Introduction

In this blog post, we will explore how to solve the LeetCode problem "2902" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given a 0-indexed array nums of non-negative integers, and two integers l and r. Return the count of sub-multisets within nums where the sum of elements in each subset falls within the inclusive range of [l, r]. Since the answer may be large, return it modulo 109 + 7. A sub-multiset is an unordered collection of elements of the array in which a given value x can occur 0, 1, ..., occ[x] times, where occ[x] is the number of occurrences of x in the array. Note that: Two sub-multisets are the same if sorting both sub-multisets results in identical multisets. The sum of an empty multiset is 0. Example 1: Input: nums = [1,2,2,3], l = 6, r = 6 Output: 1 Explanation: The only subset of nums that has a sum of 6 is {1, 2, 3}. Example 2: Input: nums = [2,1,4,2,7], l = 1, r = 5 Output: 7 Explanation: The subsets of nums that have a sum within the range [1, 5] are {1}, {2}, {4}, {2, 2}, {1, 2}, {1, 4}, and {1, 2, 2}. Example 3: Input: nums = [1,2,1,3,5,2], l = 3, r = 5 Output: 9 Explanation: The subsets of nums that have a sum within the range [3, 5] are {3}, {5}, {1, 2}, {1, 3}, {2, 2}, {2, 3}, {1, 1, 2}, {1, 1, 3}, and {1, 2, 2}. Constraints: 1 <= nums.length <= 2 104 0 <= nums[i] <= 2 104 Sum of nums does not exceed 2 104. 0 <= l <= r <= 2 104

Explanation

Here's an efficient solution to the problem:

• Handle Zeroes: Count the number of zeroes in the input array. Each zero can either be included or excluded in a sub-multiset without changing its sum. The number of combinations due to zeroes can be efficiently calculated using powers of 2.
• Dynamic Programming: Use dynamic programming to count the number of sub-multisets with sums in the range [l, r]. dp[i] stores the number of sub-multisets with sum i considering only the non-zero elements.

• Final Calculation: Multiply the DP results for sums in the range [l, r] by the number of combinations due to zeroes to get the final count.

• Runtime Complexity: O(n + r), where n is the length of nums and r is the upper bound of the target sum range. Storage Complexity: O(r)

Code

    def sub_multiset_count(nums, l, r):
    """
    Calculates the count of sub-multisets with sums within the range [l, r].

    Args:
        nums: A list of non-negative integers.
        l: The lower bound of the sum range.
        r: The upper bound of the sum range.

    Returns:
        The count of sub-multisets modulo 10^9 + 7.
    """
    MOD = 10**9 + 7
    zero_count = 0
    for num in nums:
        if num == 0:
            zero_count += 1

    non_zero_nums = [num for num in nums if num != 0]
    max_sum = r  # Sum of nums does not exceed 2 * 10^4, as stated in the problem

    dp = [0] * (max_sum + 1)
    dp[0] = 1

    for num in non_zero_nums:
        for i in range(max_sum, num - 1, -1):
            dp[i] = (dp[i] + dp[i - num]) % MOD

    result = 0
    for i in range(l, r + 1):
        result = (result + dp[i]) % MOD

    result = (result * pow(2, zero_count, MOD)) % MOD

    return result