add more algorithms

array/merge_intervals.py

@@ -0,0 +1,40 @@
+"""
+Given a collection of intervals, merge all overlapping intervals.
+
+For example,
+Given [1,3],[2,6],[8,10],[15,18],
+return [1,6],[8,10],[15,18].
+"""
+
+# Definition for an interval.
+class Interval(object):
+    def __init__(self, s=0, e=0):
+        self.start = s
+        self.end = e
+
+def merge(intervals):
+    """
+    :type intervals: List[Interval]
+    :rtype: List[Interval]
+    """
+    out = []
+    for i in sorted(intervals, key=lambda i: i.start):
+        if out and i.start <= out[-1].end:
+            out[-1].end = max(out[-1].end, i.end)
+        else:
+            out += i,
+    return out
+
+def print_intervals(intervals):
+    res = []
+    for i in intervals:
+        res.append('['+str(i.start)+','+str(i.end)+']')
+    print("".join(res))
+
+if __name__ == "__main__":
+    given = [[1,3],[2,6],[8,10],[15,18]]
+    intervals = []
+    for l, r in given:
+        intervals.append(Interval(l,r))
+    print_intervals(intervals)
+    print_intervals(merge(intervals))

divide-and-conquer/expression_add_operators.py

@@ -23,16 +23,15 @@ def add_operator(num, target):
     return res
 
 def helper(res, path, num, target, pos, prev, multed):
-    print(res, path, num, target, pos, prev, multed)
     if pos == len(num):
         if (target == prev):
             res.append(path)
         return
     for i in range(pos, len(num)):
-        if i != pos and num[pos] == '0': break
+        if i != pos and num[pos] == '0': # all digits have to be used
+            break
         cur = int(num[pos:i+1])
-        print(cur)
-        if (pos == 0):
+        if pos == 0:
             helper(res, path + str(cur), num, target, i+1, cur, cur)
         else:
             helper(res, path + "+" + str(cur), num, target, i+1, prev + cur, cur)
@@ -44,4 +43,11 @@ def helper(res, path, num, target, pos, prev, multed):
 s = "123"
 target = 6
 print(add_operator(s, target))
+# "232", 8 -> ["2*3+2", "2+3*2"]
+s = "232"
+target = 8
+print(add_operator(s, target))
 
+s = "123045"
+target = 3
+print(add_operator(s, target))

heap/merge_sorted_k_lists.py

@@ -0,0 +1,63 @@
+"""
+Merge k sorted linked lists and return it as one sorted list. Analyze and describe its complexity.
+"""
+
+# Definition for singly-linked list.
+# class ListNode(object):
+#     def __init__(self, x):
+#         self.val = x
+#         self.next = None
+
+from heapq import heappush, heappop, heapreplace, heapify
+
+def mergeKLists(lists):
+    dummy = node = ListNode(0)
+    h = [(n.val, n) for n in lists if n]
+    heapify(h)
+    while h:
+        v, n = h[0]
+        if n.next is None:
+            heappop(h) #only change heap size when necessary
+        else:
+            heapreplace(h, (n.next.val, n.next))
+        node.next = n
+        node = node.next
+
+    return dummy.next
+
+from Queue import PriorityQueue
+
+def merge_k_lists(lists):
+    dummy = ListNode(None)
+    curr = dummy
+    q = PriorityQueue()
+    for node in lists:
+        if node: q.put((node.val,node))
+    while q.qsize()>0:
+        curr.next = q.get()[1]
+        curr=curr.next
+        if curr.next: q.put((curr.next.val, curr.next))
+    return dummy.next
+
+
+"""
+I think my code's complexity is also O(nlogk) and not using heap or priority queue,
+n means the total elements and k means the size of list.
+
+The mergeTwoLists functiony in my code comes from the problem Merge Two Sorted Lists
+whose complexity obviously is O(n), n is the sum of length of l1 and l2.
+
+To put it simpler, assume the k is 2^x, So the progress of combination is like a full binary tree,
+from bottom to top. So on every level of tree, the combination complexity is n,
+beacause every level have all n numbers without repetition.
+The level of tree is x, ie logk. So the complexity is O(nlogk).
+
+for example, 8 ListNode, and the length of every ListNode is x1, x2,
+x3, x4, x5, x6, x7, x8, total is n.
+
+on level 3: x1+x2, x3+x4, x5+x6, x7+x8 sum: n
+
+on level 2: x1+x2+x3+x4, x5+x6+x7+x8 sum: n
+
+on level 1: x1+x2+x3+x4+x5+x6+x7+x8 sum: n
+"""

tree/binary_tree_paths.py

@@ -0,0 +1,14 @@
+def binaryTreePaths(root):
+    res = []
+    if not root:
+        return res
+    DFS(res, root, str(root.val))
+    return res
+
+def DFS(res, root, cur):
+    if not root.left and not root.right:
+        res.append(cur)
+    if root.left:
+        DFS(res, root.left, cur+'->'+str(root.left.val))
+    if root.right:
+        DFS(res, root.right, cur+'->'+str(root.right.val))