combination_sum_iv.md

This code is a Go implementation of a dynamic programming approach to solve the "Combination Sum IV" problem. The problem statement is to count the number of possible combinations of the given nums array that add up to a specific target value. Combinations are counted without considering the order of elements in the combination.

Here's a step-by-step explanation of the code:

1. Import the "sort" package, which is used later to sort the nums array.

2. Define a helper function called helper. This function takes three parameters: nums (the input array of numbers), n (the target value to reach), and memo (a memoization map to store computed results for subproblems).

3. Check if the result for the current target n is already computed and stored in the memo map. If so, return the stored value to avoid redundant calculations.

4. If n equals 0, it means a valid combination is found, so return 1 to count it.

5. If n is less than the smallest number in the nums array, return 0, as it's impossible to form the target value with the given numbers.

6. Initialize a count variable to 0, which will be used to count the valid combinations.

7. Iterate through the nums array, and for each number num, recursively call the helper function with the updated target n - num. Add the result to the count variable. This step calculates the number of combinations that include the current number.

8. Store the count in the memo map for the current n to avoid recomputation.

9. Return the final count as the result.

10. Define the combinationSum4 function, which is the entry point for solving the problem. Inside this function:

    • Sort the nums array in ascending order to optimize the algorithm.
    • Create an empty memoization map memo.
    • Call the helper function with nums, target, and memo as arguments and return the result.

The time complexity of this solution depends on the input values. In the worst case, it can be exponential, but memoization is used to store previously computed results, which can significantly reduce redundant calculations. Therefore, the average time complexity is much better than the worst case, and it can be considered O(N * T), where N is the length of the nums array, and T is the target value.

The space complexity is O(T), where T is the target value, due to the space required for the memo map.