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In this optimized version of the code, we have improved the efficiency of calculating the number of ways to make change for a given amount 'n' using a set of coin denominations specified in the 'arr' array. Let's walk through the key changes and improvements: 1. Switching to 1D Array: - We have replaced the 2D array 'table' with a 1D list called 'table'. - This change simplifies the code and reduces memory consumption because we only need to keep track of the number of ways to make change for each amount from 0 to 'n'. 2. Initialization: - We initialize 'table[0]' to 1. This represents the base case where there is one way to make change for an amount of 0, which is by not using any coins. 3. Iterative Update: - We iterate through the coin denominations in the 'arr' array and the amounts from 'S[i]' to 'n'. - For each coin denomination, we iteratively update 'table[j]' by adding 'table[j - S[i]]'. This represents the number of ways to make change for 'j' by either including the current coin denomination 'S[i]' or excluding it. By implementing these changes, we have reduced the time complexity of the code to O(n*m), where 'n' is the target amount and 'm' is the number of coin denominations. This optimization simplifies the code while making it more memory-efficient and faster for larger input values, providing a scalable solution for solving the Coin Change Problem.
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In this optimized version of the code, we have improved the efficiency of calculating the number of ways to make change for a given amount 'n' using a set of coin denominations specified in the 'arr' array. Let's walk through the key changes and improvements:
Switching to 1D Array:
Initialization:
Iterative Update:
By implementing these changes, we have reduced the time complexity of the code to O(n*m), where 'n' is the target amount and 'm' is the number of coin denominations. This optimization simplifies the code while making it more memory-efficient and faster for larger input values, providing a scalable solution for solving the Coin Change Problem.