1818. 绝对差值和

合集 - LeetCode 二分法(17)

1.35. 搜索插入位置2024-09-092.704. 二分查找2024-09-093.744. 寻找比目标字母大的最小字母2024-09-094.2529. 正整数和负整数的最大计数2024-09-095.1385. 两个数组间的距离值2024-09-096.2300. 咒语和药水的成功对数2024-09-097.2389. 和有限的最长子序列2024-09-098.1170. 比较字符串最小字母出现频次2024-09-099.2080. 区间内查询数字的频率2024-09-0910.2563. 统计公平数对的数目2024-09-0911.981. 基于时间的键值存储2024-09-1012.1146. 快照数组2024-09-1013.658. 找到 K 个最接近的元素2024-09-10

14.1818. 绝对差值和2024-09-10

15.911. 在线选举2024-09-1016.LCP 08. 剧情触发时间2024-09-1017.[模板题] - 300. 最长递增子序列2024-09-13

收起

题目链接	1818. 绝对差值和
思路	排序+二分
题解链接	运用「二分」找最佳替换方案
关键点	转换为查找最小值delta：对nums1进行排序后，从中二分查找nums2[i]的最接近值（考虑到绝对值，需要检查left & right两个位置）
时间复杂度	$O(n\log n)$
空间复杂度	$O(n)$

代码实现：

class Solution:
    def minAbsoluteSumDiff(self, nums1: List[int], nums2: List[int]) -> int:
        total = 0
        sorted_ = sorted(nums1)
        n = len(nums1)
        delta = inf
        for i in range(n):
            diff = abs(nums1[i] - nums2[i])
            total += diff
 
            left, right = -1, n
            while left + 1 < right:
                mid = (left+right) // 2
                if sorted_[mid] < nums2[i]:
                    left = mid
                else:
                    right = mid
 
            if left >= 0:
                delta = min(delta, abs(sorted_[left] - nums2[i]) - diff)
            if right < n:
                delta = min(delta, abs(sorted_[right] - nums2[i]) - diff)
        return (total + delta) % (10 ** 9 + 7)

Python-标准库

class Solution:
    def minAbsoluteSumDiff(self, nums1: List[int], nums2: List[int]) -> int:
        total = 0
        sorted_ = sorted(nums1)
        n = len(nums1)
        delta = inf
        for i in range(n):
            diff = abs(nums1[i] - nums2[i])
            total += diff
 
            right = bisect_left(sorted_, nums2[i])
            left = right-1
            if left >= 0:
                delta = min(delta, abs(sorted_[left] - nums2[i]) - diff)
            if right < n:
                delta = min(delta, abs(sorted_[right] - nums2[i]) - diff)
        return (total + delta) % (10 ** 9 + 7)