A12306 | $Trucks and Cities$

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题目描述

There are $n$ cities along the road, which can be represented as a straight line. The $i$ -th city is situated at the distance of $a_i$ kilometers from the origin. All cities are situated in the same direction from the origin. There are $m$ trucks travelling from one city to another. Each truck can be described by $4$ integers: starting city $s_i$ , finishing city $f_i$ , fuel consumption $c_i$ and number of possible refuelings $r_i$ . The $i$ -th truck will spend $c_i$ litres of fuel per one kilometer. When a truck arrives in some city, it can be refueled (but refueling is impossible in the middle of nowhere). The $i$ -th truck can be refueled at most $r_i$ times. Each refueling makes truck's gas-tank full. All trucks start with full gas-tank. All trucks will have gas-tanks of the same size $V$ litres. You should find minimum possible $V$ such that all trucks can reach their destinations without refueling more times than allowed.

First line contains two integers $n$ and $m$ ( $2 \le n \le 400$ , $1 \le m \le 250000$ ) — the number of cities and trucks. The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^9$ , $a_i < a_{i+1}$ ) — positions of cities in the ascending order. Next $m$ lines contains $4$ integers each. The $i$ -th line contains integers $s_i$ , $f_i$ , $c_i$ , $r_i$ ( $1 \le s_i < f_i \le n$ , $1 \le c_i \le 10^9$ , $0 \le r_i \le n$ ) — the description of the $i$ -th truck.

Print the only integer — minimum possible size of gas-tanks $V$ such that all trucks can reach their destinations.

输入 #1

7 6
2 5 7 10 14 15 17
1 3 10 0
1 7 12 7
4 5 13 3
4 7 10 1
4 7 10 1
1 5 11 2

输出 #1

C++ 编辑器

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