标签：最长递增子序列 find sort 题目 style 数组 大于 length seq
Given an unsorted array of integers, find the number of longest increasing subsequence.
Example 1:
Input: [1,3,5,4,7] Output: 2 Explanation: The two longest increasing subsequence are [1, 3, 4, 7] and [1, 3, 5, 7].
Example 2:
Input: [2,2,2,2,2] Output: 5 Explanation: The length of longest continuous increasing subsequence is 1, and there are 5 subsequences‘ length is 1, so output 5.
求出最长递增子序列的个数，我们使用lens[i]表示以nums[i]为结尾的递增子序列中元素的个数也就是长度，以time[i]表示以nums[i]为结尾的递增子序列出现的次数，遍历nums数组，维护这两个数组。
遍历nums[i]这个元素，都要和i前面的元素进行比较(用j进行遍历)，如果nums[i]大于nums[j]，意味着nums[i]可以拼接到nums[j]后面，产生一个更长的子序列，如果lens[i] < lens[j] +1，更新lens数组lens[i] = lens[j]+1，同时times[i] = times[j]。
如果lens[i]恰好等于lens[j] +1，意味着此时已经有和当前长度相同的子序列了，我们要更新times[i] += times[j]，因为以nums[i]为结尾的子序列(长度为lens[i])已经出现过了，我们要加上出现的次数。
最后统计最大长度出现的次数，返回答案即可。
C++
class Solution { public: int findNumberOfLIS(vector<int>& nums) { auto lens = vector<int>(nums.size(), 1); auto times = vector<int>(nums.size(), 1); for(int i = 1; i < nums.size(); ++i){ for(int j = 0; j < i; ++j){ if(nums[j] >= nums[i]) continue; if(lens[j] + 1 > lens[i]){ lens[i] = lens[j] + 1; times[i] = times[j]; } else if(lens[j] + 1 == lens[i]) times[i] += times[j]; } } int maxLen = 0; int res = 0; for(int i = 0; i < lens.size(); ++i){ if(maxLen < lens[i]){ maxLen = lens[i]; res = times[i]; } else if(lens[i] == maxLen) res += times[i]; } return res; } };
Java
class Solution { public int findNumberOfLIS(int[] nums) { if(nums.length == 0) return 0; int[] lens = new int[nums.length]; int[] times = new int[nums.length]; int maxLen = 1; for(int i = 0; i < nums.length; ++i){ lens[i] = 1; times[i] = 1; for(int j = 0; j < i; ++j){ if(nums[i] <= nums[j]) continue; if(lens[j] + 1 > lens[i]){ lens[i] = lens[j] + 1; times[i] = times[j]; } else if(lens[j] + 1 == lens[i]){ times[i] += times[j]; } } maxLen = Math.max(maxLen, lens[i]); } int res = 0; for(int i = 0; i < lens.length; ++i){ if(lens[i] == maxLen) res += times[i]; } return res; } }
LeetCode 673. Number of Longest Increasing Subsequence 最长递增子序列的个数 (C++/Java)
标签：最长递增子序列 find sort 题目 style 数组 大于 length seq
原文地址：https://www.cnblogs.com/silentteller/p/12206983.html
