一 原题

Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day i he will make a pile of snow of volume Vi and put it in her garden.

Each day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is Ti, each pile will reduce its volume by Ti. If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other.

Note that the pile made on day i already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.

You are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day.

The first line contains a single integer N (1 ≤ N ≤ 105) — the number of days.

The second line contains N integers V1, V2, ..., VN (0 ≤ Vi ≤ 109), where Vi is the initial size of a snow pile made on the day i.

The third line contains N integers T1, T2, ..., TN (0 ≤ Ti ≤ 109), where Ti is the temperature on the day i.

Output a single line with N integers, where the i-th integer represents the total volume of snow melted on day i.

In the first sample, Bob first makes a snow pile of volume 10, which melts to the size of 5 on the same day. On the second day, he makes another pile of size 10. Since it is a bit warmer than the day before, the first pile disappears completely while the second pile shrinks to 3. At the end of the second day, he has only a single pile of size 3. On the third day he makes a smaller pile than usual, but as the temperature dropped too, both piles survive till the end of the day.

二 分析

题意：每天给你体积为V(i)的一堆雪，每天所有的雪堆会融化T(i)（体积不会为负）。求1-N天内每天融化的雪的体积。1=<N<=1e5，0<=V(i), T(i) <= 1e9

思路：暴力的做法是O(n^2)的。一个更好的做法是：维护T的前缀和Pre，Pre(i)=T(1)+T(2)+...+T(i-1)。对于第i天新增的雪堆，不妨假设它第一天就存在，那么它的初始体积为V'(i)=V(i)+Pre(i-1)，在第k天（k>=i）如果V'(i)<=Pre(k)，那么这堆雪融化完，在第k天它融化的体积为V'(i)-Pre(k-1)，否则就是T(k)。用一个multiset维护目前所有的V'，总复杂度O(n*lgn)。

三 代码

#include <cstdio>
#include <set>#define LL long longusing std::multiset;const int maxn = 1e5 + 10;int n, v[maxn], t[maxn];
LL ans = 0, pre[maxn];
multiset<LL> s;int main() {scanf("%d", &n);for (int i = 1; i <= n; i++) scanf("%d", &v[i]);for (int i = 1; i <= n; i++) scanf("%d", &t[i]);for (int i = 1; i <= n; i++) {ans = 0;s.insert(v[i] + pre[i - 1]);pre[i] = pre[i - 1] + t[i];while (!s.empty() && *s.begin() <= pre[i]) {ans += *s.begin() - pre[i - 1];s.erase(s.begin());}ans += s.size() * t[i];printf("%lld ", ans);}return 0;
}