A14252 | Travelling Salesman Problem
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题目描述
There are $n$ cities numbered from $1$ to $n$ , and city $i$ has beauty $a_i$ .
A salesman wants to start at city $1$ , visit every city exactly once, and return to city $1$ .
For all $i\ne j$ , a flight from city $i$ to city $j$ costs $\max(c_i,a_j-a_i)$ dollars, where $c_i$ is the price floor enforced by city $i$ . Note that there is no absolute value. Find the minimum total cost for the salesman to complete his trip.
A salesman wants to start at city $1$ , visit every city exactly once, and return to city $1$ .
For all $i\ne j$ , a flight from city $i$ to city $j$ costs $\max(c_i,a_j-a_i)$ dollars, where $c_i$ is the price floor enforced by city $i$ . Note that there is no absolute value. Find the minimum total cost for the salesman to complete his trip.
输入格式
The first line contains a single integer $n$ ( $2\le n\le 10^5$ ) — the number of cities.
The $i$ -th of the next $n$ lines contains two integers $a_i$ , $c_i$ ( $0\le a_i,c_i\le 10^9$ ) — the beauty and price floor of the $i$ -th city.
The $i$ -th of the next $n$ lines contains two integers $a_i$ , $c_i$ ( $0\le a_i,c_i\le 10^9$ ) — the beauty and price floor of the $i$ -th city.
输出格式
Output a single integer — the minimum total cost.
输入输出样例
输入 #1
3 1 9 2 1 4 1
输出 #1
11
输入 #2
6 4 2 8 4 3 0 2 3 7 1 0 1
输出 #2
13
In the first test case, we can travel in order $1\to 3\to 2\to 1$ .
- The flight $1\to 3$ costs $\max(c_1,a_3-a_1)=\max(9,4-1)=9$ .
- The flight $3\to 2$ costs $\max(c_3, a_2-a_3)=\max(1,2-4)=1$ .
- The flight $2\to 1$ costs $\max(c_2,a_1-a_2)=\max(1,1-2)=1$ .
The total cost is $11$ , and we cannot do better.
- The flight $1\to 3$ costs $\max(c_1,a_3-a_1)=\max(9,4-1)=9$ .
- The flight $3\to 2$ costs $\max(c_3, a_2-a_3)=\max(1,2-4)=1$ .
- The flight $2\to 1$ costs $\max(c_2,a_1-a_2)=\max(1,1-2)=1$ .
The total cost is $11$ , and we cannot do better.
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评测结果：Accepted