How do you solve Coin Change II on LeetCode?

Coin Change II (LeetCode #518) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * m) time complexity and O(n) space complexity. Key insight: Dynamic programming can significantly reduce the time complexity of combinatorial problems.

What is the brute force solution for Coin Change II?

The brute force approach for Coin Change II is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible combinations of coins to see which ones sum up to the target amount. This method is straightforward but inefficient, as it can lead to exponential time complexity due to the vast number of combinations. The optimal Optimal Solution approach improves this to O(n * m).

What algorithm or data structure is used to solve Coin Change II?

Coin Change II uses the following concepts: Array, Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Combinatorial Counting.

What are the interview tips for Coin Change II?

Always explain your thought process clearly while coding. Consider edge cases, such as when the amount is 0 or when there are no coins. Practice similar problems to get comfortable with dynamic programming techniques.

What are common mistakes when solving Coin Change II?

Forgetting to initialize the base case in the dp array. Not considering all coin denominations when updating the dp array.

#518

Coin Change II

Medium

ArrayDynamic ProgrammingDynamic ProgrammingCombinatorial Counting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n * m)Space O(n)

The optimal solution uses dynamic programming to build up the number of ways to reach each amount from 0 to the target amount. We use an array to store the number of combinations for each amount, updating it as we iterate through the coin denominations.

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Algorithm

3 steps

1Step 1: Initialize a dp array of size (amount + 1) with dp[0] = 1 (base case).
2Step 2: For each coin, update the dp array for all amounts from the coin value to the target amount.
3Step 3: For each amount, add the number of combinations from the current coin to the previous amounts.

solution.py9 lines

1# Full working Python code
2
3def coinChangeII(amount, coins):
4    dp = [0] * (amount + 1)
5    dp[0] = 1
6    for coin in coins:
7        for x in range(coin, amount + 1):
8            dp[x] += dp[x - coin]
9    return dp[amount]

ℹ

Complexity note: The time complexity is O(n * m) where n is the amount and m is the number of coin denominations. We iterate through each coin and update the dp array for each amount up to the target.

1Dynamic programming can significantly reduce the time complexity of combinatorial problems.
2Understanding how to build solutions incrementally is crucial in dynamic programming.

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