Travelling Salesman Problem

2000ms

262144K

Description:

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.

Input:

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.

Output:

Output a single integer — the minimum total cost.

Sample Input:

Sample Output:

Sample Input:

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF1503C