動機

sliding window的新招式

  • binary search的range是左閉右開
    • lower bound: >=的第一個值
    • upper bound: >的第一個值
  • sliding window是左閉右閉
    • atMost: <=目標的所有區間總數

Problem

Given an integer array nums and an integer k, return the number of good subarrays of nums.

A good array is an array where the number of different integers in that array is exactly k.

  • For example, [1,2,3,1,2] has 3 different integers: 1, 2, and 3.

A subarray is a contiguous part of an array.

 

Example 1:

Input: nums = [1,2,1,2,3], k = 2Output: 7Explanation: Subarrays formed with exactly 2 different integers: [1,2], [2,1], [1,2], [2,3], [1,2,1], [2,1,2], [1,2,1,2]

Example 2:

Input: nums = [1,2,1,3,4], k = 3Output: 3Explanation: Subarrays formed with exactly 3 different integers: [1,2,1,3], [2,1,3], [1,3,4].

 

Constraints:

  • 1 <= nums.length <= 2 * 104
  • 1 <= nums[i], k <= nums.length

Sol

class Solution:
    def subarraysWithKDistinct(self, nums: List[int], k: int) -> int:
        def atmost(bound):
            ret = i = 0
            cnts = defaultdict(int)
            for j,n in enumerate(nums):
                cnts[n] += 1
                while i <= j and len(cnts) > bound:
                    if cnts[nums[i]] == 1:
                        del cnts[nums[i]]
                    else:
                        cnts[nums[i]] -= 1
                    i += 1
                ret += j-i+1
            return ret
        return atmost(k)-atmost(k-1)