How do you solve Number of Dice Rolls With Target Sum on LeetCode?

Number of Dice Rolls With Target Sum (LeetCode #1155) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * target * k) time complexity and O(n * target) space complexity. Key insight: Dynamic programming allows us to break down the problem into smaller subproblems, making it more manageable.

What is the brute force solution for Number of Dice Rolls With Target Sum?

The brute force approach for Number of Dice Rolls With Target Sum is Brute Force, with O(k^n) time complexity and O(n) space complexity. The brute force approach involves simulating all possible outcomes of rolling n dice. For each die, we can roll a number between 1 and k, and we check if any combination of rolls sums up to the target. The optimal Optimal Solution approach improves this to O(n * target * k).

What algorithm or data structure is used to solve Number of Dice Rolls With Target Sum?

Number of Dice Rolls With Target Sum uses the following concepts: Dynamic Programming. The recommended patterns to study are: Dynamic Programming, Memoization.

What are the interview tips for Number of Dice Rolls With Target Sum?

Always clarify the constraints and edge cases before diving into coding. Explain your thought process as you code; it shows your understanding. Practice writing both brute force and optimal solutions to strengthen your problem-solving skills.

What are common mistakes when solving Number of Dice Rolls With Target Sum?

Failing to consider the modulo operation can lead to overflow errors. Not properly initializing the DP table can cause incorrect results.

#1155

Number of Dice Rolls With Target Sum

Medium

Dynamic ProgrammingDynamic ProgrammingMemoization

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(k^n)	O(n * target * k)
Space	O(n)	O(n * target)

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Intuition

Time O(n * target * k)Space O(n * target)

Using dynamic programming, we can build a table that keeps track of the number of ways to achieve each possible sum with a certain number of dice. This avoids redundant calculations and significantly reduces the time complexity.

⚙️

Algorithm

3 steps

1Step 1: Create a 2D DP array where dp[i][j] represents the number of ways to achieve sum j with i dice.
2Step 2: Initialize dp[0][0] to 1 (base case: 0 dice can only achieve sum 0).
3Step 3: Iterate through each die and each possible sum, updating the DP table based on previous results.

solution.py9 lines

1def numRollsToTarget(n, k, target):
2    MOD = 10**9 + 7
3    dp = [[0] * (target + 1) for _ in range(n + 1)]
4    dp[0][0] = 1
5    for i in range(1, n + 1):
6        for j in range(1, target + 1):
7            for face in range(1, min(k, j) + 1):
8                dp[i][j] = (dp[i][j] + dp[i - 1][j - face]) % MOD
9    return dp[n][target]

ℹ

Complexity note: The time complexity is O(n * target * k) because we fill a table of size n x target and for each cell, we may iterate up to k times. The space complexity is O(n * target) for the DP table.

1Dynamic programming allows us to break down the problem into smaller subproblems, making it more manageable.
2Understanding the base cases and how to build upon them is crucial in dynamic programming.

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