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花花酱 LeetCode 2824. Count Pairs Whose Sum is Less than Target

By zxi on August 23, 2023

Given a 0-indexed integer array nums of length n and an integer target, return the number of pairs(i, j)where0 <= i < j < nandnums[i] + nums[j] < target.

Example 1:

Input: nums = [-1,1,2,3,1], target = 2
Output: 3
Explanation: There are 3 pairs of indices that satisfy the conditions in the statement:
- (0, 1) since 0 < 1 and nums[0] + nums[1] = 0 < target
- (0, 2) since 0 < 2 and nums[0] + nums[2] = 1 < target 
- (0, 4) since 0 < 4 and nums[0] + nums[4] = 0 < target
Note that (0, 3) is not counted since nums[0] + nums[3] is not strictly less than the target.

Example 2:

Input: nums = [-6,2,5,-2,-7,-1,3], target = -2
Output: 10
Explanation: There are 10 pairs of indices that satisfy the conditions in the statement:
- (0, 1) since 0 < 1 and nums[0] + nums[1] = -4 < target
- (0, 3) since 0 < 3 and nums[0] + nums[3] = -8 < target
- (0, 4) since 0 < 4 and nums[0] + nums[4] = -13 < target
- (0, 5) since 0 < 5 and nums[0] + nums[5] = -7 < target
- (0, 6) since 0 < 6 and nums[0] + nums[6] = -3 < target
- (1, 4) since 1 < 4 and nums[1] + nums[4] = -5 < target
- (3, 4) since 3 < 4 and nums[3] + nums[4] = -9 < target
- (3, 5) since 3 < 5 and nums[3] + nums[5] = -3 < target
- (4, 5) since 4 < 5 and nums[4] + nums[5] = -8 < target
- (4, 6) since 4 < 6 and nums[4] + nums[6] = -4 < target

Constraints:

1 <= nums.length == n <= 50
-50 <= nums[i], target <= 50

Solution 1: Brute force

Enumerate all pairs.

Time complexity: O(n²)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int countPairs(vector<int>& nums, int target) {

const int n = nums.size();

int ans = 0;

for (int i = 0; i < n; ++i)

for (int j = i + 1; j < n; ++j)

ans += nums[i] + nums[j] < target;

return ans;

}

};

Solution 2: Two Pointers

Sort the numbers.

Use two pointers i, and j.
Set i to 0 and j to n – 1.
while (nums[i] + nums[j] >= target) –j
then we have nums[i] + nums[k] < target (i < k <= j), in total (j – i) pairs.
++i, move to the next starting number.
Time complexity: O(nlogn + n)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int countPairs(vector<int>& nums, int target) {

const int n = nums.size();

sort(begin(nums), end(nums));

int ans = 0;

for (int i = 0, j = n - 1; i < n; ++i) {

while (j >= i && nums[i] + nums[j] >= target) --j;

ans += max(0, j - i);

}

return ans;

}

};

花花酱 LeetCode 2815. Max Pair Sum in an Array

By zxi on August 13, 2023

You are given a 0-indexed integer array nums. You have to find the maximum sum of a pair of numbers from nums such that the maximum digit in both numbers are equal.

Return the maximum sum or -1 if no such pair exists.

Example 1:

Input: nums = [51,71,17,24,42]
Output: 88
Explanation: 
For i = 1 and j = 2, nums[i] and nums[j] have equal maximum digits with a pair sum of 71 + 17 = 88. 
For i = 3 and j = 4, nums[i] and nums[j] have equal maximum digits with a pair sum of 24 + 42 = 66.
It can be shown that there are no other pairs with equal maximum digits, so the answer is 88.

Example 2:

Input: nums = [1,2,3,4]
Output: -1
Explanation: No pair exists in nums with equal maximum digits.

Constraints:

2 <= nums.length <= 100
1 <= nums[i] <= 10⁴

Solution: Brute Force

Enumerate all pairs of nums and check their sum and max digit.

