Question

475. 供暖器

English Version

题目描述

冬季已经来临。 你的任务是设计一个有固定加热半径的供暖器向所有房屋供暖。

在加热器的加热半径范围内的每个房屋都可以获得供暖。

现在，给出位于一条水平线上的房屋 houses 和供暖器 heaters 的位置，请你找出并返回可以覆盖所有房屋的最小加热半径。

注意：所有供暖器 heaters 都遵循你的半径标准，加热的半径也一样。

 

示例 1:

输入: houses = [1,2,3], heaters = [2]
输出: 1
解释: 仅在位置 2 上有一个供暖器。如果我们将加热半径设为 1，那么所有房屋就都能得到供暖。

示例 2:

输入: houses = [1,2,3,4], heaters = [1,4]
输出: 1
解释: 在位置 1, 4 上有两个供暖器。我们需要将加热半径设为 1，这样所有房屋就都能得到供暖。

示例 3：

输入：houses = [1,5], heaters = [2]
输出：3

 

提示：

• 1 <= houses.length, heaters.length <= 3 * 104
• 1 <= houses[i], heaters[i] <= 109

解法

方法一

class Solution:
  def findRadius(self, houses: List[int], heaters: List[int]) -> int:
    houses.sort()
    heaters.sort()

    def check(r):
      m, n = len(houses), len(heaters)
      i = j = 0
      while i < m:
        if j >= n:
          return False
        mi = heaters[j] - r
        mx = heaters[j] + r
        if houses[i] < mi:
          return False
        if houses[i] > mx:
          j += 1
        else:
          i += 1
      return True

    left, right = 0, int(1e9)
    while left < right:
      mid = (left + right) >> 1
      if check(mid):
        right = mid
      else:
        left = mid + 1
    return left

class Solution {
  public int findRadius(int[] houses, int[] heaters) {
    Arrays.sort(heaters);
    int res = 0;
    for (int x : houses) {
      int i = Arrays.binarySearch(heaters, x);
      if (i < 0) {
        i = ~i;
      }
      int dis1 = i > 0 ? x - heaters[i - 1] : Integer.MAX_VALUE;
      int dis2 = i < heaters.length ? heaters[i] - x : Integer.MAX_VALUE;
      res = Math.max(res, Math.min(dis1, dis2));
    }
    return res;
  }
}

class Solution {
public:
  int findRadius(vector<int>& houses, vector<int>& heaters) {
    sort(houses.begin(), houses.end());
    sort(heaters.begin(), heaters.end());
    int left = 0, right = 1e9;
    while (left < right) {
      int mid = left + right >> 1;
      if (check(houses, heaters, mid))
        right = mid;
      else
        left = mid + 1;
    }
    return left;
  }

  bool check(vector<int>& houses, vector<int>& heaters, int r) {
    int m = houses.size(), n = heaters.size();
    int i = 0, j = 0;
    while (i < m) {
      if (j >= n) return false;
      int mi = heaters[j] - r;
      int mx = heaters[j] + r;
      if (houses[i] < mi) return false;
      if (houses[i] > mx)
        ++j;
      else
        ++i;
    }
    return true;
  }
};

func findRadius(houses []int, heaters []int) int {
  sort.Ints(houses)
  sort.Ints(heaters)
  m, n := len(houses), len(heaters)

  check := func(r int) bool {
    var i, j int
    for i < m {
      if j >= n {
        return false
      }
      mi, mx := heaters[j]-r, heaters[j]+r
      if houses[i] < mi {
        return false
      }
      if houses[i] > mx {
        j++
      } else {
        i++
      }
    }
    return true
  }
  left, right := 0, int(1e9)
  for left < right {
    mid := (left + right) >> 1
    if check(mid) {
      right = mid
    } else {
      left = mid + 1
    }
  }
  return left
}

function findRadius(houses: number[], heaters: number[]): number {
  houses.sort((a, b) => a - b);
  heaters.sort((a, b) => a - b);
  const m = houses.length,
    n = heaters.length;
  let ans = 0;
  for (let i = 0, j = 0; i < m; i++) {
    let cur = Math.abs(houses[i] - heaters[j]);
    while (
      j + 1 < n &&
      Math.abs(houses[i] - heaters[j]) >= Math.abs(houses[i] - heaters[j + 1])
    ) {
      cur = Math.min(Math.abs(houses[i] - heaters[++j]), cur);
    }
    ans = Math.max(cur, ans);
  }
  return ans;
}