How do you solve Minimum Number of Coins to be Added on LeetCode?

Minimum Number of Coins to be Added (LeetCode #2952) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(1) space complexity. Key insight: Understanding how to build up obtainable sums helps in optimizing the solution.

What is the time complexity of Minimum Number of Coins to be Added?

The optimal solution for Minimum Number of Coins to be Added runs in O(n log n) time and uses O(1) space. The sorting step dominates the complexity, making it O(n log n), while the subsequent iterations are linear.

What is the brute force solution for Minimum Number of Coins to be Added?

The brute force approach for Minimum Number of Coins to be Added is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach tries to generate all possible sums from the given coins and checks which integers from 1 to the target are obtainable. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Minimum Number of Coins to be Added?

Minimum Number of Coins to be Added uses the following concepts: Array, Greedy, Sorting. The recommended patterns to study are: Greedy, Sorting.

What are the interview tips for Minimum Number of Coins to be Added?

Always clarify the problem requirements and constraints before jumping into coding. Think about edge cases, such as when the coins array is empty. Explain your thought process clearly while coding to demonstrate your understanding.

What are common mistakes when solving Minimum Number of Coins to be Added?

Failing to sort the coins before processing them. Not correctly identifying the smallest unobtainable sum.

#2952

Minimum Number of Coins to be Added

Medium

ArrayGreedySortingGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n log n)
Space	O(1)	O(1)

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Intuition

Time O(n log n)Space O(1)

The optimal approach uses a greedy strategy to determine the smallest unobtainable integer and adds coins as needed to cover the range up to the target. This is efficient because it systematically builds the range of obtainable sums without unnecessary computations.

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Algorithm

5 steps

1Step 1: Sort the coins array.
2Step 2: Initialize a variable to track the smallest unobtainable sum, starting at 1.
3Step 3: Iterate through the sorted coins, checking if the current coin can cover the smallest unobtainable sum.
4Step 4: If the current coin is greater than the smallest unobtainable sum, add coins to cover the gap.
5Step 5: Continue until all integers up to the target are obtainable.

solution.py16 lines

1# Full working Python code
2
3def min_coins_to_add(coins, target):
4    coins.sort()
5    missing_count = 0
6    smallest_unobtainable = 1
7    for coin in coins:
8        while coin > smallest_unobtainable:
9            missing_count += 1
10            smallest_unobtainable *= 2
11        smallest_unobtainable += coin
12    while smallest_unobtainable <= target:
13        missing_count += 1
14        smallest_unobtainable *= 2
15    return missing_count
16

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Complexity note: The sorting step dominates the complexity, making it O(n log n), while the subsequent iterations are linear.

1Understanding how to build up obtainable sums helps in optimizing the solution.
2Using a greedy approach allows us to minimize the number of coins needed efficiently.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.