[Usaco2006 Mar]Mooo 奶牛的歌声（单调栈裸题）

1657: [Usaco2006 Mar]Mooo 奶牛的歌声

Time Limit: 5 Sec Memory Limit: 64 MB
Submit: 961 Solved: 679
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Description

Farmer John's N (1 <= N <= 50,000) cows are standing in a very straight row and mooing. Each cow has a unique height h in the range 1..2,000,000,000 nanometers (FJ really is a stickler for precision). Each cow moos at some volume v in the range 1..10,000. This "moo" travels across the row of cows in both directions (except for the end cows, obviously). Curiously, it is heard only by the closest cow in each direction whose height is strictly larger than that of the mooing cow (so each moo will be heard by 0, 1 or 2 other cows, depending on not whether or taller cows exist to the mooing cow's right or left). The total moo volume heard by given cow is the sum of all the moo volumes v for all cows whose mooing reaches the cow. Since some (presumably taller) cows might be subjected to a very large moo volume, FJ wants to buy earmuffs for the cow whose hearing is most threatened. Please compute the loudest moo volume heard by any cow.

Farmer John的N(1<=N<=50,000)头奶牛整齐地站成一列“嚎叫”。每头奶牛有一个确定的高度h(1<=h<=2000000000)，叫的音量为v (1<=v<=10000)。每头奶牛的叫声向两端传播，但在每个方向都只会被身高严格大于它的最近的一头奶牛听到，所以每个叫声都只会被0，1，2头奶牛听到（这取决于它的两边有没有比它高的奶牛）。一头奶牛听到的总音量为它听到的所有音量之和。自从一些奶牛遭受巨大的音量之后，Farmer John打算买一个耳罩给被残害得最厉害的奶牛，请你帮他计算最大的总音量。

Input

* Line 1: A single integer, N.

* Lines 2..N+1: Line i+1 contains two space-separated integers, h and v, for the cow standing at location i.

第1行：一个正整数N.

第2到N+1行：每行包括2个用空格隔开的整数，分别代表站在队伍中第i个位置的奶牛的身高以及她唱歌时的音量．

Output

* Line 1: The loudest moo volume heard by any single cow.

队伍中的奶牛所能听到的最高的总音量．

Sample Input

3
4 2
3 5
6 10

INPUT DETAILS:

Three cows: the first one has height 4 and moos with volume 2, etc.

Sample Output

HINT

队伍中的第3头奶牛可以听到第1头和第2头奶牛的歌声，于是她能听到的总音量为2+5=7．虽然她唱歌时的音量为10，但并没有奶牛可以听见她的歌声．

Source

Silver

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思路：

显然的一道单调栈裸题

我们开一个非严格单调递减栈

如果当前的的元素比栈顶元素小或相等

那么根据题意，声波就一定撞不上

如果大于，那么前面的声音就会撞在这个上面，我们就要出栈

出栈时记下来是因为哪个元素而出栈的即可

因为声波是双向的，所以我们要正着跑一遍，反着跑一遍

顺手吐槽一下版子题为什么是权限题qwq

代码：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#define rii register int i
#define rij register int j
using namespace std;
int l[50005],r[50005],h[50005],stack[50005],v[50005],ans[50005];
int n;
bool cmp(int lk,int kl)
{
    return lk>kl;
}
int main()
{
    scanf("%d",&n);
    for(rii=1;i<=n;i++)
    {
        scanf("%d%d",&h[i],&v[i]);
    }
    int cnt=0;
    for(rii=1;i<=n;i++)
    {
        if(cnt==0)
        {
            cnt++;
            stack[cnt]=i;
            continue;
        }
        if(h[stack[cnt]]>h[i])
        {
            cnt++;
            stack[cnt]=i;
            continue;
        }
        while(1)
        {
            if(h[stack[cnt]]<h[i])
            {
                r[stack[cnt]]=i;
                cnt--;
            }
            else
            {
                cnt++;
                stack[cnt]=i;
                break;
            }
            if(cnt==0)
            {
                cnt++;
                stack[cnt]=i;
                break;
            }
        }
    }
    while(cnt!=0)
    {
        r[stack[cnt]]=n+1;
        cnt--;
    }
    for(rii=n;i>=1;i--)
    {
        if(cnt==0)
        {
            cnt++;
            stack[cnt]=i;
            continue;
        }
        if(h[stack[cnt]]>h[i])
        {
            cnt++;
            stack[cnt]=i;
            continue;
        }
        while(1)
        {
            if(h[stack[cnt]]<h[i])
            {
                l[stack[cnt]]=i;
                cnt--;
            }
            else
            {
                cnt++;
                stack[cnt]=i;
                break;
            }
            if(cnt==0)
            {
                cnt++;
                stack[cnt]=i;
                break;
            }
        }
    }
    while(cnt!=0)
    {
        l[stack[cnt]]=0;
        cnt--;
    }
    for(rii=1;i<=n;i++)
    {
        ans[l[i]]+=v[i];
        ans[r[i]]+=v[i];
    }
    sort(ans+1,ans+n+1,cmp);
    cout<<ans[1];
}