#1652

Easy

auto_awesomeSliding window with running state updates

LeetCode Problem Workspace

Defuse the Bomb

Defuse the Bomb uses a sliding window to update a circular array based on a key, with efficient state updates.

Problem Statement

In the 'Defuse the Bomb' problem, you are provided with a circular array called 'code' and a key 'k'. The goal is to decrypt the code by replacing each element with the sum of the next k elements, considering the circular nature of the array. The array wraps around, so the last element will connect to the first one, and the first one will connect to the last.

The decryption process happens simultaneously for all elements. The sum of the next k elements must be calculated for each code[i]. If k is negative, the sum will consider previous elements in the circular array. For example, a positive k sums the next k elements, while a negative k sums the previous k elements, and zero would result in all zeros in the output array.

Examples

Example 1

Input: code = [5,7,1,4], k = 3

Output: [12,10,16,13]

Each number is replaced by the sum of the next 3 numbers. The decrypted code is [7+1+4, 1+4+5, 4+5+7, 5+7+1]. Notice that the numbers wrap around.

Example 2

Input: code = [1,2,3,4], k = 0

Output: [0,0,0,0]

When k is zero, the numbers are replaced by 0.

Example 3

Input: code = [2,4,9,3], k = -2

Output: [12,5,6,13]

The decrypted code is [3+9, 2+3, 4+2, 9+4]. Notice that the numbers wrap around again. If k is negative, the sum is of the previous numbers.

Constraints

n == code.length
1 <= n <= 100
1 <= code[i] <= 100
-(n - 1) <= k <= n - 1

Solution Approach

Sliding Window Technique

Use the sliding window technique to maintain a sum of the next k elements for each position in the array. As the array is circular, use modulo arithmetic to wrap around the indices. The sliding window ensures you can compute the sum in O(n) time.

Efficient Updates with Running State

Instead of recalculating the sum for every index from scratch, update the sum dynamically by adding the next element and removing the previous one. This results in efficient state updates while maintaining the correct sum for the sliding window.

Handle Negative k Values

If k is negative, the problem essentially asks you to sum the previous k elements instead of the next ones. Adjust your sliding window logic to account for both positive and negative k values by using modulo for circular indexing.

Complexity Analysis

Metric	Value
Time	O(n)
Space	O(n)

The time complexity is O(n), as we only iterate through the array once with the sliding window approach. The space complexity is also O(n), as we need to store the result array, which has the same length as the input array.

What Interviewers Usually Probe

Evaluate understanding of the sliding window approach, especially with circular arrays.
Check if the candidate handles negative k values correctly and adapts the sliding window accordingly.
Look for efficient use of space, ensuring the algorithm uses O(n) space and doesn't recompute sums unnecessarily.

Common Pitfalls or Variants

Common pitfalls

Overcomplicating the solution by using nested loops or redundant calculations.
Not using modulo arithmetic correctly to handle the circular nature of the array.
Failing to consider edge cases, like k being 0 or negative.

Follow-up variants

Modify the problem to return the product of the next k numbers instead of the sum.
Change the problem to use an array of negative values and see if the candidate can adjust the solution.
Allow k to be larger than the length of the array and check if the candidate can handle that with modulo arithmetic.

FAQ

What is the primary pattern used in solving 'Defuse the Bomb'?

The primary pattern is the sliding window with running state updates, applied in a circular array context.

How do you handle negative values of k in the 'Defuse the Bomb' problem?

Negative k values mean you sum the previous k elements instead of the next ones, and you must handle this by adjusting your sliding window logic accordingly.

Can the array size exceed 100 in the 'Defuse the Bomb' problem?

No, the problem constraints ensure that the array size is at most 100, so your solution should handle arrays of that size efficiently.

What should the output be when k equals 0 in 'Defuse the Bomb'?

When k equals 0, all elements in the decrypted code will be 0, as no elements are summed.

How does GhostInterview help with the circular array in this problem?

GhostInterview helps by providing guidance on using modulo arithmetic to handle the circular nature of the array efficiently.

terminal

Solution

Solution 1: Simulation

We define an answer array `ans` of length `n`, initially all elements are `0`. According to the problem, if `k` is `0`, return `ans` directly.

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class Solution:
    def decrypt(self, code: List[int], k: int) -> List[int]:
        n = len(code)
        ans = [0] * n
        if k == 0:
            return ans
        for i in range(n):
            if k > 0:
                for j in range(i + 1, i + k + 1):
                    ans[i] += code[j % n]
            else:
                for j in range(i + k, i):
                    ans[i] += code[(j + n) % n]
        return ans

Solution 2: Prefix Sum

In Solution 1, for each position $i$, we need to traverse $k$ positions, which involves a lot of repeated calculations. We can optimize this by using prefix sums.

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class Solution:
    def decrypt(self, code: List[int], k: int) -> List[int]:
        n = len(code)
        ans = [0] * n
        if k == 0:
            return ans
        for i in range(n):
            if k > 0:
                for j in range(i + 1, i + k + 1):
                    ans[i] += code[j % n]
            else:
                for j in range(i + k, i):
                    ans[i] += code[(j + n) % n]
        return ans

Continue Practicing

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