How do you solve Concatenate Non-Zero Digits and Multiply by Sum II on LeetCode?

Concatenate Non-Zero Digits and Multiply by Sum II (LeetCode #3756) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Use prefix sums for efficient range queries.

What is the time complexity of Concatenate Non-Zero Digits and Multiply by Sum II?

The optimal solution for Concatenate Non-Zero Digits and Multiply by Sum II runs in O(n) time and uses O(n) space. Prefix arrays allow for O(1) retrieval of concatenated values and sums, making the solution efficient.

What is the brute force solution for Concatenate Non-Zero Digits and Multiply by Sum II?

The brute force approach for Concatenate Non-Zero Digits and Multiply by Sum II is Brute Force, with O(n²) time complexity and O(1) space complexity. Extract the substring for each query, concatenate non-zero digits, compute the sum, and multiply. This method is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Concatenate Non-Zero Digits and Multiply by Sum II?

Concatenate Non-Zero Digits and Multiply by Sum II uses the following concepts: Math, String, Prefix Sum. The recommended patterns to study are: Prefix Sum, String Manipulation.

What are the interview tips for Concatenate Non-Zero Digits and Multiply by Sum II?

Explain your thought process clearly. Discuss edge cases like empty substrings. Practice similar problems to build confidence.

What are common mistakes when solving Concatenate Non-Zero Digits and Multiply by Sum II?

Not handling leading zeros correctly. Forgetting to take modulo for large numbers.

#3756

Concatenate Non-Zero Digits and Multiply by Sum II

Medium

MathStringPrefix SumPrefix SumString Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

Use prefix arrays to store cumulative non-zero digit concatenations and their sums, allowing O(1) retrieval for each query.

⚙️

Algorithm

3 steps

1Step 1: Create prefix arrays for concatenated non-zero digits and their sums.
2Step 2: For each query, calculate the result using the prefix arrays to quickly get x and sum.
3Step 3: Return the results modulo 10^9 + 7.

solution.py17 lines

1def concatenate_and_multiply(s, queries):
2    mod = 10**9 + 7
3    n = len(s)
4    prefix_x = [''] * (n + 1)
5    prefix_sum = [0] * (n + 1)
6    for i in range(1, n + 1):
7        prefix_x[i] = prefix_x[i - 1]
8        prefix_sum[i] = prefix_sum[i - 1]
9        if s[i - 1] != '0':
10            prefix_x[i] += s[i - 1]
11            prefix_sum[i] += int(s[i - 1])
12    result = []
13    for l, r in queries:
14        x = int(prefix_x[r + 1]) if prefix_x[r + 1] else 0
15        sum_digits = prefix_sum[r + 1] - prefix_sum[l]
16        result.append(x * sum_digits % mod)
17    return result

ℹ

Complexity note: Prefix arrays allow for O(1) retrieval of concatenated values and sums, making the solution efficient.

1Use prefix sums for efficient range queries.
2Track non-zero digits separately for concatenation.

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