Python | Get the smallest window in a string containing all characters of given pattern

Given two strings str and pattern, find the smallest substring in str containing all characters of pattern efficiently. Examples:

Input : str = 'geeksforgeeks' pattern = 'gks' 
Output : geeks

Input : str = 'new string' pattern = 'rg' 
Output : ring

Approach #1 : Using Python enumerate() This method uses Python enumerate(). need[k] store how many times we need character k and missing tells how many characters are still missing. In the loop, first add the new character to the window. Then, if nothing is missing, remove as much as possible from the window start and then update the result. 

Python3

string = 'new string'
pattern = 'rg'

# let's find the index of r and g in String and the
# store them in index list (index[])
index=[]
for x in range(len(pattern)):
    if pattern[x] in string:
        index.append(string.index(pattern[x]))

# sorting the r and g index's
index.sort()

# save first index in l
l = len(index)
low = int(index[0])

# save  last index in h
high = int(index[l-1])
h = high +1
for i in range(low,h):
    print(string[i],end=" ")

Output:

ksf

Approach #2 : Using collections.defaultdict() This method make use of two defaultdicts ‘src’ and ‘dest’. A defaultdict works exactly like a normal dict, but it is initialized with a function (“default factory”) that takes no arguments. source is empty while target consist of pattern elements as keys and the count of occurrence as value. In every iteration ‘i’, we check if the i^th element of str is present in target dictionary or not and update source dictionary accordingly. 

Python3

# Python3 code to Find the smallest
# window in a string containing all
# characters of another string
from collections import defaultdict
import sys
def min_window(str, pattern):

        # Function to check validity of source and
        # destination
        def isValid(i, j):
            for item in j:
                if item not in i or i[item] < j[item]:
                    return False
            return True

        source = defaultdict(int)
        target = defaultdict(int)

        # Target consist pattern elements and 1
        # as key:value pair
        for e in pattern:
            target[e] += 1

        # Minimum length for window
        minLen = sys.maxsize
        n = len(str)
        ans, j = '', 0
        for i in range(n):

            # Update source for valid source - target pair
            while j < n and (isValid(source, target) == False):
                source[str[j]] += 1
                j += 1

            # Checking validity of source-target pair
            if isValid(source, target):
                if minLen > j-i + 1:
                    minLen = j-i + 1
                    ans = str[i:j]
            source[str[i]] -= 1
        return ans

# Driver Code
string = "geekforgeeks"
pattern = "gks"
print(min_window(string, pattern))

Output:

geeks

Approach #3 : Dynamic approach In this method, we use a for loop and in every iteration, say i, we find the shortest interval that ends in i and includes all letters in the pattern. This can be done by taking two data structures in account i.e. ‘rpos’ and ‘rdict’. rpos is a sorted list of positions where rightmost positions of characters of pattern in str are kept and rdict is a dictionary mapping from a character to the position. values of rdict is same as rpos. 

Python3

# Python3 code to Find the smallest
# window in a string containing all
# characters of another string
from collections import Counter, defaultdict

def min_window(str, pattern):

    rdict, count = defaultdict(list), Counter(pattern)
    rpos, res = [], ""

    # Loop only over c exist in pattern
    for i, c in filter(lambda x: x[1] in pattern, enumerate(str)):
        if len(rdict) == count:

            # If reached limit, remove
            rpos.remove(rdict.pop(0))

        # Add to dict
        rdict[i].append(i)

        # Add to list
        rpos.append(i)

        if (len(rpos) == len(pattern) and
           (res =="" or rpos[-1]-rpos[0]<len(res))):
            res = str[rpos[0]:rpos[-1]+1]

    return res

# Driver Code
string = "geeksforgeeks"
pattern = "gks"
print(min_window(string, pattern))

Output:

geeks

Method#4: Using brute force

Approach

Iterate through all possible starting and ending indices of the window, check if the current window contains all characters of the pattern, and update the smallest window and smallest substring if the current window is smaller than the previous smallest window. Return the smallest substring.

Algorithm

1. Initialize the smallest window to be the length of the string and the smallest substring to be an empty string.
2. Iterate through all possible starting indices of the window, i.e., from 0 to (len(string)-len(pattern)).
3. For each starting index, iterate through all possible ending indices of the window, i.e., from (starting index + len(pattern)) to len(string).
4. Check if the current window contains all characters of the pattern.
5. If it does, update the smallest window and smallest substring if the current window is smaller than the previous smallest window.
6. Return the smallest substring.

Python3

def smallest_window(string, pattern):
    smallest_window_size = len(string)
    smallest_substring = ''
    for i in range(len(string) - len(pattern) + 1):
        for j in range(i + len(pattern), len(string) + 1):
            window = string[i:j]
            if all(char in window for char in pattern):
                if len(window) < smallest_window_size:
                    smallest_window_size = len(window)
                    smallest_substring = window
    return smallest_substring
string='geeksforgeeks'
pattern='gks'
print(smallest_window(string, pattern))

Output

geeks

Time Complexity: O(n^3) – where n is the length of the string. This is because we have three nested loops.
Space Complexity: O(1) – constant space is used.