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Minimum Consecutive Cards to Pick Up

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Arrays

You are given an integer array cards where cards[i] represents the value of the i^th card. A pair of cards are matching if the cards have the same value.

Return the minimum number of consecutive cards you have to pick up to have a pair of matching cards among the picked cards. If it is impossible to have matching cards, return -1.

Example 1:

Input: cards = [3,4,2,3,4,7]
Output: 4
Explanation: We can pick up the cards [3,4,2,3] which contain a matching pair of cards with value 3. Note that picking up the cards [4,2,3,4] is also optimal.

Example 2:

Input: cards = [1,0,5,3]
Output: -1
Explanation: There is no way to pick up a set of consecutive cards that contain a pair of matching cards.

Constraints:

1 <= cards.length <= 10⁵
0 <= cards[i] <= 10⁶

Try coding it in LeetCode

Minimum Consecutive Cards to Pick Up

Medium

Asked by:

46 views

Topics:

Arrays

You are given an integer array cards where cards[i] represents the value of the i^th card. A pair of cards are matching if the cards have the same value.

Return the minimum number of consecutive cards you have to pick up to have a pair of matching cards among the picked cards. If it is impossible to have matching cards, return -1.

Example 1:

Input: cards = [3,4,2,3,4,7]
Output: 4
Explanation: We can pick up the cards [3,4,2,3] which contain a matching pair of cards with value 3. Note that picking up the cards [4,2,3,4] is also optimal.

Example 2:

Input: cards = [1,0,5,3]
Output: -1
Explanation: There is no way to pick up a set of consecutive cards that contain a pair of matching cards.

Constraints:

1 <= cards.length <= 10⁵
0 <= cards[i] <= 10⁶

Try coding it in LeetCode

Solution

Clarifying Questions

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:

What is the maximum size of the `cards` array? Is it small enough to fit comfortably in memory?
Can the card values in the `cards` array be any non-negative integer, or are there constraints on their range?
If there are no pairs of matching cards in the `cards` array, what should I return?
If there are multiple sets of consecutive cards that satisfy the condition, should I return the shortest one, or is any valid solution acceptable?
Are the card values guaranteed to be integers or could they be other data types such as strings or floats?

Brute Force Solution

Approach

The brute force method means we'll check every possible set of cards to find the smallest one that contains a matching pair. We'll go through all the combinations, no matter how inefficient it is, to guarantee we find the minimum length.

Here's how the algorithm would work step-by-step:

Start by looking at every possible set of two consecutive cards.
Check if any two cards in the set are the same.
If you find a matching pair, remember the length of the set (which is 2 in this case).
Next, look at every possible set of three consecutive cards.
Again, check if any two cards in the set are the same.
If you find a matching pair, remember the length of this set (which is 3).
Continue this process, increasing the size of the set of consecutive cards you examine each time.
Keep track of the length of the shortest set where you found a matching pair.
Once you've checked every possible set of cards, the shortest length you recorded is your answer.

Code Implementation

def minimum_consecutive_cards_brute_force(cards):
    number_of_cards = len(cards)
    minimum_length = float('inf')

    for window_size in range(2, number_of_cards + 1):
        for start_index in range(number_of_cards - window_size + 1):
            end_index = start_index + window_size
            sub_array = cards[start_index:end_index]

            # This is the core logic, checking for duplicates.
            for first_card_index in range(window_size):
                for second_card_index in range(first_card_index + 1, window_size):
                    if sub_array[first_card_index] == sub_array[second_card_index]:
                        minimum_length = min(minimum_length, window_size)
                        break

                if minimum_length == window_size:
                    break

    # If no match found, return -1 as specified.
    if minimum_length == float('inf'):
        return -1
    else:
        return minimum_length

Big(O) Analysis

Time Complexity

O(n^3) – The brute force approach iterates through all possible subarrays. The outer loop determines the length of the subarray, ranging from 2 to n. The middle loop iterates through all possible starting positions for each subarray length, which is O(n). For each subarray, we check for duplicate cards, which takes O(n) time in the worst case. Therefore, the overall time complexity is O(n * n * n) = O(n^3).

