What is the optimal time complexity of solving Coin Change Problem?

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 Coin Change Problem?

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 Coin Change Problem?

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 Coin Change Problem?

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

Coin Change Problem

Learn how to solve the 'Coin Change Problem' problem. This detailed resource details brute force and optimized approaches.

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Problem Statement

Easy

Write a function count_coin_change(coins, n) that returns the number of distinct ways to make change for a target amount n using an unlimited supply of the given coin denominations coins.

Constraints

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

Examples

Example 1

Input

count_coin_change([1, 2, 3], 4)

Output

Explanation

There are 4 ways: {1,1,1,1}, {1,1,2}, {2,2}, {1,3}.

Example 2

Input

count_coin_change([2, 5, 3, 6], 10)

Output

Explanation

There are 5 ways: {2,2,2,2,2}, {2,2,3,3}, {2,2,6}, {2,3,5}, {5,5}.

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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