coin-change-2

Coin Change 2

LeetCode #: 518

Difficulty: Medium

Topics: -

Problem

You are given coins of different denominations and a total amount of money. Write a function to compute the number of combinations that make up that amount. You may assume that you have infinite number of each kind of coin.

Example 1:

Input: amount = 5, coins = [1, 2, 5]
Output: 4
Explanation: there are four ways to make up the amount:
5=5
5=2+2+1
5=2+1+1+1
5=1+1+1+1+1

Example 2:

Input: amount = 3, coins = [2]
Output: 0
Explanation: the amount of 3 cannot be made up just with coins of 2.

Example 3:

Input: amount = 10, coins = [10] 
Output: 1

Note:

You can assume that

• 0 <= amount <= 5000
• 1 <= coin <= 5000
• the number of coins is less than 500
• the answer is guaranteed to fit into signed 32-bit integer

Solution Explanation

This is a knapsack problem which can be solved by using dynamic programming.

Reference: Knapsack problem - Java solution with thinking process O(nm) Time and O(m) Space by tankztc

Complexity Analysis

Assume m is the amount and n is the number of coins.

Time complexity: O(mn)

Space complexity: O(m)