Space Complexity

O(1) – The brute force method, as described, does not explicitly create any auxiliary data structures that scale with the input size N (number of cards). It primarily involves iterative checking of consecutive card sets and storing the minimum length found so far, which can be done using a constant number of variables. Therefore, the algorithm's auxiliary space complexity is constant, independent of the input size N. This means the space required remains the same regardless of how many cards are in the input.

Optimal Solution

Approach

The goal is to find the smallest section of cards that contains at least one matching pair. Instead of checking every possible section, we can efficiently find the minimum length by keeping track of where each card value appears.

Here's how the algorithm would work step-by-step:

Remember the last position where you saw each card value.
Go through the cards one by one from the beginning.
For each card, check if you've seen that value before.
If you have, calculate the distance between the current position and the last position you saw that value. This distance represents the length of a possible solution.
Keep track of the shortest distance you've found so far.
Update the last seen position of the current card's value.
After checking all the cards, the shortest distance you tracked is the answer (or say no matching cards were found, if the distance is the initial maximum distance)

Code Implementation

def minimum_consecutive_cards_to_pick_up(cards):
    last_seen_position = {}
    minimum_length = float('inf')

    for current_position, card_value in enumerate(cards):
        # Check if the current card has been seen before.
        if card_value in last_seen_position:

            distance = current_position - last_seen_position[card_value] + 1
            minimum_length = min(minimum_length, distance)

        # Update the last seen position for the current card.
        last_seen_position[card_value] = current_position

    # If no matching pairs were found.
    if minimum_length == float('inf'):
        return -1
    else:
        return minimum_length

Big(O) Analysis

Time Complexity

O(n) – The algorithm iterates through the cards array once, where n is the number of cards. Inside the loop, it performs constant-time operations: checking if a card value has been seen before (using a hash map), calculating the distance, and updating the last seen position. Therefore, the time complexity is directly proportional to the number of cards, resulting in O(n).

Space Complexity

O(N) – The algorithm uses a hash map (or dictionary) to store the last seen position of each card value. In the worst case, all the card values are distinct, requiring us to store N key-value pairs in the hash map, where N is the number of cards. Therefore, the auxiliary space required grows linearly with the number of cards. This results in a space complexity of O(N).

Edge Cases

Case	How to Handle
Null or empty input array	Return -1 to indicate no solution exists as no cards can be picked.
Input array with only one element	Return -1 since there must be at least two identical cards to pick up.
All cards in the array are unique	Return -1 because no matching card pairs can be found in the array.
All cards in the array are identical	Return 2, since only two consecutive cards are required in this case.
Very large input array exceeding memory constraints	Consider streaming the input or using an external storage solution for intermediate results.
Integer overflow when calculating minimum length	Use a data type with sufficient range, like long or BigInteger, to prevent potential integer overflows.
Input array contains a very long sequence without duplicate numbers	The algorithm should efficiently scan the array until a duplicate number is found.
Array contains negative or zero card values.	The hash map implementation should correctly store and retrieve negative or zero keys.

Null or empty input array

How to Handle:

Return -1 to indicate no solution exists as no cards can be picked.

Input array with only one element

How to Handle:

Return -1 since there must be at least two identical cards to pick up.

All cards in the array are unique

How to Handle:

Return -1 because no matching card pairs can be found in the array.

All cards in the array are identical

How to Handle:

Return 2, since only two consecutive cards are required in this case.

Very large input array exceeding memory constraints

How to Handle:

Consider streaming the input or using an external storage solution for intermediate results.

Integer overflow when calculating minimum length

How to Handle:

Use a data type with sufficient range, like long or BigInteger, to prevent potential integer overflows.

Input array contains a very long sequence without duplicate numbers

How to Handle:

The algorithm should efficiently scan the array until a duplicate number is found.

Array contains negative or zero card values.

How to Handle:

The hash map implementation should correctly store and retrieve negative or zero keys.

Solution

Clarifying Questions

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:

What is the maximum size of the `cards` array? Is it small enough to fit comfortably in memory?
Can the card values in the `cards` array be any non-negative integer, or are there constraints on their range?
If there are no pairs of matching cards in the `cards` array, what should I return?
If there are multiple sets of consecutive cards that satisfy the condition, should I return the shortest one, or is any valid solution acceptable?
Are the card values guaranteed to be integers or could they be other data types such as strings or floats?

