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‎Problemset/0673-Number of Longest Increasing Subsequence/README.md

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# 673. Number of Longest Increasing Subsequence
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Given an integer array `nums`, return *the number of longest increasing subsequences*.
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**Notice** that the sequence has to be **strictly** increasing.
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#### Example 1:
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<pre>
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<strong>Input:</strong> nums = [1,3,5,4,7]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> The two longest increasing subsequences are [1, 3, 4, 7] and [1, 3, 5, 7].
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</pre>
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#### Example 2:
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<pre>
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<strong>Input:</strong> nums = [2,2,2,2,2]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong> The length of the longest increasing subsequence is 1, and there are 5 increasing subsequences of length 1, so output 5.
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</pre>
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#### Constraints:
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* `1 <= nums.length <= 2000`
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* <code>-10<sup>6</sup> <= nums[i] <= 10<sup>6</sup></code>
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## Solutions (Python)
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### 1. Solution
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```Python
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class Solution:
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def findNumberOfLIS(self, nums: List[int]) -> int:
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dp = [[[10000001, 0], [-1000001, 1]]]
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for num in nums:
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if dp[-1][-1][0] < num:
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dp.append([[1000001, 0]])
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i = bisect.bisect_left(dp, num, key=lambda x: x[-1][0])
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j = bisect.bisect_left(dp[i - 1][::-1], num, key=lambda x: x[0])
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count = dp[i][-1][1] + dp[i - 1][-1][1] - dp[i - 1][-j - 1][1]
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dp[i].append([num, count])
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return dp[-1][-1][1]
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```

‎Problemset/0673-Number of Longest Increasing Subsequence/README_CN.md

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# 673. 最长递增子序列的个数
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给定一个未排序的整数数组 `nums` ， *返回最长递增子序列的个数* 。
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**注意** 这个数列必须是 **严格** 递增的。
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#### 示例 1:
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<pre>
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<strong>输入:</strong> nums = [1,3,5,4,7]
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<strong>输出:</strong> 2
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<strong>解释:</strong> 有两个最长递增子序列，分别是 [1, 3, 4, 7] 和[1, 3, 5, 7]。
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</pre>
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#### 示例 2:
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<pre>
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<strong>输入:</strong> nums = [2,2,2,2,2]
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<strong>输出:</strong> 5
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<strong>解释:</strong> 最长递增子序列的长度是1，并且存在5个子序列的长度为1，因此输出5。
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</pre>
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#### 提示:
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* `1 <= nums.length <= 2000`
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* <code>-10<sup>6</sup> <= nums[i] <= 10<sup>6</sup></code>
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## 题解 (Python)
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### 1. 题解
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```Python
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class Solution:
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def findNumberOfLIS(self, nums: List[int]) -> int:
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dp = [[[10000001, 0], [-1000001, 1]]]
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for num in nums:
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if dp[-1][-1][0] < num:
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dp.append([[1000001, 0]])
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i = bisect.bisect_left(dp, num, key=lambda x: x[-1][0])
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j = bisect.bisect_left(dp[i - 1][::-1], num, key=lambda x: x[0])
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count = dp[i][-1][1] + dp[i - 1][-1][1] - dp[i - 1][-j - 1][1]
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dp[i].append([num, count])
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return dp[-1][-1][1]
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```

‎Problemset/0673-Number of Longest Increasing Subsequence/Solution.py

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class Solution:
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def findNumberOfLIS(self, nums: List[int]) -> int:
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dp = [[[10000001, 0], [-1000001, 1]]]
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for num in nums:
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if dp[-1][-1][0] < num:
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dp.append([[1000001, 0]])
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i = bisect.bisect_left(dp, num, key=lambda x: x[-1][0])
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j = bisect.bisect_left(dp[i - 1][::-1], num, key=lambda x: x[0])
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count = dp[i][-1][1] + dp[i - 1][-1][1] - dp[i - 1][-j - 1][1]
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dp[i].append([num, count])
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return dp[-1][-1][1]

