/**
 * [2616] Minimize the Maximum Difference of Pairs
 */
#include <bits/stdc++.h>
#include <gtest/gtest.h>
using namespace std;

// submission codes start here

class Solution {
public:
  int minimizeMax(vector<int> &nums, int p) {
    ranges::sort(nums);

    auto check = [&](int value) -> bool {
      int count = 0;

      for (int i = 0; i < nums.size() - 1; ++i) {
        if (nums[i + 1] - nums[i] <= value) {
          count += 1;
          i += 1;
        }
      }

      return count >= p;
    };

    int left = 0, right = nums.back() - nums[0];

    while (left < right) {
      int middle = (left + right) >> 1;
      if (check(middle)) {
        right = middle;
      } else {
        left = middle + 1;
      }
    }

    return left;
  }
};

// submission codes end.

TEST(P2616, Test1) {
  vector nums = {10, 1, 2, 7, 1, 3};
  Solution s;
  ASSERT_EQ(s.minimizeMax(nums, 2), 1);
}