How do you solve Sum of Good Subsequences on LeetCode?

Sum of Good Subsequences (LeetCode #3351) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + k), where k is the range of numbers (up to 100000) time complexity and O(k) space complexity. Key insight: Counting occurrences of each number helps in calculating contributions to subsequences efficiently.

What is the time complexity of Sum of Good Subsequences?

The optimal solution for Sum of Good Subsequences runs in O(n + k), where k is the range of numbers (up to 100000) time and uses O(k) space. The time complexity is linear with respect to the input size plus the range of numbers, making it efficient for large inputs.

What is the brute force solution for Sum of Good Subsequences?

The brute force approach for Sum of Good Subsequences is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible subsequences of the array and checking if they are 'good'. This means we will consider every combination of elements and sum those that meet the criteria. The optimal Optimal Solution approach improves this to O(n + k), where k is the range of numbers (up to 100000).

What algorithm or data structure is used to solve Sum of Good Subsequences?

Sum of Good Subsequences uses the following concepts: Array, Hash Table, Dynamic Programming. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Sum of Good Subsequences?

Always clarify the problem requirements and constraints before diving into coding. Think about edge cases, such as arrays with all identical elements or large ranges of numbers. Explain your thought process clearly while coding; it shows your understanding and helps the interviewer follow along.

What are common mistakes when solving Sum of Good Subsequences?

Failing to consider subsequences of size 1 as good. Not properly handling large numbers and forgetting to apply modulo.

#3351

Sum of Good Subsequences

Hard

ArrayHash TableDynamic ProgrammingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n + k), where k is the range of numbers (up to 100000)
Space	O(1)	O(k)

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Intuition

Time O(n + k), where k is the range of numbers (up to 100000)Space O(k)

The optimal solution uses dynamic programming to count how many times each element can appear in good subsequences. We track the sum of subsequences ending with each number and build upon previous results.

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Algorithm

5 steps

1Step 1: Count the frequency of each number in the array.
2Step 2: Initialize a DP array to store the sum of good subsequences for each number.
3Step 3: Iterate through the unique numbers and calculate the sum of good subsequences based on the previous number's results.
4Step 4: For each number, update the DP array using the frequency of the current number and the previous number.
5Step 5: Return the total sum from the DP array modulo 10^9 + 7.

solution.py14 lines

1# Full working Python code
2from collections import Counter
3
4def sum_good_subsequences(nums):
5    MOD = 10**9 + 7
6    count = Counter(nums)
7    dp = {}  # dp[number] = sum of good subsequences ending with 'number'
8    total_sum = 0
9
10    for num in sorted(count.keys()):
11        dp[num] = (num * count[num] + (dp.get(num - 1, 0) * count[num]) % MOD) % MOD
12        total_sum = (total_sum + dp[num]) % MOD
13
14    return total_sum

ℹ

Complexity note: The time complexity is linear with respect to the input size plus the range of numbers, making it efficient for large inputs.

1Counting occurrences of each number helps in calculating contributions to subsequences efficiently.
2Dynamic programming allows us to build upon previous results, avoiding redundant calculations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.