How do you solve Valid Permutations for DI Sequence on LeetCode?

Valid Permutations for DI Sequence (LeetCode #903) 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: Dynamic programming can reduce the complexity of counting problems.

What is the time complexity of Valid Permutations for DI Sequence?

The optimal solution for Valid Permutations for DI Sequence runs in O(n) time and uses O(n) space. The time complexity is O(n) because we iterate through the string once to fill the DP array. The space complexity is O(n) due to the DP array.

What is the brute force solution for Valid Permutations for DI Sequence?

The brute force approach for Valid Permutations for DI Sequence is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach generates all possible permutations of the numbers from 0 to n and checks each one against the given string 's' to see if it satisfies the increasing and decreasing conditions. While straightforward, this method is inefficient due to the factorial growth of permutations. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Valid Permutations for DI Sequence?

Valid Permutations for DI Sequence uses the following concepts: String, Dynamic Programming, Prefix Sum. The recommended patterns to study are: Dynamic Programming, Combinatorics.

What are the interview tips for Valid Permutations for DI Sequence?

Explain your thought process clearly when discussing brute-force solutions. Be prepared to discuss the trade-offs between brute-force and optimized approaches. Practice writing clean and efficient code under time constraints.

What are common mistakes when solving Valid Permutations for DI Sequence?

Failing to consider edge cases like all 'I's or all 'D's. Not using modulo operations to prevent overflow.

#903

Valid Permutations for DI Sequence

Hard

StringDynamic ProgrammingPrefix SumDynamic ProgrammingCombinatorics

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)

The optimal solution uses dynamic programming to count valid permutations based on the number of increasing and decreasing sequences. By leveraging combinatorial properties, we can efficiently compute the result without generating all permutations.

⚙️

Algorithm

3 steps

1Step 1: Initialize a DP array where dp[i] represents the number of valid permutations for the first i characters of s.
2Step 2: Use combinatorial logic to fill the DP array based on the counts of 'I' and 'D' in the string.
3Step 3: Return dp[n] as the result.

solution.py12 lines

1def count_valid_permutations(s):
2    MOD = 10**9 + 7
3    n = len(s)
4    dp = [0] * (n + 1)
5    dp[0] = 1
6
7    for i in range(1, n + 1):
8        dp[i] = dp[i - 1] * (i + 1) % MOD
9        if s[i - 1] == 'D':
10            dp[i] = dp[i - 1] * i % MOD
11
12    return dp[n]

ℹ

Complexity note: The time complexity is O(n) because we iterate through the string once to fill the DP array. The space complexity is O(n) due to the DP array.

1Dynamic programming can reduce the complexity of counting problems.
2Understanding combinatorial properties is crucial for optimization.

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