You are given two non-increasing 0-indexed integer arrays nums1​​​​​​ and nums2​​​​​​.

A pair of indices (i, j), where 0 <= i < nums1.length and 0 <= j < nums2.length, is valid if both i <= j and nums1[i] <= nums2[j]. The distance of the pair is j - i​​​​.

Return the maximum distance of any valid pair (i, j). If there are no valid pairs, return 0.

An array arr is non-increasing if arr[i-1] >= arr[i] for every 1 <= i < arr.length.

Example 1:

Input: nums1 = [55,30,5,4,2], nums2 = [100,20,10,10,5]
Output: 2
Explanation: The valid pairs are (0,0), (2,2), (2,3), (2,4), (3,3), (3,4), and (4,4).
The maximum distance is 2 with pair (2,4).


Example 2:

Input: nums1 = [2,2,2], nums2 = [10,10,1]
Output: 1
Explanation: The valid pairs are (0,0), (0,1), and (1,1).
The maximum distance is 1 with pair (0,1).


Example 3:

Input: nums1 = [30,29,19,5], nums2 = [25,25,25,25,25]
Output: 2
Explanation: The valid pairs are (2,2), (2,3), (2,4), (3,3), and (3,4).
The maximum distance is 2 with pair (2,4).


Example 4:

Input: nums1 = [5,4], nums2 = [3,2]
Output: 0
Explanation: There are no valid pairs, so return 0.


Constraints:

• 1 <= nums1.length <= 105
• 1 <= nums2.length <= 105
• 1 <= nums1[i], nums2[j] <= 105
• Both nums1 and nums2 are non-increasing.

## Solution: Two Pointers

For each i, find the largest j such that nums[j] >= nums[i].

Time complexity: O(n + m)
Space complexity: O(1)

## C++

You are given a 2D integer array logs where each logs[i] = [birthi, deathi] indicates the birth and death years of the ith person.

The population of some year x is the number of people alive during that year. The ith person is counted in year x‘s population if x is in the inclusive range [birthi, deathi - 1]. Note that the person is not counted in the year that they die.

Return the earliest year with the maximum population.

Example 1:

Input: logs = [[1993,1999],[2000,2010]]
Output: 1993
Explanation: The maximum population is 1, and 1993 is the earliest year with this population.


Example 2:

Input: logs = [[1950,1961],[1960,1971],[1970,1981]]
Output: 1960
Explanation:
The maximum population is 2, and it had happened in years 1960 and 1970.
The earlier year between them is 1960.

Constraints:

• 1 <= logs.length <= 100
• 1950 <= birthi < deathi <= 2050

## Solution: Simulation

Time complexity: O(n*y)
Space complexity: O(y)

## C++

You are given a 2D integer array intervals, where intervals[i] = [lefti, righti] describes the ith interval starting at lefti and ending at righti (inclusive). The size of an interval is defined as the number of integers it contains, or more formally righti - lefti + 1.

You are also given an integer array queries. The answer to the jth query is the size of the smallest interval i such that lefti <= queries[j] <= righti. If no such interval exists, the answer is -1.

Return an array containing the answers to the queries.

Example 1:

Input: intervals = [[1,4],[2,4],[3,6],[4,4]], queries = [2,3,4,5]
Output: [3,3,1,4]
Explanation: The queries are processed as follows:
- Query = 2: The interval [2,4] is the smallest interval containing 2. The answer is 4 - 2 + 1 = 3.
- Query = 3: The interval [2,4] is the smallest interval containing 3. The answer is 4 - 2 + 1 = 3.
- Query = 4: The interval [4,4] is the smallest interval containing 4. The answer is 4 - 4 + 1 = 1.
- Query = 5: The interval [3,6] is the smallest interval containing 5. The answer is 6 - 3 + 1 = 4.


Example 2:

Input: intervals = [[2,3],[2,5],[1,8],[20,25]], queries = [2,19,5,22]
Output: [2,-1,4,6]
Explanation: The queries are processed as follows:
- Query = 2: The interval [2,3] is the smallest interval containing 2. The answer is 3 - 2 + 1 = 2.
- Query = 19: None of the intervals contain 19. The answer is -1.
- Query = 5: The interval [2,5] is the smallest interval containing 5. The answer is 5 - 2 + 1 = 4.
- Query = 22: The interval [20,25] is the smallest interval containing 22. The answer is 25 - 20 + 1 = 6.


