Maximize the Profit as the Salesman — LeetCode 2830 Python Solution

The problem

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] = [starti, endi, goldi], indicating that ith buyer wants to buy all the houses from starti to endi for goldi amount of gold.

Example

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.

Python solution

class Solution:
    def maximizeTheProfit(self, n: int, offers: List[List[int]]) -> int:
        offers.sort(key=lambda x: x[1])
        f = [0] * (len(offers) + 1)
        g = [x[1] for x in offers]
        for i, (s, _, v) in enumerate(offers, 1):
            j = bisect_left(g, s)
            f[i] = max(f[i - 1], f[j] + v)
        return f[-1]

Complexity

Pattern: Binary Search

Halve the search space each step — over an array, or over the answer itself. LeetCode 2830. Maximize the Profit as the Salesman is filed here because LeetCode tags it Binary Search, which is the vocabulary this hub collects.

The binary search guide has the Python template for the pattern and the 254 LeetCode problems that use it.

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