Codeforces I. Producing Snow（优先队列）

题目描述：

C. Producing Snow
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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.
Input

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

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

3
10 10 5
5 7 2

Output

5 12 4

Input
Copy

5
30 25 20 15 10
9 10 12 4 13

Output

9 20 35 11 25

Note

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.

思路：

题目是说，每天造出一堆雪，同时所有堆雪每天融化一点，如果融完了这堆雪就没了，求每一天的所有堆雪的融雪量。刚开始，模拟嘛，就见一个链表，每个节点模拟一堆雪，融完就删节点，比数组标记起来会快一点。每次从头统计一下融雪量。但是这样做太too young too simple了，数据量稍大一点就会超时。因为每次都要遍历一遍链表，最坏的情况是没有雪融完，链表越来越长，要遍历\(1+2+3+...+10^5\approx10^{10}\)，不潮湿？超时！而且我还中间因为链表指针没搞清楚，在删除链表末的节点时漏了处理一个指向链表尾的重要指针，一直莫名错误，改了好久，放个代码。

#include <cstdio>
#define max_n 100005
using namespace std;
int N;
int V[max_n];
int T[max_n];
struct Node
{
    Node* nxt;
    int vol;
};
Node* head;
Node* p;
inline void read(int& x)
{
    x=0;
    int f=0;
    char ch=getchar();
    while('0'>ch||ch>'9')
    {
        if(ch=='-')
            f=1;
        ch=getchar();
    }
    while('0'<=ch&&ch<='9')
    {
        x=10*x+ch-'0';
        ch=getchar();
    }
    x=f?-x:x;
}
inline Node* del(Node* fro,Node* ite)
{
    Node* nxt = ite->nxt;
    /*cout << "vol" << ite->vol << endl;
    if(nxt==NULL)
    {
        printf("Yes\n");
    }*/
    if(nxt==NULL)
    {
        p = fro;
    }
    fro->nxt = nxt;
    ite->nxt = NULL;
    delete ite;
    ite = nxt;
    return ite;
    //cout << "ite->nxt " << ite->vol << endl;
}
#pragma optimize(2) 
int main()
{
    head = new Node;
    head->nxt = NULL;
    p = head;
    read(N);
    for(int i = 0; i<N; i++)
    {
        read(V[i]);
    }
    for(int j = 0; j<N; j++)
    {
        read(T[j]);
    }
    for(int i = 0; i<N; i++)
    {

        Node* node = new Node;
        node->vol = V[i];
        node->nxt = NULL;
        p->nxt = node;
        p = node;
        long long reduce = 0;
        Node* ite = head->nxt;
        Node* fro = head;
        while(ite!=NULL)
        {
            //cout << "T " << T[i] << endl;
            //cout << "ite " << ite->vol << endl;
            if(ite->vol<=T[i])
            {
                reduce =(long long) reduce + ite->vol;
                ite = del(fro,ite);
                //cout << "ite nxt " << ite->vol << endl;
            }
            else
            {
                reduce = (long long) reduce + T[i];
                ite->vol -= T[i];
                fro = ite;
                ite = ite->nxt;
            }
        }
        printf("%I64d ",reduce);
    }

    return 0;
}

#include <iostream>
#include <queue>
#define max_n 100005
using namespace std;
int N;
int V[max_n];
int T[max_n];
long long sum[max_n];
priority_queue<long long,vector<long long>,greater<long long> > que;
int main()
{
    cin >> N;
    for(int i = 1;i<=N;i++)
    {
        cin >> V[i];
    }
    for(int i = 1;i<=N;i++)
    {

        long long ans = 0;
        cin >> T[i];
        sum[i] = sum[i-1]+T[i];
        que.push(sum[i-1]+V[i]);
        while(!que.empty()&&que.top()<=sum[i])
        {
            ans += que.top()-sum[i-1];
            que.pop();
        }
        //cout << "sum[i]-sum[i-1] " << sum[i]-sum[i-1] << endl;
        ans += (sum[i]-sum[i-1])*que.size();
        cout << ans << " ";
    }
    return 0;
}