Constraints:

• 1 <= intervals.length <= 105
• 1 <= queries.length <= 105
• intervals[i].length == 2
• 1 <= lefti <= righti <= 107
• 1 <= queries[j] <= 107

## Solution: Offline Processing+ Priority Queue

Similar to 花花酱 LeetCode 1847. Closest Room

Sort intervals by right in descending order, sort queries in descending. Add valid intervals into the priority queue (or treeset) ordered by size in ascending order. Erase invalid ones. The first one (if any) will be the one with the smallest size that contains the current query.

Time complexity: O(nlogn + mlogm + mlogn)
Space complexity: O(m + n)

## C++

You are given a string num, representing a large integer, and an integer k.

We call some integer wonderful if it is a permutation of the digits in num and is greater in value than num. There can be many wonderful integers. However, we only care about the smallest-valued ones.

• For example, when num = "5489355142":
• The 1st smallest wonderful integer is "5489355214".
• The 2nd smallest wonderful integer is "5489355241".
• The 3rd smallest wonderful integer is "5489355412".
• The 4th smallest wonderful integer is "5489355421".

Return the minimum number of adjacent digit swaps that needs to be applied to num to reach the kth smallest wonderful integer.

The tests are generated in such a way that kth smallest wonderful integer exists.

Example 1:

Input: num = "5489355142", k = 4
Output: 2
Explanation: The 4th smallest wonderful number is "5489355421". To get this number:
- Swap index 7 with index 8: "5489355142" -> "5489355412"
- Swap index 8 with index 9: "5489355412" -> "5489355421"


Example 2:

Input: num = "11112", k = 4
Output: 4
Explanation: The 4th smallest wonderful number is "21111". To get this number:
- Swap index 3 with index 4: "11112" -> "11121"
- Swap index 2 with index 3: "11121" -> "11211"
- Swap index 1 with index 2: "11211" -> "12111"
- Swap index 0 with index 1: "12111" -> "21111"


Example 3:

Input: num = "00123", k = 1
Output: 1
Explanation: The 1st smallest wonderful number is "00132". To get this number:
- Swap index 3 with index 4: "00123" -> "00132"


Constraints:

• 2 <= num.length <= 1000
• 1 <= k <= 1000
• num only consists of digits.

## Solution: Next Permutation + Greedy

Time complexity: O(k*n + n^2)
Space complexity: O(n)

## C++

You are given a string s that consists of only digits.

Check if we can split s into two or more non-empty substrings such that the numerical values of the substrings are in descending order and the difference between numerical values of every two adjacent substrings is equal to 1.

• For example, the string s = "0090089" can be split into ["0090", "089"] with numerical values [90,89]. The values are in descending order and adjacent values differ by 1, so this way is valid.
• Another example, the string s = "001" can be split into ["0", "01"]["00", "1"], or ["0", "0", "1"]. However all the ways are invalid because they have numerical values [0,1][0,1], and [0,0,1] respectively, all of which are not in descending order.

Return true if it is possible to split s​​​​​​ as described above, or false otherwise.

substring is a contiguous sequence of characters in a string.

Example 1:

Input: s = "1234"
Output: false
Explanation: There is no valid way to split s.


Example 2:

Input: s = "050043"
Output: true
Explanation: s can be split into ["05", "004", "3"] with numerical values [5,4,3].
The values are in descending order with adjacent values differing by 1.


Example 3:

Input: s = "9080701"
Output: false
Explanation: There is no valid way to split s.


Example 4:

Input: s = "10009998"
Output: true
Explanation: s can be split into ["100", "099", "98"] with numerical values [100,99,98].
The values are in descending order with adjacent values differing by 1.


Constraints:

• 1 <= s.length <= 20
• s only consists of digits.

## Solution: DFS

Time complexity: O(2n)
Space complexity: O(n)