pushin new solution

Microsoft_Problems/Microsoft_Problem_07.py

@@ -0,0 +1,42 @@
+"""
+This problem was asked by Microsoft.
+
+Given an array of numbers, find the length of the longest increasing subsequence in the array. The subsequence does not necessarily have to be contiguous.
+
+For example, given the array [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15], the longest increasing subsequence has length 6: it is 0, 2, 6, 9, 11, 15.
+"""
+cache = None
+
+
+def get_subsequence(arr, start):
+    if start == len(arr):
+        return 0
+
+    current = arr[start]
+    length = 1
+    for index in range(start + 1, len(arr)):
+        if arr[index] >= current:
+            if index in cache:
+                count = cache[index]
+            else:
+                count = get_subsequence(arr, index) + 1
+                cache[index] = count
+            if count > length:
+                length = count
+
+    return length
+
+
+def get_subsequence_helper(arr):
+    global cache
+    cache = dict()
+    return get_subsequence(arr, 0)
+
+
+assert get_subsequence_helper([]) == 0
+assert get_subsequence_helper([0, 1]) == 2
+assert get_subsequence_helper([0, 2, 1]) == 2
+assert get_subsequence_helper([0, 1, 2]) == 3
+assert get_subsequence_helper([2, 1, 0]) == 1
+assert get_subsequence_helper(
+    [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]) == 6