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Question 1: Lexicographically Smallest String

Problem Statement:

Two strings are given, word and substr. Some of the characters in word are question marks (?). Find the lexicographically smallest string that can be obtained by replacing ? characters such that substr appears at least once. If it is not possible to do so, return "-1".

Thought Process:

1. Sliding Window Approach: Iterate over all possible starting positions in word where substr could fit. Replace the question marks (?) accordingly to match the substr.
2. Replacement Strategy: For positions that don't match substr, replace remaining ? with the lexicographically smallest letter, which is 'a'.
3. Lexicographical Order: Track the minimum lexicographical string found. If no valid replacement exists, return -1.

Solution Steps:

1. Iterate through all possible positions where substr could be inserted in word.
2. For each position, check if substr can be placed by replacing ?.
3. If possible, replace the remaining ? with 'a' to minimize the lexicographical order.
4. Return the smallest lexicographically valid string.

Sample Code:

def getSmallestString(word, substr):
    n, m = len(word), len(substr)

    def is_valid(pos):
        # Check if we can place substr at position pos
        for i in range(m):
            if word[pos + i] != '?' and word[pos + i] != substr[i]:
                return False
        return True

    def form_string(pos):
        # Form the resulting string by replacing `?`
        new_word = list(word)
        for i in range(m):
            new_word[pos + i] = substr[i]
        return ''.join(c if c != '?' else 'a' for c in new_word)

    result = None

    for i in range(n - m + 1):
        if is_valid(i):
            candidate = form_string(i)
            if result is None or candidate < result:
                result = candidate

    return result if result else "-1"

# Example usage:
word = "as?b?e?gf"
substr = "dbk"
print(getSmallestString(word, substr))  # Output: "asdbkeagf"

---

Question 2: Minimum Operations to Make Array Equal

Problem Statement:

You are given an array of integers. In one operation, you can flip any bit of any element in the array. The goal is to make all the integers in the array equal with the minimum number of operations.

Thought Process:

1. Binary Representation: Focus on the binary representation of the numbers. The number of operations required depends on flipping the bits of the numbers to match a target.
2. Bitwise Manipulation: For each number, we can flip specific bits to make it equal to other numbers in the array.
3. Flipping Strategy: For each element, determine the number of flips required to match the most common bit pattern.

Solution Steps:

1. Convert the numbers to binary and analyze their bit patterns.
2. Determine how many operations (flips) are required to make all numbers the same.
3. Count and return the minimum number of operations.

Sample Code:

def getMinOperations(arr):
    n = len(arr)
    if n == 0:
        return 0

    # Convert the numbers into binary strings
    max_bits = max(arr).bit_length()

    # Count the number of 1's and 0's at each bit position
    bit_counts = [0] * max_bits

    for num in arr:
        for i in range(max_bits):
            if num & (1 << i):
                bit_counts[i] += 1

    # We need to flip the smaller count of either 1's or 0's at each position
    total_operations = 0
    for count in bit_counts:
        total_operations += min(count, n - count)

    return total_operations

# Example usage:
arr = [1, 2]
print(getMinOperations(arr))  # Output: 2