Is Maximize the Profit as the Salesman easy or hard?

The problem is rated Medium on LeetCode because it requires recognizing the weighted interval scheduling pattern. Once the DP state and sorting strategy are clear, the implementation becomes straightforward.

Maximize the Profit as the Salesman Python/Java solution

Implement the solution by sorting offers by end index and using a DP array to track maximum profit. In Python or Java, combine sorting with binary search or maintain a mapping from ending house to offers for incremental DP updates.

How to solve Maximize the Profit as the Salesman in O(n)?

A near-linear approach iterates across houses and processes offers grouped by their ending index. Using a mapping from end house to offers, dynamic programming updates the best profit at each house. The complexity becomes O(n + m log m) due to the initial sorting step.

What is the best approach for Maximize the Profit as the Salesman?

The most efficient approach models the problem as weighted interval scheduling. Sort offers by ending house, then use dynamic programming with binary search to find the latest non-overlapping offer. This yields an O(m log m) time solution and O(m) space complexity.

Is Maximize the Profit as the Salesman asked at Google/Amazon/Meta?

This problem reflects a classic weighted interval scheduling pattern commonly used in interviews at companies like Google, Amazon, and Meta. Variants involving non-overlapping intervals and profit maximization frequently appear in dynamic programming interview rounds.

What data structure is used in Maximize the Profit as the Salesman?

Key data structures include arrays for dynamic programming, sorted lists of offers, and optionally a hash map that groups offers by ending index. Binary search is often used to efficiently find the last non-overlapping interval.

What is the time complexity of Maximize the Profit as the Salesman?

The optimal solution runs in O(m log m) time, where m is the number of offers. The log factor comes from sorting the offers and performing binary search to locate the last compatible non-overlapping offer during each DP transition.

Description Hints 3 Solution Video 15:43

2830. Maximize the Profit as the Salesman

Medium38.7% acceptance1 company

You are given an integer n representing the number of houses on a number line, numbered from 0 to n - 1.

Additionally, you are given a 2D integer array offers where offers[i] = [start_i, end_i, gold_i], indicating that i^th buyer wants to buy all the houses from start_i to end_i for gold_i amount of gold.

As a salesman, your goal is to maximize your earnings by strategically selecting and selling houses to buyers.

Return the maximum amount of gold you can earn.

Note that different buyers can't buy the same house, and some houses may remain unsold.

Example 1:

Input: n = 5, offers = [[0,0,1],[0,2,2],[1,3,2]]
Output: 3
Explanation: There are 5 houses numbered from 0 to 4 and there are 3 purchase offers.
We sell houses in the range [0,0] to 1^st buyer for 1 gold and houses in the range [1,3] to 3^rd buyer for 2 golds.
It can be proven that 3 is the maximum amount of gold we can achieve.

Example 2:

Input: n = 5, offers = [[0,0,1],[0,2,10],[1,3,2]]
Output: 10
Explanation: There are 5 houses numbered from 0 to 4 and there are 3 purchase offers.
We sell houses in the range [0,2] to 2^nd buyer for 10 golds.
It can be proven that 10 is the maximum amount of gold we can achieve.

Constraints:

1 <= n <= 10⁵
1 <= offers.length <= 10⁵
offers[i].length == 3
0 <= start_i <= end_i <= n - 1
1 <= gold_i <= 10³

Asked at 1 company

Amazon

Topics

Hints open one at a time

Hint 1

The intended solution uses a dynamic programming approach to solve the problem.

Hint 2

Sort the array offers by start_i.

Hint 3

Let dp[i] = { the maximum amount of gold if the sold houses are in the range [0 … i] }.

15:43

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def maximizeTheProfit(self, n: int, offers: List[List[int]]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

5
[[0,0,1],[0,2,2],[1,3,2]]

Input

5
[[0,0,1],[0,2,10],[1,3,2]]

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