689. Maximum sum of 3 non-overlapping subarrays three non-coincident arrays maximum value

[Copy question]:

In a given array nums of positive integers, find three non-overlapping subarrays with maximum sum.

Each subarray would be k is of size, and we want to maximize the sum of all 3*k entries.

Return The result as a list of indices representing the starting position of each interval (0-indexed). If There is multiple answers, return the lexicographically smallest one.

Example:

Input: [1,2,1,2,6,7,5,1], 2Output: [0, 3, 5]explanation:subarrays [1, 2], [2, 6], [7, 5] correspond to the starting Indic Es [0, 3, 5]. We could has also taken [2, 1], but a answer of [1, 3, 5] would be lexicographically larger.

[Brute force solution]:

Time Analysis:

Spatial Analysis:

[After optimization]:

Time Analysis:

Spatial Analysis:

[Wonderful output CONDITIONS]:

[Wonderful corner case]:

The "First I" is initialized to "item I", it is convenient to do the difference directly

 for (int i = 1; I <= n; i++) {            = sums[i-1] + nums[i-1];        }

[Thinking questions]:

Do not know why to use DP: each time to save the previous set of state, and then a forward update and parity.

Available when a set of arrays that are fixed to K-length is obtained.

// sum = Current Group and + previous Group and = Last sum of this group-DP summation before first and + of the group (starting with J-k) int cursum = sums[j]-sums[j-k] + dp[i-1][j-k];

[English data structure or algorithm, why not other data structures or algorithms]:

The results are stored in the DP array and can be extracted by continuously entering index:

int index = n;          for (int i = 2; I >= 0; i--) {            = pos[i + 1][index];            SYSTEM.OUT.PRINTLN ("index =" +index);            System.out.println ("res[i] = pos[i + 1][index] =" +res[i]);                         = Res[i];            SYSTEM.OUT.PRINTLN ("index =" +index);            System.out.println ("----------------");                   }

[a sentence of thought]:

[input]: null: Normal: Large: Extra Small: Special cases handled in the program: abnormal conditions (unreasonable input):

[Drawing]:

[One brush]:

[Two brushes]:

[Three brushes]:

[Four brushes]:

[Five brushes]:

[Results of five-minute visual debug]:

[Summary]:

[Complexity]:time Complexity:o () Space complexity:o ()

[Algorithmic thinking: Iterative/recursive/split/greedy]:

[Key templating code]:

[Other solutions]:

[Follow up]:

[The problem given by the LC becomes variable]:

[Code Style]:

[Whether to write this type of driver Funcion code for the first time]:

689. Maximum sum of 3 non-overlapping subarrays three non-coincident arrays maximum value