数据结构与算法之栈: LeetCode 1685. 有序数组中差绝对值之和 (Ts版)

有序数组中差绝对值之和

• https://leetcode.cn/problems/sum-of-absolute-differences-in-a-sorted-array/description/

描述

• 给你一个 非递减 有序整数数组 nums

• 请你建立并返回一个整数数组 result，它跟 nums 长度相同，且result[i] 等于 nums[i] 与数组中所有其他元素差的绝对值之和

• 换句话说， result[i] 等于 sum(|nums[i]-nums[j]|) ，其中 0 <= j < nums.length 且 j != i （下标从 0 开始）

示例 1

输入：nums = [2,3,5]
输出：[4,3,5]

解释：假设数组下标从 0 开始，那么

result[0] = |2-2| + |2-3| + |2-5| = 0 + 1 + 3 = 4，
result[1] = |3-2| + |3-3| + |3-5| = 1 + 0 + 2 = 3，
result[2] = |5-2| + |5-3| + |5-5| = 3 + 2 + 0 = 5

示例 2

输入：nums = [1,4,6,8,10]
输出：[24,15,13,15,21]

提示

• 2 <= nums.length <= $10^5$
• 1 <= nums[i] <= nums[i + 1] <= $10^4$

Typescript 版算法实现

1 ) 方案1：前缀和

function getSumAbsoluteDifferences(nums: number[]): number[] {
    const n = nums.length;
    let leftSum = 0;
    let rightSum = nums.reduce((acc, val) => acc + val, 0);
    const result: number[] = new Array(n);

    for (let i = 0; i < n; i++) {
        rightSum -= nums[i];
        result[i] = i * nums[i] - leftSum + rightSum - (n - i - 1) * nums[i];
        leftSum += nums[i];
    }

    return result;
}

2 ) 方案：另一种方案

function getSumAbsoluteDifferences(nums: number[]): number[] {
    // 计算前缀和数组
    const prefixSums: number[] = [0];
    for (let i = 0; i < nums.length; i++) {
        prefixSums.push(prefixSums[i] + nums[i]);
    }

    const ans: number[] = [];
    const n = nums.length;

    for (let i = 0; i < n; i++) {
        const x = nums[i];
        const left = i * x - prefixSums[i];
        const right = prefixSums[n] - prefixSums[i + 1] - x * (n - 1 - i);
        ans.push(left + right);
    }

    return ans;
}

3 ) 方案3：动态规划，转换成坐标轴上点的距离之和

function getSumAbsoluteDifferences(nums: number[]): number[] {
    const n = nums.length;
    const ans: number[] = new Array(n).fill(0);
    const sumTotal = nums.reduce((a, b) => a + b, 0);
    ans[0] = sumTotal - nums[0] * n;
    for (let i = 1; i < n; i++) {
        const d = nums[i] - nums[i - 1];
        ans[i] = ans[i - 1] - (n - 2 * i) * d;
    }
    return ans;
}