Largest Sum Of Averages Problem


Description

LeetCode Problem 813.

You are given an integer array nums and an integer k. You can partition the array into at most k non-empty adjacent subarrays. The score of a partition is the sum of the averages of each subarray.

Note that the partition must use every integer in nums, and that the score is not necessarily an integer. Return the maximum score you can achieve of all the possible partitions. Answers within 10^-6 of the actual answer will be accepted.

Example 1:

1
2
3
4
5
6
Input: nums = [9,1,2,3,9], k = 3
Output: 20.00000
Explanation: 
The best choice is to partition nums into [9], [1, 2, 3], [9]. The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20.
We could have also partitioned nums into [9, 1], [2], [3, 9], for example.
That partition would lead to a score of 5 + 2 + 6 = 13, which is worse.

Example 2:

1
2
Input: nums = [1,2,3,4,5,6,7], k = 4
Output: 20.50000

Constraints:

  • 1 <= nums.length <= 100
  • 1 <= nums[i] <= 10^4
  • 1 <= k <= nums.length


Sample C++ Code

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
class Solution {
public:
    int n;
    vector<int> pre;
    double dfs(int curr, int k, vector<int>&nums, vector<vector<double>>&dp) {
        if (curr == n && k != 0) 
            return 0;
        if (k == 0) {
            return curr != 0 ? (double)(pre[n-1]-pre[curr-1]) / (n-curr) : (double)(pre[n-1]) / n;
        }
        if (dp[curr][k] != -1) 
            return dp[curr][k];
        double ans = 0, sum = 0;
        for (int i = curr; i < n - k; i++) {
            sum += nums[i];
            ans = max(ans, (double)sum / (i+1-curr) + dfs(i+1, k-1, nums, dp));
        }
        return dp[curr][k] = ans;
    }
    double largestSumOfAverages(vector<int>& nums, int k) {
        n = nums.size();
        pre = nums;
        for (int i = 1; i < n; i++) 
            pre[i] += pre[i-1];
        vector<vector<double>> dp(n, vector<double>(k, -1));
        return dfs(0, k-1, nums, dp);
    }
};




Related Posts

Valid Permutations For DI Sequence Problem

LeetCode 903. You are given a string s of length...

Tallest Billboard Problem

LeetCode 956. You are installing a billboard and want it...

Sum Of Subarray Minimums Problem

LeetCode 907. Given an array of integers arr, find the...

Stone Game Problem

LeetCode 877. Alice and Bob play a game with piles...

Split Array With Same Average Problem

LeetCode 805. You are given an integer array nums.

Soup Servings Problem

LeetCode 808. There are two types of soup, type A...