Time complexity: O(n²)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int maxSum(vector<int>& nums) {

auto maxDigit = [](int x) {

int ans = 0;

while (x) {

ans = max(ans, x % 10);

x /= 10;

}

return ans;

};

int ans = -1;

const int n = nums.size();

for (int i = 0; i < n; ++i)

for (int j = i + 1; j < n; ++j)

if (nums[i] + nums[j] > ans

&& maxDigit(nums[i]) == maxDigit(nums[j]))

ans = nums[i] + nums[j];

return ans;

}

};

花花酱 LeetCode 2771. Longest Non-decreasing Subarray From Two Arrays

By zxi on July 15, 2023

You are given two 0-indexed integer arrays nums1 and nums2 of length n.

Let’s define another 0-indexed integer array, nums3, of length n. For each index i in the range [0, n - 1], you can assign either nums1[i] or nums2[i] to nums3[i].

Your task is to maximize the length of the longest non-decreasing subarray in nums3 by choosing its values optimally.

Return an integer representing the length of the longest non-decreasing subarray in nums3.

Note: A subarray is a contiguous non-empty sequence of elements within an array.

Example 1:

Input: nums1 = [2,3,1], nums2 = [1,2,1]
Output: 2
Explanation: One way to construct nums3 is: 
nums3 = [nums1[0], nums2[1], nums2[2]] => [2,2,1]. 
The subarray starting from index 0 and ending at index 1, [2,2], forms a non-decreasing subarray of length 2. 
We can show that 2 is the maximum achievable length.

Example 2:

Input: nums1 = [1,3,2,1], nums2 = [2,2,3,4]
Output: 4
Explanation: One way to construct nums3 is: 
nums3 = [nums1[0], nums2[1], nums2[2], nums2[3]] => [1,2,3,4]. 
The entire array forms a non-decreasing subarray of length 4, making it the maximum achievable length.

Example 3:

Input: nums1 = [1,1], nums2 = [2,2]
Output: 2
Explanation: One way to construct nums3 is: 
nums3 = [nums1[0], nums1[1]] => [1,1]. 
The entire array forms a non-decreasing subarray of length 2, making it the maximum achievable length.

Constraints:

1 <= nums1.length == nums2.length == n <= 10⁵
1 <= nums1[i], nums2[i] <= 10⁹

Solution: DP

Let dp1(i), dp2(i) denote the length of the Longest Non-decreasing Subarray ends with nums1[i] and nums2[i] respectively.

init: dp1(0) = dp2(0) = 1

dp1(i) = max(dp1(i – 1) + 1 if nums1[i] >= nums1[i – 1] else 1, dp2(i – 1) + 1 if nums1[i] >= nums2[i – 1] else 1)
dp2(i) = max(dp1(i – 1) + 1 if nums2[i] >= nums1[i – 1] else 1, dp2(i – 1) + 1 if nums2[i] >= nums2[i – 1] else 1)

ans = max(dp1, dp2)

Time complexity: O(n)
Space complexity: O(n) -> O(1)

Python3

# Author: Huahua

class Solution:

def maxNonDecreasingLength(self, nums1: List[int], nums2: List[int]) -> int:

n = len(nums1)

nums = [nums1, nums2]

@cache

def dp(i: int, j: int):

if i == 0: return 1

ans = 1

for k in range(2):

if nums[j][i] >= nums[k][i - 1]:

ans = max(ans, dp(i - 1, k) + 1)

return ans

return max(max(dp(i, 0), dp(i, 1)) for i in range(n))

C++

// Author: Huahua

class Solution {

public:

int maxNonDecreasingLength(vector<int>& nums1, vector<int>& nums2) {

int ans = 1;

for (int i = 1, dp1 = 1, dp2 = 1; i < nums1.size(); ++i) {

int t1 = max(nums1[i] >= nums1[i - 1] ? dp1 + 1 : 1,

nums1[i] >= nums2[i - 1] ? dp2 + 1 : 1);

int t2 = max(nums2[i] >= nums1[i - 1] ? dp1 + 1 : 1,

nums2[i] >= nums2[i - 1] ? dp2 + 1 : 1);

dp1 = t1;

dp2 = t2;

ans = max({ans, dp1, dp2});

}

return ans;

}

};

花花酱 LeetCode 2770. Maximum Number of Jumps to Reach the Last Index

By zxi on July 11, 2023

You are given a 0-indexed array nums of n integers and an integer target.

