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2841. Maximum Sum of Almost Unique Subarray

Description

You are given an integer array nums and two positive integers m and k.

Return the maximum sum out of all almost unique subarrays of length k of nums. If no such subarray exists, return 0.

A subarray of nums is almost unique if it contains at least m distinct elements.

A subarray is a contiguous non-empty sequence of elements within an array.

 

Example 1:

Input: nums = [2,6,7,3,1,7], m = 3, k = 4
Output: 18
Explanation: There are 3 almost unique subarrays of size k = 4. These subarrays are [2, 6, 7, 3], [6, 7, 3, 1], and [7, 3, 1, 7]. Among these subarrays, the one with the maximum sum is [2, 6, 7, 3] which has a sum of 18.

Example 2:

Input: nums = [5,9,9,2,4,5,4], m = 1, k = 3
Output: 23
Explanation: There are 5 almost unique subarrays of size k. These subarrays are [5, 9, 9], [9, 9, 2], [9, 2, 4], [2, 4, 5], and [4, 5, 4]. Among these subarrays, the one with the maximum sum is [5, 9, 9] which has a sum of 23.

Example 3:

Input: nums = [1,2,1,2,1,2,1], m = 3, k = 3
Output: 0
Explanation: There are no subarrays of size k = 3 that contain at least m = 3 distinct elements in the given array [1,2,1,2,1,2,1]. Therefore, no almost unique subarrays exist, and the maximum sum is 0.

 

Constraints:

  • 1 <= nums.length <= 2 * 104
  • 1 <= m <= k <= nums.length
  • 1 <= nums[i] <= 109

Solutions

Solution 1: Sliding Window + Hash Table

We can traverse the array $nums$, maintain a window of size $k$, use a hash table $cnt$ to count the occurrence of each element in the window, and use a variable $s$ to sum all elements in the window. If the number of different elements in $cnt$ is greater than or equal to $m$, then we update the answer $ans = \max(ans, s)$.

After the traversal ends, return the answer.

The time complexity is $O(n)$, and the space complexity is $O(k)$. Here, $n$ is the length of the array.

  • class Solution {
    public long maxSum(List<Integer> nums, int m, int k) {
        Map<Integer, Integer> cnt = new HashMap<>();
        int n = nums.size();
        long s = 0;
        for (int i = 0; i < k; ++i) {
            cnt.merge(nums.get(i), 1, Integer::sum);
            s += nums.get(i);
        }
        long ans = 0;
        if (cnt.size() >= m) {
            ans = s;
        }
        for (int i = k; i < n; ++i) {
            cnt.merge(nums.get(i), 1, Integer::sum);
            if (cnt.merge(nums.get(i - k), -1, Integer::sum) == 0) {
                cnt.remove(nums.get(i - k));
            }
            s += nums.get(i) - nums.get(i - k);
            if (cnt.size() >= m) {
                ans = Math.max(ans, s);
            }
        }
        return ans;
    }
}

  • class Solution {
public:
    long long maxSum(vector<int>& nums, int m, int k) {
        unordered_map<int, int> cnt;
        long long s = 0;
        int n = nums.size();
        for (int i = 0; i < k; ++i) {
            cnt[nums[i]]++;
            s += nums[i];
        }
        long long ans = cnt.size() >= m ? s : 0;
        for (int i = k; i < n; ++i) {
            cnt[nums[i]]++;
            if (--cnt[nums[i - k]] == 0) {
                cnt.erase(nums[i - k]);
            }
            s += nums[i] - nums[i - k];
            if (cnt.size() >= m) {
                ans = max(ans, s);
            }
        }
        return ans;
    }
};

  • class Solution:
    def maxSum(self, nums: List[int], m: int, k: int) -> int:
        cnt = Counter(nums[:k])
        s = sum(nums[:k])
        ans = 0
        if len(cnt) >= m:
            ans = s
        for i in range(k, len(nums)):
            cnt[nums[i]] += 1
            cnt[nums[i - k]] -= 1
            s += nums[i] - nums[i - k]
            if cnt[nums[i - k]] == 0:
                cnt.pop(nums[i - k])
            if len(cnt) >= m:
                ans = max(ans, s)
        return ans


  • func maxSum(nums []int, m int, k int) int64 {
	cnt := map[int]int{}
	var s int64
	for _, x := range nums[:k] {
		cnt[x]++
		s += int64(x)
	}
	var ans int64
	if len(cnt) >= m {
		ans = s
	}
	for i := k; i < len(nums); i++ {
		cnt[nums[i]]++
		cnt[nums[i-k]]--
		if cnt[nums[i-k]] == 0 {
			delete(cnt, nums[i-k])
		}
		s += int64(nums[i]) - int64(nums[i-k])
		if len(cnt) >= m {
			ans = max(ans, s)
		}
	}
	return ans
}

  • function maxSum(nums: number[], m: number, k: number): number {
    const n = nums.length;
    const cnt: Map<number, number> = new Map();
    let s = 0;
    for (let i = 0; i < k; ++i) {
        cnt.set(nums[i], (cnt.get(nums[i]) || 0) + 1);
        s += nums[i];
    }
    let ans = cnt.size >= m ? s : 0;
    for (let i = k; i < n; ++i) {
        cnt.set(nums[i], (cnt.get(nums[i]) || 0) + 1);
        cnt.set(nums[i - k], cnt.get(nums[i - k])! - 1);
        if (cnt.get(nums[i - k]) === 0) {
            cnt.delete(nums[i - k]);
        }
        s += nums[i] - nums[i - k];
        if (cnt.size >= m) {
            ans = Math.max(ans, s);
        }
    }
    return ans;
}


  • public class Solution {
    public long MaxSum(IList<int> nums, int m, int k) {
        Dictionary<int, int> cnt = new Dictionary<int, int>();
        int n = nums.Count;
        long s = 0;
        
        for (int i = 0; i < k; ++i) {
            if (!cnt.ContainsKey(nums[i])) {
                cnt[nums[i]] = 1;
            }
            else {
                cnt[nums[i]]++;
            }
            s += nums[i];
        }
        
        long ans = cnt.Count >= m ? s : 0;
        
        for (int i = k; i < n; ++i) {
            if (!cnt.ContainsKey(nums[i])) {
                cnt[nums[i]] = 1;
            }
            else {
                cnt[nums[i]]++;
            }
            if (cnt.ContainsKey(nums[i - k])) {
                cnt[nums[i - k]]--;
                if (cnt[nums[i - k]] == 0) {
                    cnt.Remove(nums[i - k]);
                }
            }
            
            s += nums[i] - nums[i - k];
            
            if (cnt.Count >= m) {
                ans = Math.Max(ans, s);
            }
        }
        
        return ans;
    }
}

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