Brute Force Solution

Approach

Here's how the algorithm would work step-by-step:

Start by looking at every possible set of two consecutive cards.
Check if any two cards in the set are the same.
If you find a matching pair, remember the length of the set (which is 2 in this case).
Next, look at every possible set of three consecutive cards.
Again, check if any two cards in the set are the same.
If you find a matching pair, remember the length of this set (which is 3).
Continue this process, increasing the size of the set of consecutive cards you examine each time.
Keep track of the length of the shortest set where you found a matching pair.
Once you've checked every possible set of cards, the shortest length you recorded is your answer.

Code Implementation

def minimum_consecutive_cards_brute_force(cards):
    number_of_cards = len(cards)
    minimum_length = float('inf')

    for window_size in range(2, number_of_cards + 1):
        for start_index in range(number_of_cards - window_size + 1):
            end_index = start_index + window_size
            sub_array = cards[start_index:end_index]

            # This is the core logic, checking for duplicates.
            for first_card_index in range(window_size):
                for second_card_index in range(first_card_index + 1, window_size):
                    if sub_array[first_card_index] == sub_array[second_card_index]:
                        minimum_length = min(minimum_length, window_size)
                        break

                if minimum_length == window_size:
                    break

    # If no match found, return -1 as specified.
    if minimum_length == float('inf'):
        return -1
    else:
        return minimum_length

Big(O) Analysis

Time Complexity

Space Complexity

Optimal Solution

Approach

Here's how the algorithm would work step-by-step:

Remember the last position where you saw each card value.
Go through the cards one by one from the beginning.
For each card, check if you've seen that value before.
If you have, calculate the distance between the current position and the last position you saw that value. This distance represents the length of a possible solution.
Keep track of the shortest distance you've found so far.
Update the last seen position of the current card's value.
After checking all the cards, the shortest distance you tracked is the answer (or say no matching cards were found, if the distance is the initial maximum distance)

Code Implementation

def minimum_consecutive_cards_to_pick_up(cards):
    last_seen_position = {}
    minimum_length = float('inf')

    for current_position, card_value in enumerate(cards):
        # Check if the current card has been seen before.
        if card_value in last_seen_position:

            distance = current_position - last_seen_position[card_value] + 1
            minimum_length = min(minimum_length, distance)

        # Update the last seen position for the current card.
        last_seen_position[card_value] = current_position

    # If no matching pairs were found.
    if minimum_length == float('inf'):
        return -1
    else:
        return minimum_length

Big(O) Analysis

Time Complexity

Space Complexity

Edge Cases

Case	How to Handle
Null or empty input array	Return -1 to indicate no solution exists as no cards can be picked.
Input array with only one element	Return -1 since there must be at least two identical cards to pick up.
All cards in the array are unique	Return -1 because no matching card pairs can be found in the array.
All cards in the array are identical	Return 2, since only two consecutive cards are required in this case.
Very large input array exceeding memory constraints	Consider streaming the input or using an external storage solution for intermediate results.
Integer overflow when calculating minimum length	Use a data type with sufficient range, like long or BigInteger, to prevent potential integer overflows.
Input array contains a very long sequence without duplicate numbers	The algorithm should efficiently scan the array until a duplicate number is found.
Array contains negative or zero card values.	The hash map implementation should correctly store and retrieve negative or zero keys.

Null or empty input array

How to Handle:

Return -1 to indicate no solution exists as no cards can be picked.

Input array with only one element

How to Handle:

Return -1 since there must be at least two identical cards to pick up.

All cards in the array are unique

How to Handle:

Return -1 because no matching card pairs can be found in the array.

All cards in the array are identical

How to Handle:

Return 2, since only two consecutive cards are required in this case.

Very large input array exceeding memory constraints

How to Handle:

Consider streaming the input or using an external storage solution for intermediate results.

Integer overflow when calculating minimum length

How to Handle:

Use a data type with sufficient range, like long or BigInteger, to prevent potential integer overflows.

Input array contains a very long sequence without duplicate numbers

How to Handle:

The algorithm should efficiently scan the array until a duplicate number is found.

Array contains negative or zero card values.

How to Handle:

The hash map implementation should correctly store and retrieve negative or zero keys.