You are given a binary string s
of length n
and an integer numOps
. You are allowed to perform the following operation on s
at most numOps
times:
i
(where 0 <= i < n
) and flip s[i]
. If s[i] == '1'
, change s[i]
to '0'
and vice versa.You need to minimize the length of the longest substring of s
such that all the characters in the substring are identical.
Return the minimum length after the operations.
Example 1:
s = "000001", numOps = 1
Output: 2
Explanation: By changing s[2]
to '1'
, s
becomes "001001"
. The longest substrings with identical characters are s[0..1]
and s[3..4]
.
Example 2:
s = "0000", numOps = 2
Output: 1
Explanation: By changing s[0]
and s[2]
to '1'
, s
becomes "1010"
.
Example 3:
s = "0101", numOps = 0
Output: 1
Constraints:
1 <= n == s.length <= 1000
s
consists only of '0'
and '1'
.0 <= numOps <= n
When you get asked this question in a real-life environment, it will often be ambiguous (especially at FAANG). Make sure to ask these questions in that case:
The brute force approach to finding the smallest substring with identical characters involves examining every possible substring. We achieve this by systematically checking each potential substring and verifying if it meets the problem's conditions. This exhaustive search guarantees we'll find the shortest valid substring.
Here's how the algorithm would work step-by-step:
def find_smallest_substring_brute_force(input_string):
string_length = len(input_string)
smallest_substring_length = float('inf')
# Iterate through all possible substring lengths
for substring_length in range(1, string_length + 1):
# Iterate through all possible starting positions for each substring length
for start_index in range(string_length - substring_length + 1):
substring = input_string[start_index:start_index + substring_length]
# Check if all characters in the substring are identical
if len(set(substring)) == 1:
#Update the smallest substring length if a shorter one is found
smallest_substring_length = substring_length
break
if smallest_substring_length != float('inf'):
break
if smallest_substring_length == float('inf'):
return 0
else:
return smallest_substring_length
To find the shortest segment with all identical characters, we don't need to check every possible segment. Instead, we can cleverly jump from one possible solution to another, quickly narrowing down the possibilities until we find the absolute shortest one.
Here's how the algorithm would work step-by-step:
def find_shortest_segment(input_string):
string_length = len(input_string)
if string_length < 3:
return string_length
shortest_length = float('inf')
# Check for initial consecutive identical characters.
for i in range(string_length - 2):
if input_string[i] == input_string[i+1] == input_string[i+2]:
shortest_length = 3
break
for i in range(string_length - 1):
if input_string[i] == input_string[i+1]:
# Found a pair, find the entire run length.
current_length = 2
start_index = i
while i + current_length < string_length and input_string[start_index] == input_string[i + current_length]:
current_length += 1
# Update shortest length if needed.
if current_length < shortest_length:
shortest_length = current_length
if shortest_length == float('inf'):
return -1
else:
return shortest_length
Case | How to Handle |
---|---|
Null or empty input string | Return 0 (or appropriate sentinel value indicating no substring found) immediately, preventing null pointer exceptions or invalid operations. |
Input string with only one character | Return 1, as a single character is a substring with identical characters. |
Input string with all identical characters | Return 1, as any single character substring is the smallest. |
Input string with length approaching maximum allowed string length | Ensure the algorithm has a time complexity that can handle large strings (e.g., O(n) or O(n log n)). |
String contains Unicode or other non-ASCII characters | Ensure the character comparison and storage mechanisms (e.g., hash maps) correctly handle Unicode characters. |
No substring with identical characters exists (e.g., 'abc') | Return 0, indicating that no valid substring exists. |
String contains only whitespace characters | Treat whitespace as any other character and find smallest substring of identical whitespace characters, returning 1 if it exists, 0 otherwise. |
Integer overflow in length calculations (if applicable) | Use appropriate data types (e.g., long instead of int) to prevent integer overflows when calculating substring lengths. |