How do you solve Sort Integers by The Power Value on LeetCode?

Sort Integers by The Power Value (LeetCode #1387) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: Memoization can drastically reduce redundant calculations, improving performance.

What is the brute force solution for Sort Integers by The Power Value?

The brute force approach for Sort Integers by The Power Value is Brute Force, with O(n²) time complexity and O(n) space complexity. The brute force approach calculates the power value for each integer in the range [lo, hi] and sorts them based on these values. This is straightforward but inefficient for larger ranges. The optimal Optimal Solution approach improves this to O(n log n).

What algorithm or data structure is used to solve Sort Integers by The Power Value?

Sort Integers by The Power Value uses the following concepts: Dynamic Programming, Memoization, Sorting. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Sort Integers by The Power Value?

Always consider memoization for problems involving repeated calculations. Clarify how to handle ties in sorting when multiple integers have the same power value. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Sort Integers by The Power Value?

Not using memoization, leading to excessive recalculations. Forgetting to handle ties in power values during sorting.

#1387

Sort Integers by The Power Value

Medium

Dynamic ProgrammingMemoizationSortingHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log n)Space O(n)

Using memoization, we can store the power values of integers that we have already computed, significantly reducing redundant calculations and improving efficiency.

⚙️

Algorithm

5 steps

1Step 1: Create a memoization dictionary to store computed power values.
2Step 2: Define a recursive function to calculate the power value, checking the memoization dictionary first.
3Step 3: Iterate through the range [lo, hi], using the recursive function to get power values.
4Step 4: Store the integers and their power values in a list.
5Step 5: Sort the list by power values and return the k-th integer.

solution.py23 lines

1# Full working Python code
2
3def power(x, memo):
4    if x in memo:
5        return memo[x]
6    steps = 0
7    original = x
8    while x != 1:
9        if x % 2 == 0:
10            x //= 2
11        else:
12            x = 3 * x + 1
13        steps += 1
14    memo[original] = steps
15    return steps
16
17def getKth(lo, hi, k):
18    memo = {}
19    power_values = []
20    for i in range(lo, hi + 1):
21        power_values.append((power(i, memo), i))
22    power_values.sort()
23    return power_values[k - 1][1]

ℹ

Complexity note: The time complexity is O(n log n) due to sorting the power values, while the memoization allows us to compute the power values in O(n) time overall, making it efficient.

1Memoization can drastically reduce redundant calculations, improving performance.
2Sorting requires careful handling of ties in power values, which can be managed with tuple sorting.

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