[LeetCode] questions conclusion_ Binary Search
Binary Search
T(n) = T(n/2) + O(1) => T(n) = O(lg n)
proof:
如果能用iterable , 就用while loop, 可以防止用recursion的时候stack overflow( process in Linux is 8Mb), stack room is static for each process. (堆空间, heap room 是内存, 是动态的。)层数越多,存储更多中间/临时变量,最终超过系统配的stack空间,就会出现stack overflow。
建议:
- 如果问题不复杂,能用iterable就用iterable
- 如果问题比较复杂,还是用recursive吧
1) ask 是否有duplicates?
1.1 如果没有duplicates
标准的binary search:
a) l + 1 < r 相当于如果l, r 相邻就跳出,这样能够避免死循环. 但是while loop之后需要加一个判断, 也就是d选项
b) l + (r - l)//2 # 不用(l+r)//2 , 因为l + r 有可能overflow,强行装*,当l + r 之和超过int的最大值,2的32次方减1,会溢出。
c) A[mid] ==, <, > # 为了bug free, 建议举个小栗子, 然后画图去判断.
d) A[l], A[r] ? target
Code
def BinarySearch(self, nums, target): # nums is sorted
if not nums or target < nums[0] or target > nums[-1]: return -1
l, r = 0, len(nums) -1 # note here is len(nums) -1
while l + 1 < r:
mid = l + (r - l)//2
if nums[mid] > target:
r = mid
elif nums[mid] < target:
l = mid
else:
return mid
if nums[l] == target:
return l
if nums[r] == target:
return r
return -1
1.2 如果有duplicates
a) ask 是first index, last index or dont matter?
如果是first index:
if A[mid] == target: r = mid
最后判断 A[l] 和A[r] 的时候先判断 A[l]
如果是last index:
if A[mid] == target: l = mid
最后判断 A[l] 和A[r] 的时候先判断 A[r]
Questions:
[LeetCode] 704. Binary Search_Easy tag: Binary Search
[LeetCode] 374. Guess Number Higher or Lower_Easy tag: Binary Search
[LeetCode] 34. Find First and Last Position of Element in Sorted Array == [LintCode] 61. Search for a Range_Easy tag: Binary Search first index and last index == target in duplicates.
[LeetCode] 35. Search Insert Position_Easy tag: Binary Search first index >= target, without duplicates
[LeetCode] 278. First Bad Version_Easy tag: Binary Search first index, without duplicates
[LeetCode] 162. Find Peak Element(852. Peak Index in a Mountain Array)_Medium tag: Binary Search
[LeetCode] 74. Search a 2D Matrix_Medium tag: Binary Search
[LeetCode] 240. Search a 2D Matrix II_Medium tag: Binary Search
[LeetCode] 69. Sqrt(x)_Easy tag: Binary Search
[LeetCode] 153. Find Minimum in Rotated Sorted Array_Medium tag: Binary Search first index <= nums[-1]
[LeetCode] 154. Find Minimum in Rotated Sorted Array II_Hard tag: not real binary search anymore
[LeetCode] 33. Search in Rotated Sorted Array_Medium tag: Binary Search
[LeetCode] 81. Search in Rotated Sorted Array II_Medium tag: not real binary search anymore
[LeetCode] 702. Search in a Sorted Array of Unknown Size_Medium tag: Binary Search
[LeetCode] 4. Median of Two Sorted Arrays_Hard tag: Array, Binary Search
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