Detonate The Maximum Bombs - Leetcode Solution

Problem Statement: Given an array of integers nums and an integer k. You need to maximize the number of unique integers in the array by detonating exactly k neighboring bombs and cannot detonate more than one bomb at the same position. Return the maximum number of unique integers that can be obtained.

Solution: To maximize the number of unique integers in the array, we should sort the array first. After sorting the array, we can iterate through it and count the number of occurrences of each integer using a hashmap. We can then create a prefix sum array for the count of each integer. This prefix sum array will help us in determining the number of unique integers that we can obtain by detonating k neighboring bombs.

We will start with the leftmost index of the prefix sum array. We will then consider detonating a bomb at the index i. If we detonate a bomb at index i, we will be able to remove all repetitions of the integer at index i. The number of unique integers that we can obtain after detonating a bomb at index i will be the difference between the current prefix sum at index i and the prefix sum at index i-k-1 (if i-k-1 is a valid index). If this difference is greater than the current number of unique integers, we can update our answer accordingly.

We will continue to move the detonation index i towards the right. At each index i, we will calculate the number of unique integers that we can obtain after detonating a bomb at index i. If this number is greater than the current answer, we will update our answer.

Finally, we return the maximum number of unique integers that we can obtain after detonating exactly k bombs.

Time Complexity: O(nlogn + n) where n is the length of the nums array. Sorting the array takes O(nlogn) time and iterating through it takes O(n) time.

Space Complexity: O(n) for the hashmap and prefix sum array.

Implementation:

def max_unique_integers(nums, k):
    nums.sort()
    count = {}
    for num in nums:
        if num not in count:
            count[num] = 0
        count[num] += 1
    prefix_sum = [0] * len(count)
    i = 0
    for num in count:
        prefix_sum[i] = count[num] + (prefix_sum[i-1] if i > 0 else 0)
        i += 1
    ans = 0
    for i in range(len(prefix_sum)):
        if i >= k:
            ans = max(ans, prefix_sum[i] - prefix_sum[i-k-1])
        else:
            ans = max(ans, prefix_sum[i])
    return ans

Example: Input: nums = [5,7,5,5,1,2,2,4], k = 2 Output: 4 Explanation: We can detonate bombs at indices 0 and 2 to obtain [1,2,4,7].

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