Pak Chanek observes that the carriages of a train is always full on morning departure hours and afternoon departure hours. Therefore, the balance between carriages is needed so that it is not too crowded in only a few carriages.
A train contains $$$N$$$ carriages that are numbered from $$$1$$$ to $$$N$$$ from left to right. Carriage $$$i$$$ initially contains $$$A_i$$$ passengers. All carriages are connected by carriage doors, namely for each $$$i$$$ ($$$1\leq i\leq N-1$$$), carriage $$$i$$$ and carriage $$$i+1$$$ are connected by a two-way door.
Each passenger can move between carriages, but train regulation regulates that for each $$$i$$$, a passenger that starts from carriage $$$i$$$ cannot go through more than $$$D_i$$$ doors.
Define $$$Z$$$ as the most number of passengers in one same carriage after moving. Pak Chanek asks, what is the minimum possible value of $$$Z$$$?
The first line contains a single integer $$$N$$$ ($$$1 \leq N \leq 2\cdot10^5$$$) — the number of carriages.
The second line contains $$$N$$$ integers $$$A_1, A_2, A_3, \ldots, A_N$$$ ($$$0 \leq A_i \leq 10^9$$$) — the initial number of passengers in each carriage.
The third line contains $$$N$$$ integers $$$D_1, D_2, D_3, \ldots, D_N$$$ ($$$0 \leq D_i \leq N-1$$$) — the maximum limit of the number of doors for each starting carriage.
An integer representing the minimum possible value of $$$Z$$$.
7 7 4 2 0 5 8 3 4 0 0 1 3 1 3
5
One strategy that is optimal is as follows:
The number of passengers in each carriage becomes $$$[2,4,5,5,4,5,4]$$$.
Name |
---|