issumsubset2 4 6 8 5 false issumsubset2 4 6 8 14 true a subset value says 1 if that subset sum can be formed else 0 initially no subsets can be formed hence false0 for each arr value a sum of zero0 can be formed by not taking any element hence true1 sum is not zero and set is empty then false is_sum_subset 2 4 6 8 5 false is_sum_subset 2 4 6 8 14 true a subset value says 1 if that subset sum can be formed else 0 initially no subsets can be formed hence false 0 for each arr value a sum of zero 0 can be formed by not taking any element hence true 1 sum is not zero and set is empty then false
def is_sum_subset(arr: list[int], required_sum: int) -> bool:
    
    
    
    arr_len = len(arr)
    subset = [[False] * (required_sum + 1) for _ in range(arr_len + 1)]

    
    
    for i in range(arr_len + 1):
        subset[i][0] = True

    
    for i in range(1, required_sum + 1):
        subset[0][i] = False

    for i in range(1, arr_len + 1):
        for j in range(1, required_sum + 1):
            if arr[i - 1] > j:
                subset[i][j] = subset[i - 1][j]
            if arr[i - 1] <= j:
                subset[i][j] = subset[i - 1][j] or subset[i - 1][j - arr[i - 1]]

    return subset[arr_len][required_sum]


if __name__ == "__main__":
    import doctest

    doctest.testmod()