Question

A string made of an even number of characters ("<" and/or ">") is called symmetric if all characters in its first half are "<" and all characters in its second half are ">".

Examples of symmetric strings are: "" (empty string), "<>", "<<>>", "<<<>>>", etc.
Write a function:
function solution(S);
that, given a string S made of N characters ("<", ">" and/or "?")", returns the length of the longest symmetric substring that can be obtained after replacing question marks with "<" or ">" characters.
Examples:
1. For S ="<><??>>", after replacing all question marks with "<", the string "<><<<>>" is obtained. Its longest symmetric substring is "<<>>", so the function should return 4.
2. For S = "??????", the optimal option is to replace the first three question marks with "<" and the next three question marks with ">" thus obtaining the string "<<<>>>". The function should return 6.
3. For S ="<<?", the function should return 2.
Write an efficient algorithm for the following assumptions:
- the length of string S is within the range [1..200,000];
- string S is made only of the following characters: '<', '>' and/or '?'

Answer 1

The solution involves creating a function that processes the input string with '<', '>', and '?' characters to find and return the length of the longest symmetric substring by replacing '?' with the optimal character to maximize symmetry.

Step-by-step explanation:

To solve the problem of finding the longest symmetric substring after replacing '?' characters, we need to write a function solution(S). The main goal of this function is to iterate over the input string S, count the maximum number of '<' and '>' characters that can form a symmetric substring, and replace '?' with the appropriate character to maximize the length of the symmetric substring.

Algorithm to Solve the Problem:

• Initialize two pointers, one at the start and one at the end of the string.

• While both pointers have not met, move them towards each other, increasing the count of '<' when possible, or decreasing the count of '>', creating symmetrical pairs.

• Every time a '?' is encountered, decide whether it should be a '<' or a '>' to maximize symmetry. Treat non-matching pairs as if a '?' could potentially correct them.

• Maintain a record of the maximum length of a symmetric substring found thus far.

• Continue this process until the pointers meet or cross over, implying we've checked the whole string.

• The record maintained in step 4 is our final answer, the length of the longest symmetric string possible.

Let's consider the provided examples for clarity:

1. For S = "<>>", replace '?' with '<' and then '>', yielding "<<>>" as the longest symmetric substring with the length of 4.
2. For S = "??????", we can split the sequence of '?'s into half '<' and half '>', resulting in "<<<>>>" with the longest symmetric substring length of 6.
3. For S = "<2.

By following this method, we will be able to create an efficient algorithm even for strings with lengths up to 200,000 characters.

Answer 2

Below is a Python algorithm to know the length of the longest symmetric substring that can be obtained after replacing question marks with "<" or ">" characters:

def solution(S):

# Initialize variables

max_len = 0

left = 0

right = 0

open_count = 0

close_count = 0

# Iterate through the string S

for i in range(len(S)):

# Check for question marks

if S[i] == "?":

open_count += 1 # Increment open count if encountering a '?'

close_count += 1 # Increment close count as well

# Check for '<'

elif S[i] == "<":

# If open count is more than close count, update the range

if open_count > close_count:

while (left < i) and (S[left] == "?"):

open_count -= 1 # Decrement open count for each '<'

close_count -= 1 # Decrement close count for each '?'

left += 1

# Check for '>'

elif S[i] == ">":

# If close count is more than open count, update the range

if close_count > open_count:

while (right < i) and (S[right] == "?"):

open_count -= 1 # Decrement open count for each '<'

close_count -= 1 # Decrement close count for each '?'

right += 1

# Calculate the length of the symmetric substring

sym_len = min(open_count, close_count) * 2 + 1

# Update the maximum length

max_len = max(max_len, sym_len)

return max_len

So, the above algorithm is one that helps to know the longest symmetric substring by maintaining two counters for open and close parentheses, keeping track of the current range and updating the maximum length when a valid symmetric substring is encountered.

See full text below

A string made of an even number of characters ("<" and/or ">") is called symmetric if all characters in its first half are "<" and all characters in its second half are ">".

Examples of symmetric strings are: "" (empty string), "<>", "<<>>", "<<<>>>", etc.

Write a function:

function solution(S);

that, given a string S made of N characters ("<", ">" and/or "?")", returns the length of the longest symmetric substring that can be obtained after replacing question marks with "<" or ">" characters.

Examples:

1. For S ="<><??>>", after replacing all question marks with "<", the string "<><<<>>" is obtained. Its longest symmetric substring is "<<>>", so the function should return 4.

2. For S = "??????", the optimal option is to replace the first three question marks with "<" and the next three question marks with ">" thus obtaining the string "<<<>>>". The function should return 6.

3. For S ="<<?", the function should return 2.

Write an efficient algorithm for the following assumptions:

- the length of string S is within the range [1..200,000];

- string S is made only of the following characters: '<', '>' and/or '?'.