【LeetCode 673】 Number of Longest Increasing Subsequence

题目描述

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.

思路

动态规划，dp[i] 维护以数字i结尾的最长递增子序列长度。更新dp[i]时，维护paths[i]路径个数。

代码

class Solution {
public:
    int findNumberOfLIS(vector<int>& nums) {
        int n = nums.size();
        vector<int> dp(n+1, 1);
        vector<int> paths(n+1, 1);
        
        for (int i=2; i<=n; ++i) {
            for (int j=1; j<i; ++j) {
                if (nums[i-1] > nums[j-1]) {
                    if (dp[j] + 1 > dp[i]) {
                        dp[i] = dp[j] + 1;
                        paths[i] = paths[j];
                    }else if (dp[i] == dp[j] + 1) {
                        paths[i] += paths[j];
                    }
                }
            }
        }
        
        int ans = 0;
        auto it = max_element(dp.begin(), dp.end());
        for (int i=1; i<=n; ++i) {
            if (dp[i] == *it) {
                ans += paths[i];
            } 
        }
        return ans;
    }
};