[673. Number of Longest Increasing Subsequence](https://leetcode.com/problems/number-of-longest-increasing-subsequence/)

### 題目描述

Given an integer array `nums`, return *the number of longest increasing subsequences*.

**Notice** that the sequence has to be **strictly** increasing.

### 範例

**Example 1:**

Input: nums = [1,3,5,4,7]
Output: 2
Explanation: The two longest increasing subsequences are [1, 3, 4, 7] and [1, 3, 5, 7].

**Example 2:**

Input: nums = [2,2,2,2,2]
Output: 5
Explanation: The length of the longest increasing subsequence is 1, and there are 5 increasing subsequences of length 1, so output 5.

**Constraints**:

* 1 <= `nums.length` <= 2000
* -10^6^ <= `nums[i]` <= 10^6^

### 解答
#### Python

class Solution:
    def findNumberOfLIS(self, nums: List[int]) -> int:
        N = len(nums)
        d = [1] * N
        c = [1] * N
        for j in range(1, N):
            for i in range(j):
                if nums[i] < nums[j]:
                    if d[i] + 1 > d[j]:
                        d[j] = d[i] + 1
                        c[j] = c[i]
                    elif d[i] + 1 == d[j]:
                        c[j] += c[i]
        L = max(d)
        return sum(c[i] for i in range(N) if d[i] == L)

> [name=Yen-Chi Chen][time=Fri, Jul 21, 2023]

### Reference

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