Design an algorithm to solve the given problem: You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money. Return the number of combinations that make up that amount. If that amount of money cannot be made up by any combination of the coins, return 0. You may assume that you have an infinite number of each kind of coin. Task 1: Draw a decision tree and identify repeated sub-problems Task 2: Design a DP algorithm to store repeated sub-problems Task 3: Can this problem be solved using a different method, if so what is the time complexity of such algorithms, and can it be better than DP? Input: amount = 7, coins = [1,2,5] Output: 6 Explanation: there are six ways to make up the amount: 7=5+2 7=5+1+1 7=2+2+2+1 7=2+2+1+1+1 7=2+1+1+1+1+1 7=1+1+1+1+1+1+1
Design an
You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.
Return the number of combinations that make up that amount. If that amount of money cannot be made up by any combination of the coins, return 0.
You may assume that you have an infinite number of each kind of coin.
Task 1: Draw a decision tree and identify repeated sub-problems
Task 2: Design a DP algorithm to store repeated sub-problems
Task 3: Can this problem be solved using a different method, if so what is the time complexity of such algorithms, and can it be better than DP?
Input: amount = 7, coins = [1,2,5]
Output: 6
Explanation: there are six ways to make up the amount:
7=5+2
7=5+1+1
7=2+2+2+1
7=2+2+1+1+1
7=2+1+1+1+1+1
7=1+1+1+1+1+1+1
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