leetcode 376. Wiggle Subsequence
2016-08-26 10:34
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/* leetcode 376. Wiggle Subsequence A sequence of numbers is called a wiggle sequence if the differences between successive numbers strictly alternate between positive and negative. The first difference (if one exists) may be either positive or negative. A sequence with fewer than two elements is trivially a wiggle sequence. For example, [1,7,4,9,2,5] is a wiggle sequence because the differences (6,-3,5,-7,3) are alternately positive and negative. In contrast, [1,4,7,2,5] and [1,7,4,5,5] are not wiggle sequences, the first because its first two differences are positive and the second because its last difference is zero. Given a sequence of integers, return the length of the longest subsequence that is a wiggle sequence. A subsequence is obtained by deleting some number of elements (eventually, also zero) from the original sequence, leaving the remaining elements in their original order. Examples: Input: [1,7,4,9,2,5] Output: 6 The entire sequence is a wiggle sequence. Input: [1,17,5,10,13,15,10,5,16,8] Output: 7 There are several subsequences that achieve this length. One is [1,17,10,13,10,16,8]. Input: [1,2,3,4,5,6,7,8,9] Output: 2 Follow up: Can you do it in O(n) time? 解题思路:dp 用两个数组up和down,up[i],down[i]分别表示以nums[i]结尾的上升或下降的最长序列长度 递推关系有如下几种: 1、nums[i] > nums[i - 1] up[i] = down[i - 1] + 1; down[i] = down[i - 1]; 2、nums[i] < nums[i - 1] up[i] = up[i - 1]; down[i] = up[i - 1] + 1; 3、相等: up[i] = up[i - 1]; down[i] = down[i - 1]; */ #include <iostream> #include <string> #include <vector> #include <algorithm> using namespace std; class Solution { public: int wiggleMaxLength(vector<int>& nums) { int length = nums.size(); if (length == 0 || length == 1) return length; vector<int> up(nums.size(), 0); vector<int> down(nums.size(), 0); up[0] = down[0] = 1; //初始条件 for (int i = 1; i < length; ++i) { if (nums[i] > nums[i - 1]) { up[i] = down[i - 1] + 1; down[i] = down[i - 1]; } else if (nums[i] < nums[i - 1]) { up[i] = up[i - 1]; down[i] = up[i - 1] + 1; } else { up[i] = up[i - 1]; down[i] = down[i - 1]; } //cout << up[i] << " " << down[i] << endl; } return max(up[length-1], down[length-1]); } }; void test() { vector<int> nums1{ 1,7,4,9,2,5 }; vector<int> nums2{ 1,17,5,10,13,15,10,5,16,8 }; vector<int> nums3{ 1,2,3,4,5,6,7,8,9 }; Solution sol; cout << sol.wiggleMaxLength(nums1) << endl; cout << sol.wiggleMaxLength(nums2) << endl; cout << sol.wiggleMaxLength(nums3) << endl; } int main() { test(); return 0; }
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