You are initially positioned at index 0. In one step, you can jump from index i to any index j such that:

0 <= i < j < n
-target <= nums[j] - nums[i] <= target

Return the maximum number of jumps you can make to reach index n - 1.

If there is no way to reach index n - 1, return -1.

Example 1:

Input: nums = [1,3,6,4,1,2], target = 2
Output: 3
Explanation: To go from index 0 to index n - 1 with the maximum number of jumps, you can perform the following jumping sequence:
- Jump from index 0 to index 1. 
- Jump from index 1 to index 3.
- Jump from index 3 to index 5.
It can be proven that there is no other jumping sequence that goes from 0 to n - 1 with more than 3 jumps. Hence, the answer is 3.

Example 2:

Input: nums = [1,3,6,4,1,2], target = 3
Output: 5
Explanation: To go from index 0 to index n - 1 with the maximum number of jumps, you can perform the following jumping sequence:
- Jump from index 0 to index 1.
- Jump from index 1 to index 2.
- Jump from index 2 to index 3.
- Jump from index 3 to index 4.
- Jump from index 4 to index 5.
It can be proven that there is no other jumping sequence that goes from 0 to n - 1 with more than 5 jumps. Hence, the answer is 5.

Example 3:

Input: nums = [1,3,6,4,1,2], target = 0
Output: -1
Explanation: It can be proven that there is no jumping sequence that goes from 0 to n - 1. Hence, the answer is -1.

Constraints:

2 <= nums.length == n <= 1000
-10⁹ <= nums[i] <= 10⁹
0 <= target <= 2 * 10⁹

Solution: DP

Let dp(i) denotes the maximum jumps from index i to index n-1.

For each index i, try jumping to all possible index j.

dp(i) = max(1 + dp(j)) if j > i and abs(nums[j] – nums[i) <= target else -1

Time complexity: O(n²)
Space complexity: O(n)

Python3

# Author: Huahua

class Solution:

def maximumJumps(self, nums: List[int], target: int) -> int:

n = len(nums)

@cache

def dp(i):

if i == n - 1: return 0

ans = -1

for j in range(i + 1, n):

if abs(nums[j] - nums[i]) <= target and dp(j) != -1:

ans = max(ans, 1 + dp(j))

return ans

return dp(0)

花花酱 LeetCode 2769. Find the Maximum Achievable Number

By zxi on July 11, 2023

You are given two integers, num and t.

An integer x is called achievable if it can become equal to num after applying the following operation no more than t times:

Increase or decrease x by 1, and simultaneously increase or decrease num by 1.

Return the maximum possible achievable number. It can be proven that there exists at least one achievable number.

Example 1:

Input: num = 4, t = 1
Output: 6
Explanation: The maximum achievable number is x = 6; it can become equal to num after performing this operation:
1- Decrease x by 1, and increase num by 1. Now, x = 5 and num = 5. 
It can be proven that there is no achievable number larger than 6.

Example 2:

Input: num = 3, t = 2
Output: 7
Explanation: The maximum achievable number is x = 7; after performing these operations, x will equal num: 
1- Decrease x by 1, and increase num by 1. Now, x = 6 and num = 4.
2- Decrease x by 1, and increase num by 1. Now, x = 5 and num = 5.
It can be proven that there is no achievable number larger than 7.

Constraints:

1 <= num, t <= 50

Solution: Greedy

Always decrease x and always increase num, the max achievable number x = num + t * 2

Time complexity: O(1)
Space complexity: O(1)

C++

// Author: Huahua

class Solution {

public:

int theMaximumAchievableX(int num, int t) {

return num + t * 2;

}

};