maximum gap

Author: springuper

maximumGap.py

@@ -0,0 +1,55 @@
+# @param num, a list of integer
+# @return an integer
+# @link http://cgm.cs.mcgill.ca/~godfried/teaching/dm-reading-assignments/Maximum-Gap-Problem.pdf
+def maximumGap(num):
+    length = len(num)
+    if length < 2:
+        return 0
+    elif length == 2:
+        return num[0] - num[1] if num[0] > num[1] else num[1] - num[0]
+
+    # find max and min
+    maximum = minimum = num[0]
+    for item in num:
+        if item > maximum:
+            maximum = item
+        elif item < minimum:
+            minimum = item
+
+    # split buckets
+    span = (maximum - minimum) * 1.0 / (length - 1)
+    buckets = [[] for i in range(length - 1)]
+    buckets[0] = [minimum, minimum]
+    buckets[length - 2] = [maximum, maximum]
+    for item in num:
+        if item == maximum:
+            continue
+        index = int((item - minimum) / span)
+        if len(buckets[index]) == 0:
+            buckets[index] = [item, item]
+        else:
+            if buckets[index][0] > item:
+                buckets[index][0] = item
+            elif buckets[index][1] < item:
+                buckets[index][1] = item
+
+    # find max gap
+    maximumGap = 0
+    previousMax = minimum
+    for bucket in buckets:
+        if len(bucket) == 0:
+            continue
+        gap = bucket[0] - previousMax
+        if gap > maximumGap:
+            maximumGap = gap
+        previousMax = bucket[1]
+
+    return maximumGap
+
+
+assert maximumGap([]) == 0
+assert maximumGap([1]) == 0
+print maximumGap([1, 100000])
+assert maximumGap([1, 100000]) == 99999
+assert maximumGap([1, 2, 3, 4, 6, 7, 8]) == 2
+assert maximumGap([5, 4, 1, 2, 8.5, 3]) == 3.5