Devide-and-Conquer

![https://leetcode.com/problems/largest-values-from-labels/] We have a set of items: the i-th item has value values[i] and label labels[i]. Then, we choose a subset S of these items, such that: |S| <= num_wanted For every label L, the number of items in S with label L is <= use_limit. Return the largest possible sum of the subset S. Example 1: Input: values = [5,4,3,2,1], labels = [1,1,2,2,3], num_wanted = 3, use_limit = 1 Output: 9 Explanation: The subset chosen is the first, third, and fifth item. Example 2: Input: values = [5,4,3,2,1], labels = [1,3,3,3,2], num_wanted = 3, use_limit = 2 Output: 12 Explanation: The subset chosen is the first, second, and third item. Example 3: Input: values = [9,8,8,7,6], labels = [0,0,0,1,1], num_wanted = 3, use_limit = 1 Output: 16 Explanation: The subset chosen is the first and fourth item. Example 4: Input: values = [9,8,8,7,6], labels = [0,0,0,1,1], num_wanted = 3, use_limit = 2 Output: 24 Explanation: The subset chosen is the first, second, and fourth item. Note: ...

![https://leetcode.com/problems/search-a-2d-matrix-ii/] Write an efficient algorithm that searches for a target value in an m x n integer matrix. The matrix has the following properties: Integers in each row are sorted in ascending from left to right. Integers in each column are sorted in ascending from top to bottom. Example 1: Input: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 5 Output: true Example 2: Input: matrix = [[1,4,7,11,15],[2,5,8,12,19],[3,6,9,16,22],[10,13,14,17,24],[18,21,23,26,30]], target = 20 Output: false Constraints: ...

![https://leetcode.com/problems/majority-element/] Given an array nums of size n, return the majority element. The majority element is the element that appears more than ⌊n / 2⌋ times. You may assume that the majority element always exists in the array. Example 1: Input: nums = [3,2,3] Output: 3 Example 2: Input: nums = [2,2,1,1,1,2,2] Output: 2 Constraints: n == nums.length 1 <= n <= 5 * 104 -231 <= nums[i] <= 231 - 1 Follow-up: Could you solve the problem in linear time and in O(1) space? ...

![https://leetcode.com/problems/kth-largest-element-in-an-array/] Find the kth largest element in an unsorted array. Note that it is the kth largest element in the sorted order, not the kth distinct element. Example 1: Input: [3,2,1,5,6,4] and k = 2 Output: 5 Example 2: Input: [3,2,3,1,2,4,5,5,6] and k = 4 Output: 4 Note: You may assume k is always valid, 1 ≤ k ≤ array’s length. class Solution { public int findKthLargest(int[] nums, int k) { int lo = 0; int hi = nums.length - 1; k = nums.length - k; while (lo < hi) { int j = partition(nums, lo, hi); if (j < k) { lo = j + 1; } else if (j > k) { hi = j - 1; } else { return nums[k]; } } return nums[k]; } int partition(int[] a, int lo, int hi) { int i = lo; int j = hi + 1; while (true) { while (a[++i] < a[lo]) { if (i == hi) break; } while (a[lo] < a[--j]) { if (j == lo) break; } if (i >= j) break; swap(a, i, j); } swap(a, lo, j); return j; } void swap(int[] a, int i, int j) { int temp = a[i]; a[i] = a[j]; a[j] = temp; } }