[LeetCode] Minimum Size Subarray Sum 最短子数组之和
2015-05-13 22:37
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Given an array of n positive integers and a positive integer s, find the minimal length of a subarray of which the sum ≥ s. If there isn't one, return 0 instead.
For example, given the array
the subarray
click to show more practice.
More practice:
If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log n).
Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.
这道题给定了我们一个数字,让我们求子数组之和大于等于给定值的最小长度,跟之前那道 Maximum Subarray 最大子数组有些类似,并且题目中要求我们实现O(n)和O(nlgn)两种解法,那么我们先来看O(n)的解法,我们需要定义两个指针left和right,分别记录子数组的左右的边界位置,然后我们让right向右移,直到子数组和大于等于给定值或者right达到数组末尾,此时我们更新最短距离,并且将left像右移一位,然后再sum中减去移去的值,然后重复上面的步骤,直到right到达末尾,且left到达临界位置,即要么到达边界,要么再往右移动,和就会小于给定值。代码如下:
解法一
下面我们再来看看O(nlgn)的解法,这个解法要用到二分查找法,思路是,我们建立一个比原数组长一位的sums数组,其中sums[i]表示nums数组中[0, i - 1]的和,然后我们对于sums中每一个值sums[i],用二分查找法找到子数组的右边界位置,使该子数组之和大于sums[i] + s,然后我们更新最短长度的距离即可。代码如下:
解法二
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For example, given the array
[2,3,1,2,4,3]and
s = 7,
the subarray
[4,3]has the minimal length under the problem constraint.
click to show more practice.
More practice:
If you have figured out the O(n) solution, try coding another solution of which the time complexity is O(n log n).
Credits:
Special thanks to @Freezen for adding this problem and creating all test cases.
这道题给定了我们一个数字,让我们求子数组之和大于等于给定值的最小长度,跟之前那道 Maximum Subarray 最大子数组有些类似,并且题目中要求我们实现O(n)和O(nlgn)两种解法,那么我们先来看O(n)的解法,我们需要定义两个指针left和right,分别记录子数组的左右的边界位置,然后我们让right向右移,直到子数组和大于等于给定值或者right达到数组末尾,此时我们更新最短距离,并且将left像右移一位,然后再sum中减去移去的值,然后重复上面的步骤,直到right到达末尾,且left到达临界位置,即要么到达边界,要么再往右移动,和就会小于给定值。代码如下:
解法一
// O(n) class Solution { public: int minSubArrayLen(int s, vector<int>& nums) { if (nums.empty()) return 0; int left = 0, right = 0, sum = 0, len = nums.size(), res = len + 1; while (right < len) { while (sum < s && right < len) { sum += nums[right++]; } while (sum >= s) { res = min(res, right - left); sum -= nums[left++]; } } return res == len + 1 ? 0 : res; } };
下面我们再来看看O(nlgn)的解法,这个解法要用到二分查找法,思路是,我们建立一个比原数组长一位的sums数组,其中sums[i]表示nums数组中[0, i - 1]的和,然后我们对于sums中每一个值sums[i],用二分查找法找到子数组的右边界位置,使该子数组之和大于sums[i] + s,然后我们更新最短长度的距离即可。代码如下:
解法二
// O(nlgn) class Solution { public: int minSubArrayLen(int s, vector<int>& nums) { int len = nums.size(), sums[len + 1] = {0}, res = len + 1; for (int i = 1; i < len + 1; ++i) sums[i] = sums[i - 1] + nums[i - 1]; for (int i = 0; i < len + 1; ++i) { int right = searchRight(i + 1, len, sums[i] + s, sums); if (right == len + 1) break; if (res > right - i) res = right - i; } return res == len + 1 ? 0 : res; } int searchRight(int left, int right, int key, int sums[]) { while (left <= right) { int mid = (left + right) / 2; if (sums[mid] >= key) right = mid - 1; else left = mid + 1; } return left; } };
LeetCode All in One 题目讲解汇总(持续更新中...)
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