README_EN.md

2551. Put Marbles in Bags

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Description

You have k bags. You are given a 0-indexed integer array weights where weights[i] is the weight of the ith marble. You are also given the integer k.

Divide the marbles into the k bags according to the following rules:

• No bag is empty.
• If the ith marble and jth marble are in a bag, then all marbles with an index between the ith and jth indices should also be in that same bag.
• If a bag consists of all the marbles with an index from i to j inclusively, then the cost of the bag is weights[i] + weights[j].

The score after distributing the marbles is the sum of the costs of all the k bags.

Return the difference between the maximum and minimum scores among marble distributions.

 

Example 1:

Input: weights = [1,3,5,1], k = 2
Output: 4
Explanation: 
The distribution [1],[3,5,1] results in the minimal score of (1+1) + (3+1) = 6. 
The distribution [1,3],[5,1], results in the maximal score of (1+3) + (5+1) = 10. 
Thus, we return their difference 10 - 6 = 4.

Example 2:

Input: weights = [1, 3], k = 2
Output: 0
Explanation: The only distribution possible is [1],[3]. 
Since both the maximal and minimal score are the same, we return 0.

 

Constraints:

• 1 <= k <= weights.length <= 105
• 1 <= weights[i] <= 109

Solutions

Python3

class Solution:
    def putMarbles(self, weights: List[int], k: int) -> int:
        arr = sorted(a + b for a, b in pairwise(weights))
        return sum(arr[len(arr) - k + 1 :]) - sum(arr[: k - 1])

Java

class Solution {
    public long putMarbles(int[] weights, int k) {
        int n = weights.length;
        int[] arr = new int[n - 1];
        for (int i = 0; i < n - 1; ++i) {
            arr[i] = weights[i] + weights[i + 1];
        }
        Arrays.sort(arr);
        long ans = 0;
        for (int i = 0; i < k - 1; ++i) {
            ans -= arr[i];
            ans += arr[n - 2 - i];
        }
        return ans;
    }
}

C++

class Solution {
public:
    long long putMarbles(vector<int>& weights, int k) {
        int n = weights.size();
        vector<int> arr(n - 1);
        for (int i = 0; i < n - 1; ++i) {
            arr[i] = weights[i] + weights[i + 1];
        }
        sort(arr.begin(), arr.end());
        long long ans = 0;
        for (int i = 0; i < k - 1; ++i) {
            ans -= arr[i];
            ans += arr[n - 2 - i];
        }
        return ans;
    }
};

Go

func putMarbles(weights []int, k int) (ans int64) {
	n := len(weights)
	arr := make([]int, n-1)
	for i, w := range weights[:n-1] {
		arr[i] = w + weights[i+1]
	}
	sort.Ints(arr)
	for i := 0; i < k-1; i++ {
		ans += int64(arr[n-2-i] - arr[i])
	}
	return
}

TypeScript

function putMarbles(weights: number[], k: number): number {
    const n = weights.length;
    const arr: number[] = [];
    for (let i = 0; i < n - 1; ++i) {
        arr.push(weights[i] + weights[i + 1]);
    }
    arr.sort((a, b) => a - b);
    let ans = 0;
    for (let i = 0; i < k - 1; ++i) {
        ans += arr[n - i - 2] - arr[i];
    }
    return ans;
}

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