How do you solve Count Ways to Choose Coprime Integers from Rows on LeetCode?

Count Ways to Choose Coprime Integers from Rows (LeetCode #3725) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(m * n * log(max_value)) time complexity and O(max_value) space complexity. Key insight: GCD properties help reduce combinations.

What is the time complexity of Count Ways to Choose Coprime Integers from Rows?

The optimal solution for Count Ways to Choose Coprime Integers from Rows runs in O(m * n * log(max_value)) time and uses O(max_value) space. The time complexity is driven by iterating through each element and calculating GCD, while space is limited to the number of unique GCDs.

What is the brute force solution for Count Ways to Choose Coprime Integers from Rows?

The brute force approach for Count Ways to Choose Coprime Integers from Rows is Brute Force, with O(n²) time complexity and O(1) space complexity. Generate all combinations of integers from each row and check their GCD. This is straightforward but inefficient for larger matrices. The optimal Optimal Solution approach improves this to O(m * n * log(max_value)).

What are the interview tips for Count Ways to Choose Coprime Integers from Rows?

Explain your thought process clearly. Discuss edge cases and constraints. Practice coding without an IDE.

What are common mistakes when solving Count Ways to Choose Coprime Integers from Rows?

Not considering all GCD values. Forgetting to use modulo for large numbers.

#3725

Count Ways to Choose Coprime Integers from Rows

Hard

ArrayMathDynamic ProgrammingMatrixCombinatoricsNumber TheoryDynamic ProgrammingCombinatorics

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(m * n * log(max_value))
Space	O(1)	O(max_value)

💡

Intuition

Time O(m * n * log(max_value))Space O(max_value)

Use dynamic programming to track the number of ways to achieve each GCD as we process each row, avoiding redundant calculations.

⚙️

Algorithm

3 steps

1Step 1: Initialize a DP array to count ways for each GCD value.
2Step 2: For each row, update the DP array based on current integers and their GCDs.
3Step 3: Sum the counts for GCD value 1 from the DP array.

solution.py12 lines

1def countCoprime(mat):
2    from math import gcd
3    from collections import defaultdict
4    dp = defaultdict(int)
5    dp[0] = 1
6    for row in mat:
7        new_dp = defaultdict(int)
8        for num in row:
9            for g in dp:
10                new_dp[gcd(g, num)] = (new_dp[gcd(g, num)] + dp[g]) % (10**9 + 7)
11        dp = new_dp
12    return dp[1]

ℹ

Complexity note: The time complexity is driven by iterating through each element and calculating GCD, while space is limited to the number of unique GCDs.

1GCD properties help reduce combinations.
2Dynamic programming can efficiently track states.

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