CF1503C Travelling Salesman Problem

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.

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 a single integer — the minimum total cost.

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.