Count ways to make change (DP)

## Problem You are given an integer `amount` and an array of **positive, distinct** integers `coins`, where each coin value can be used **unlimited times**. Return the number of **distinct combinations** of coins that sum to exactly `amount`. Notes: - The **order does not matter**. For example, `2+1` and `1+2` are the same combination. - If `amount = 0`, there is exactly **one** way: choose no coins. ## Input/Output - **Input:** integer `amount`, integer array `coins` - **Output:** integer `ways` ## Examples - `amount = 5, coins = [1,2,5]` → `4` - Combinations: `5`, `2+2+1`, `2+1+1+1`, `1+1+1+1+1` - `amount = 3, coins = [2]` → `0` - `amount = 0, coins = [1,2]` → `1` ## Constraints (assume) - `0 ≤ amount ≤ 10^4` - `1 ≤ len(coins) ≤ 300` - Result fits in 64-bit signed integer