What is the optimal time complexity of solving Minimum number of coins?

The optimized solution achieves a time complexity of O(n) by using sorting, mathematical shortcuts, or hash table lookups.

What is the auxiliary space complexity for Minimum number of coins?

The space complexity is O(1) since we only use a minimal/constant amount of extra memory for tracking variables (or auxiliary space if dynamic structures are allocated).

What are the typical edge cases we must handle in Minimum number of coins?

Key edge cases include empty collections, negative or large bounds causing integer overflow, arrays with only one element, or inputs where target criteria are not met.

How can we optimize the brute force approach for Minimum number of coins?

Brute force methods often inspect all possible combinations. We optimize this by sorting the input list to enable binary search, or tracking processed items in a set to avoid redundant nested loop lookups.

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Competitive ProgrammingEasy

Minimum number of coins

Learn how to solve the 'Minimum number of coins' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function min_coins(coins, V) that returns the minimum number of coins needed to make a target change V using the given coin denominations coins. If it is impossible to make change, return -1.

Constraints

•1 <= len(coins) <= 100
•1 <= V <= 10000
•1 <= coins[i] <= 1000

Examples

Example 1

Input

min_coins([9, 6, 5, 1], 11)

Output

Explanation

We can make 11 using coins 6 and 5 (2 coins).

Example 2

Input

min_coins([5, 10], 7)

Output

-1

Explanation

We cannot make change for 7 using only coins of value 5 and 10.

Need a Hint?

Define subproblem states, establish the recurrence relation, and use memoization (top-down) or tabulation (bottom-up).

Edge Cases to Watch

Empty list or null input variables
Single item lists/arrays
Extremely large input bounds causing integer or stack overflow

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