How do you solve Ways to Express an Integer as Sum of Powers on LeetCode?

Ways to Express an Integer as Sum of Powers (LeetCode #2787) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * m) time complexity and O(n) space complexity. Key insight: Dynamic programming allows us to build solutions incrementally.

What is the brute force solution for Ways to Express an Integer as Sum of Powers?

The brute force approach for Ways to Express an Integer as Sum of Powers is Brute Force, with O(n²) time complexity and O(1) space complexity. We can try every combination of unique integers to see if their x-th powers sum up to n. This is straightforward but inefficient, as it explores many unnecessary combinations. The optimal Optimal Solution approach improves this to O(n * m).

What algorithm or data structure is used to solve Ways to Express an Integer as Sum of Powers?

Ways to Express an Integer as Sum of Powers uses the following concepts: Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Combinatorial Counting.

What are the interview tips for Ways to Express an Integer as Sum of Powers?

Explain your thought process clearly while coding. Discuss edge cases and how your solution handles them. Practice writing clean and efficient code.

What are common mistakes when solving Ways to Express an Integer as Sum of Powers?

Forgetting to use unique integers in combinations. Not considering the modulo operation when counting combinations.

#2787

Ways to Express an Integer as Sum of Powers

Medium

Dynamic ProgrammingDynamic ProgrammingCombinatorial Counting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

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

We can use dynamic programming to build up the number of ways to express each integer up to n using unique integers raised to the x-th power. This avoids redundant calculations and efficiently counts combinations.

⚙️

Algorithm

3 steps

1Step 1: Create a DP table where dp[k][j] represents the number of ways to express k using unique integers up to j.
2Step 2: Iterate through each integer j from 1 to the maximum integer whose x-th power is <= n.
3Step 3: For each k from n down to the x-th power of j, update dp[k] by adding dp[k - j^x].

solution.py12 lines

1# Full working Python code
2MOD = 10**9 + 7
3
4def sum_of_powers(n, x):
5    dp = [0] * (n + 1)
6    dp[0] = 1
7    max_base = int(n**(1/x))
8    for j in range(1, max_base + 1):
9        power = j ** x
10        for k in range(n, power - 1, -1):
11            dp[k] = (dp[k] + dp[k - power]) % MOD
12    return dp[n]

ℹ

Complexity note: The time complexity is O(n * m), where m is the number of unique integers whose x-th power is less than or equal to n. This is efficient as we only compute valid combinations once.

1Dynamic programming allows us to build solutions incrementally.
2Unique integers mean we can't reuse numbers, which simplifies our state transitions.

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