673. Number of Longest Increasing Subsequence

#week11

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.

Note: Length of the given array will be not exceed 2000 and the answer is guaranteed to be fit in 32-bit signed int.

分析

这个和平常的最长子序列的不同的点在于是要求该子序列的个数

因此需要在DP时再加一维用来存放个数

初始化每个状态的每个维都为1

状态变换：

if(dp[i].first == dp[j].first + 1)dp[i].second += dp[j].second;
if(dp[i].first < dp[j].first + 1)dp[i] = {dp[j].first + 1, dp[j].second};

题解

class Solution {
public:
    int findNumberOfLIS(vector<int>& nums) {
        int n = nums.size(), res = 0, max_len = 0;
        vector<pair<int,int>> dp(n,{1,1});            //dp[i]: {length, number of LIS which ends with nums[i]}
        for(int i = 0; i<n; i++){
            for(int j = 0; j <i ; j++){
                if(nums[i] > nums[j]){
                    if(dp[i].first == dp[j].first + 1)dp[i].second += dp[j].second;
                    if(dp[i].first < dp[j].first + 1)dp[i] = {dp[j].first + 1, dp[j].second};
                }
            }
            if(max_len == dp[i].first)res += dp[i].second;
            if(max_len < dp[i].first){
                max_len = dp[i].first;
                res = dp[i].second;
            }
        }
        return res;
    }
};