In a given array nums
of positive integers, find three non-overlapping subarrays with maximum sum.
Each subarray will be of size k
, 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 are multiple answers, return the lexicographically smallest one.
Example:
Input: [1,2,1,2,6,7,5,1], 2 Output: [0, 3, 5] Explanation: Subarrays [1, 2], [2, 6], [7, 5] correspond to the starting indices [0, 3, 5]. We could have also taken [2, 1], but an answer of [1, 3, 5] would be lexicographically larger.
Note:
nums.length
will be between 1 and 20000.nums[i]
will be between 1 and 65535.k
will be between 1 and floor(nums.length / 3).
给一个由正数组成的数组,找三个长度为k的不重叠的子数组,使得三个子数组的数字之和最大。
解法: DP,思路类似于123. Best Time to Buy and Sell Stock III,先分别从左和右两个方向求出每一个位置i之前的长度为k的元素和最大值,这样做的好处是之后想要得到某一位置的最大和时能马上知道。然后在用一个循环找出三段的最大和。
Java:
class Solution { public int[] maxSumOfThreeSubarrays(int[] nums, int k) { int n = nums.length, maxsum = 0; int[] sum = new int[n+1], posLeft = new int[n], posRight = new int[n], ans = new int[3]; for (int i = 0; i < n; i++) sum[i+1] = sum[i]+nums[i]; // DP for starting index of the left max sum interval for (int i = k, tot = sum[k]-sum[0]; i < n; i++) { if (sum[i+1]-sum[i+1-k] > tot) { posLeft[i] = i+1-k; tot = sum[i+1]-sum[i+1-k]; } else posLeft[i] = posLeft[i-1]; } // DP for starting index of the right max sum interval // caution: the condition is ">= tot" for right interval, and "> tot" for left interval posRight[n-k] = n-k; for (int i = n-k-1, tot = sum[n]-sum[n-k]; i >= 0; i--) { if (sum[i+k]-sum[i] >= tot) { posRight[i] = i; tot = sum[i+k]-sum[i]; } else posRight[i] = posRight[i+1]; } // test all possible middle interval for (int i = k; i <= n-2*k; i++) { int l = posLeft[i-1], r = posRight[i+k]; int tot = (sum[i+k]-sum[i]) + (sum[l+k]-sum[l]) + (sum[r+k]-sum[r]); if (tot > maxsum) { maxsum = tot; ans[0] = l; ans[1] = i; ans[2] = r; } } return ans; } }
Python:
class Solution(object): def maxSumOfThreeSubarrays(self, nums, k): """ :type nums: List[int] :type k: int :rtype: List[int] """ n = len(nums) accu = [0] for num in nums: accu.append(accu[-1]+num) left_pos = [0] * n total = accu[k]-accu[0] for i in xrange(k, n): if accu[i+1]-accu[i+1-k] > total: left_pos[i] = i+1-k total = accu[i+1]-accu[i+1-k] else: left_pos[i] = left_pos[i-1] right_pos = [n-k] * n total = accu[n]-accu[n-k] for i in reversed(xrange(n-k)): if accu[i+k]-accu[i] > total: right_pos[i] = i; total = accu[i+k]-accu[i] else: right_pos[i] = right_pos[i+1] result, max_sum = [], 0 for i in xrange(k, n-2*k+1): left, right = left_pos[i-1], right_pos[i+k] total = (accu[i+k]-accu[i]) + (accu[left+k]-accu[left]) + (accu[right+k]-accu[right]) if total > max_sum: max_sum = total result = [left, i, right] return result
C++:
class Solution { public: vector<int> maxSumOfThreeSubarrays(vector<int>& nums, int k) { int n = nums.size(), maxsum = 0; vector<int> sum = {0}, posLeft(n, 0), posRight(n, n-k), ans(3, 0); for (int i:nums) sum.push_back(sum.back()+i); // DP for starting index of the left max sum interval for (int i = k, tot = sum[k]-sum[0]; i < n; i++) { if (sum[i+1]-sum[i+1-k] > tot) { posLeft[i] = i+1-k; tot = sum[i+1]-sum[i+1-k]; } else posLeft[i] = posLeft[i-1]; } // DP for starting index of the right max sum interval // caution: the condition is ">= tot" for right interval, and "> tot" for left interval for (int i = n-k-1, tot = sum[n]-sum[n-k]; i >= 0; i--) { if (sum[i+k]-sum[i] >= tot) { posRight[i] = i; tot = sum[i+k]-sum[i]; } else posRight[i] = posRight[i+1]; } // test all possible middle interval for (int i = k; i <= n-2*k; i++) { int l = posLeft[i-1], r = posRight[i+k]; int tot = (sum[i+k]-sum[i]) + (sum[l+k]-sum[l]) + (sum[r+k]-sum[r]); if (tot > maxsum) { maxsum = tot; ans = {l, i, r}; } } return ans; } };
类似题目:
[LeetCode] 123. Best Time to Buy and Sell Stock III 买卖股票的最佳时间 III
原文地址:https://www.cnblogs.com/lightwindy/p/9692653.html
时间: 2024-10-07 21:43:31