Initial data commit

Task/Longest-increasing-subsequence/Python/longest-increasing-subsequence-1.py

@@ -0,0 +1,33 @@
+def longest_increasing_subsequence(X):
+    """Returns the Longest Increasing Subsequence in the Given List/Array"""
+    N = len(X)
+    P = [0] * N
+    M = [0] * (N+1)
+    L = 0
+    for i in range(N):
+       lo = 1
+       hi = L
+       while lo <= hi:
+           mid = (lo+hi)//2
+           if (X[M[mid]] < X[i]):
+               lo = mid+1
+           else:
+               hi = mid-1
+
+       newL = lo
+       P[i] = M[newL-1]
+       M[newL] = i
+
+       if (newL > L):
+           L = newL
+
+    S = []
+    k = M[L]
+    for i in range(L-1, -1, -1):
+        S.append(X[k])
+        k = P[k]
+    return S[::-1]
+
+if __name__ == '__main__':
+    for d in [[3,2,6,4,5,1], [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]]:
+        print('a L.I.S. of %s is %s' % (d, longest_increasing_subsequence(d)))

Task/Longest-increasing-subsequence/Python/longest-increasing-subsequence-2.py

@@ -0,0 +1,11 @@
+def longest_increasing_subsequence(d):
+    'Return one of the L.I.S. of list d'
+    l = []
+    for i in range(len(d)):
+        l.append(max([l[j] for j in range(i) if l[j][-1] < d[i]] or [[]], key=len)
+                  + [d[i]])
+    return max(l, key=len)
+
+if __name__ == '__main__':
+    for d in [[3,2,6,4,5,1], [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]]:
+        print('a L.I.S. of %s is %s' % (d, longest_increasing_subsequence(d)))

Task/Longest-increasing-subsequence/Python/longest-increasing-subsequence-3.py

@@ -0,0 +1,29 @@
+from collections import namedtuple
+from functools import total_ordering
+from bisect import bisect_left
+
+@total_ordering
+class Node(namedtuple('Node_', 'val back')):
+    def __iter__(self):
+        while self is not None:
+            yield self.val
+            self = self.back
+    def __lt__(self, other):
+        return self.val < other.val
+    def __eq__(self, other):
+        return self.val == other.val
+
+def lis(d):
+    """Return one of the L.I.S. of list d using patience sorting."""
+    if not d:
+        return []
+    pileTops = []
+    for di in d:
+        j = bisect_left(pileTops, Node(di, None))
+        pileTops[j:j+1] = [Node(di, pileTops[j-1] if j > 0 else None)]
+    return list(pileTops[-1])[::-1]
+
+if __name__ == '__main__':
+    for d in [[3,2,6,4,5,1],
+              [0, 8, 4, 12, 2, 10, 6, 14, 1, 9, 5, 13, 3, 11, 7, 15]]:
+        print('a L.I.S. of %s is %s' % (d, lis(d)))