Add LongestIncreasingSubsequence.py

Python/Dynamic Programming/LongestIncreasingSubsequence.py

@@ -0,0 +1,17 @@
+"""
+Given an unsorted array of integers, this algorithm finds the length of the longest increasing subsequence.
+"""
+# nums is the input array which may be unsorted
+def lengthOfLIS(nums):
+    if not nums:
+        return 0
+    dp = [1 for i in range(len(nums))]    # the dp array
+    longest = 1    # variable to keep track of the longest increasing subsequence at every iteration
+    for i in range(1, len(nums)):
+        for j in range(i):
+            if nums[j] < nums[i]:
+                dp[i] = max(dp[i], dp[j] + 1)
+        longest = max(dp[i], longest)    # check if the length of LIS has changed
+    return longest
+
+print(lengthOfLIS([10,9,2,5,3,7,101,18]))