Create number_of_longest_increasing_subsequence.py

dynamic_programming/number_of_longest_increasing_subsequence.py

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+"""
+Leetcode Problem:673. Number of Longest Increasing Subsequence
+Link: https://leetcode.com/problems/number-of-longest-increasing-subsequence/description/
+
+Given an integer array nums, return the number of longest increasing subsequences.
+Notice that the sequence has to be strictly increasing.
+
+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
+The answer is guaranteed to fit inside a 32-bit integer.
+"""
+
+
+def findNumberOfLIS(nums):
+    n = len(nums)
+    if n == 0:
+        return 0
+
+    length = [1] * n
+    count = [1] * n
+
+    for i in range(n):
+        for j in range(i):
+            if nums[j] < nums[i]:
+                if length[j] + 1 > length[i]:
+                    length[i] = length[j] + 1
+                    count[i] = count[j]
+                elif length[j] + 1 == length[i]:
+                    count[i] += count[j]
+
+    max_len = max(length)
+    return sum(c for l, c in zip(length, count) if l == max_len)
+
+
+# For testing...
+n = int(input())
+nums = list(map(int, input().split()))
+print(findNumberOfLIS(nums))