‎README.md

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[670][670l] |[Maximum Swap][670] |![rs]
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[671][671l] |[Second Minimum Node In a Binary Tree][671] |![py]
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[672][672l] |[Bulb Switcher II][672] |![rs]
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[673][673l] |[Number of Longest Increasing Subsequence][673] |![py]
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[674][674l] |[Longest Continuous Increasing Subsequence][674] |![rs]
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[675][675l] |[Cut Off Trees for Golf Event][675] |![rs]
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[680][680l] |[Valid Palindrome II][680] |![py]
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[670]:Problemset/0670-Maximum%20Swap/README.md#670-maximum-swap
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[671]:Problemset/0671-Second%20Minimum%20Node%20In%20a%20Binary%20Tree/README.md#671-second-minimum-node-in-a-binary-tree
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[672]:Problemset/0672-Bulb%20Switcher%20II/README.md#672-bulb-switcher-ii
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[673]:Problemset/0673-Number%20of%20Longest%20Increasing%20Subsequence/README.md#673-number-of-longest-increasing-subsequence
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[674]:Problemset/0674-Longest%20Continuous%20Increasing%20Subsequence/README.md#674-longest-continuous-increasing-subsequence
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[675]:Problemset/0675-Cut%20Off%20Trees%20for%20Golf%20Event/README.md#675-cut-off-trees-for-golf-event
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[680]:Problemset/0680-Valid%20Palindrome%20II/README.md#680-valid-palindrome-ii
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[670l]:https://leetcode.com/problems/maximum-swap/
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[671l]:https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/
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[672l]:https://leetcode.com/problems/bulb-switcher-ii/
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[673l]:https://leetcode.com/problems/number-of-longest-increasing-subsequence/
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[674l]:https://leetcode.com/problems/longest-continuous-increasing-subsequence/
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[675l]:https://leetcode.com/problems/cut-off-trees-for-golf-event/
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[677l]:https://leetcode.com/problems/map-sum-pairs/

‎README_CN.md

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[670][670l] |[最大交换][670] |![rs]
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[671][671l] |[二叉树中第二小的节点][671] |![py]
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[672][672l] |[灯泡开关 Ⅱ][672] |![rs]
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[673][673l] |[最长递增子序列的个数][673] |![py]
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[674][674l] |[最长连续递增序列][674] |![rs]
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[675][675l] |[为高尔夫比赛砍树][675] |![rs]
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[680][680l] |[验证回文字符串 Ⅱ][680] |![py]
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[670]:Problemset/0670-Maximum%20Swap/README_CN.md#670-最大交换
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[671]:Problemset/0671-Second%20Minimum%20Node%20In%20a%20Binary%20Tree/README_CN.md#671-二叉树中第二小的节点
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[672]:Problemset/0672-Bulb%20Switcher%20II/README_CN.md#672-灯泡开关-Ⅱ
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[673]:Problemset/0673-Number%20of%20Longest%20Increasing%20Subsequence/README_CN.md#673-最长递增子序列的个数
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[674]:Problemset/0674-Longest%20Continuous%20Increasing%20Subsequence/README_CN.md#674-最长连续递增序列
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[675]:Problemset/0675-Cut%20Off%20Trees%20for%20Golf%20Event/README_CN.md#675-为高尔夫比赛砍树
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[680]:Problemset/0680-Valid%20Palindrome%20II/README_CN.md#680-验证回文字符串-ii
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[670l]:https://leetcode.cn/problems/maximum-swap/
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[671l]:https://leetcode.cn/problems/second-minimum-node-in-a-binary-tree/
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[672l]:https://leetcode.cn/problems/bulb-switcher-ii/
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[673l]:https://leetcode.cn/problems/number-of-longest-increasing-subsequence/
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[674l]:https://leetcode.cn/problems/longest-continuous-increasing-subsequence/
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[675l]:https://leetcode.cn/problems/cut-off-trees-for-golf-event/
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[677l]:https://leetcode.cn/problems/map-sum-pairs/

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