = 0 to n
{
  if(n-i < maxDeviation) break; //this is new stop point to improve 
  sub1 = substring(str,i,n);
  sub2 = substring(str,0,n-i); // you can use if(i!=0) to avoid duplication of first sentence 
  a = findMaxDeviation(sub1); // This is O(n)
  b = findMaxDeviation(sub2); // This is O(n)
  maxDeviation = max(a,b);
} 
print maxDeviation 

Pay attention to this line if(ni < maxDeviation) break; because you cannot find a deviation more than maxDeviation in a string with length of smaller than maxDeviation .

Answer 2

@Majid Hajibaba, in your solution, shouldn't it be if(ni < maxDeviation) continue; instead of if(ni < maxDeviation) break;

Answer 3

    public static int getDev(Map<String, Integer> devEntries){
        List<Integer> entries = devEntries.entrySet().stream()
                .map(x->x.getValue())
                .collect(Collectors.toList());
        Comparator<Integer> collect = Comparator.naturalOrder();
        Collections.sort(entries,collect.reversed());
        return entries.get(0) - entries.get( entries.size()-1);
    }
    public static int getMaxFreqDeviation(String s, Set<Integer> deviations ) {
        for (int x=0;x<s.length();x++) {
            for (int g=x;g<s.length()+1;g++){
                String su =s.substring(x,g);
                Map<String, Integer> map = Arrays.asList(su.split(""))
                        .stream()
                        .collect(Collectors.groupingBy(v->v,Collectors.summingInt(v->1)));
                if (map.entrySet().size()==1){
                    deviations.add(abs(0));
                }else {
                    int devcount = getDev(map);
                    deviations.add(abs(devcount));
                }
            }

        }
        return deviations.stream().collect(Collectors.toList()).get(deviations.size()-1);
    }

    public static void main(String[] args){
         String se = "abcaba";
        Set<Integer> deviations = new TreeSet<>();
        int ans = getMaxFreqDeviation(se,deviations);
        System.out.println(ans);
    }
}

Answer 4

I faced a similar question in a test and I used c#, although I failed during the challenge but picked it up to solve the next day. I came about something like the below.

var holdDict = new Dictionary<char, int>(); var sArray = s.ToCharArray();

var currentCharCount = 1;

//Add the first element
holdDict.Add(sArray[0],1);

for (int i = 1; i < s.Length-1; i++)
{
    if (sArray[i] == sArray[i - 1])
    {
        currentCharCount += 1;
    }
    else
    {
        currentCharCount = 1;
    }
    holdDict.TryGetValue(sArray[i], out var keyValue);

    if (keyValue < currentCharCount) holdDict[sArray[i]] = currentCharCount;

}

var myQueue = new PriorityQueue<string, int>();
foreach (var rec in holdDict)
{
    myQueue.Enqueue($"{rec.Key}#{rec.Value}", rec.Value);
}

int highest = 0, lowest = 0, queueCount=myQueue.Count;
while (myQueue.Count > 0)
{
    int currentValue = int.Parse(myQueue.Peek().Split('#')[1]);

    if (myQueue.Count == queueCount) lowest = currentValue;

    highest = currentValue;
    myQueue.Dequeue();
}

return highest - lowest;

Answer 5

O(n) algo (26*26*N)

import string

def maxSubarray(s, ch1, ch2):
    """Find the largest sum of any contiguous subarray."""
    """From https://en.wikipedia.org/wiki/Maximum_subarray_problem"""
    best_sum = 0
    current_sum = 0
    for x in s:
        if x == ch1:
            x = 1
        elif x == ch2:
            x = -1
        else:
            x = 0
        current_sum = max(0, current_sum + x)
        best_sum = max(best_sum, current_sum)
    return best_sum

def findMaxDiv(s):
    '''Algo from https://discuss.codechef.com/t/help-coding-strings/99427/4'''
    maxDiv = 0
    for ch1 in string.ascii_lowercase:
        for ch2 in string.ascii_lowercase:
            if ch1 == ch2:
                continue

            curDiv = maxSubarray(s, ch1, ch2)
            if curDiv > maxDiv:
                maxDiv = curDiv

    return maxDiv