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zc
2019-12-21 19:47:00
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[l,r]之间最小值位置为p,原数组为a

那么左端点在[l,p],右端点在[p,r]的区间的最小值都是a[p]

那么这部分的贡献为a[p] \times (p-l+1) \times (r-p+1)

接下来还有[l,p-1],[p+1,r]没有处理

pre_ii前第一个比a[i]小的数的位置(用单调栈筛出)

存在x,满足pre_x=p

f[l][r]表示以r为右端点,左端点在[l,r]的区间的答案

那么f[l][r]=f[l][pre_r]+a_r\times(r-pre_r)

因为f的变化只与r有关,所以可以删掉一维

那么f_r= a_r \times (r-pre_r) +f_{pre_r}

所以[p+1,r]的答案就是f_r-f_{p-1}

[l,p-1]求法类似

#include<bits/stdc++.h>
namespace ZDY{
    #pragma GCC optimize(3)
    #define il __inline__ __attribute__ ((always_inline))
    #define rg register
    #define ll long long
    #define ull unsigned long long
    #define db double
    #define sht short
    #define MB template <class T>il
    #define Fur(i,x,y) for(int i=x;i<=y;i++)
    #define Fdr(i,x,y) for(int i=x;i>=y;i--)
    //#define fl(i,x) for(int i=head[x],to;to=e[i].to,i;i=e[i].nxt)
    #define clr(x,y) memset(x,y,sizeof(x))
    #define cpy(x,y) memcpy(x,y,sizeof(x))
    #define fin(s) freopen(s".in","r",stdin)
    #define fout(s) freopen(s".out","w",stdout)
    #define fcin ios::sync_with_stdio(false)
    #define l2(n) (int(log2(n)))
    #define inf 0x3f3f3f3f
    MB T ABS(T x){return x>0?x:-x;}
    MB T MAX(T x,T y){return x>y?x:y;}
    MB T MIN(T x,T y){return x<y?x:y;}
    MB T GCD(T x,T y){return y?GCD(y,x%y):x;}
    MB void SWAP(T &x,T &y){T t=x;x=y;y=t;}
}using namespace ZDY;using namespace std;
namespace IO{const char* ln="\n";const int str=1<<20;struct IN{char buf[str],*s,*t;bool _;IN():s(buf),t(buf),_(0){}il char gc(){return s==t&&((t=(s=buf)+fread(buf,1,str,stdin))==s)?EOF:(*s++);}IN&operator>>(char&ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)_=1;else ch=c;return *this;}IN& operator>>(char* ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;*ch=c;ch++;while((c=gc())!=EOF&&!isspace(c))*ch=c,ch++;if(c==EOF)_=1;return *this;}IN& operator>>(string& ch){if(_)return *this;char c;while((c=gc())!=EOF&&isspace(c));if(c==EOF)return _=1,*this;ch+=c;while((c=gc())!=EOF&&!isspace(c))ch+=c;if(c==EOF)_=1;return *this;}template<typename T>IN&operator>>(T&x){if(_)return *this;char c=gc();bool ff=0;while(c!=EOF&&(c<'0'||c>'9'))ff^=(c=='-'),c=gc();if(c==EOF){_=1;return *this;}x=0;while(c!=EOF&&'0'<=c&&c<='9')x=(x<<3)+(x<<1)+c-48,c=gc();if(c==EOF)_=1;if(ff)x=-x;return *this;}}in;struct OUT{char buf[str],*s,*t;OUT():s(buf),t(buf+str){}~OUT(){fwrite(buf,1,s-buf,stdout);}void pt(char c){(s==t)?(fwrite(s=buf,1,str,stdout),*s++=c):(*s++=c);}OUT&operator<<(const char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(char*s){while(*s)pt(*s++);return *this;}OUT&operator<<(string s){for(int i=0;s[i];i++)pt(s[i]);return *this;}template<typename T>OUT&operator<<(T x){if(!x)return pt('0'),*this;if(x<0)pt('-'),x=-x;char a[30],t=0;while(x)a[t++]=x%10,x/=10;while(t--)pt(a[t]+'0');return *this;}}out;}using namespace IO;
#define N 100011
int n,m,f[18][N],a[N],pre[N],sta[N],tp=0,suf[N];
ll fl[N],fr[N],gl[N],gr[N];
#define cmp(x,y) ((a[x]<a[y])?x:y)
void st(){
    Fur(k,1,17)
        Fur(i,1,n)
        f[k][i]=cmp(f[k-1][i],f[k-1][i+(1<<(k-1))]);
}
int ask(int l,int r){
    int k=l2(r-l+1);
    return cmp(f[k][l],f[k][r-(1<<k)+1]);
}
int main(){
    in>>n>>m;
    Fur(i,1,n)in>>a[i],f[0][i]=i;
    st();
    Fur(i,1,n){
        while(tp&&a[sta[tp]]>a[i])suf[sta[tp--]]=i;
        pre[i]=sta[tp];
        sta[++tp]=i;
    }
    while(tp)pre[sta[tp]]=sta[tp-1],suf[sta[tp--]]=n+1;
    Fur(i,1,n)fr[i]=fr[pre[i]]+1ll*a[i]*(i-pre[i]),gr[i]=gr[i-1]+fr[i];
    Fdr(i,n,1)fl[i]=fl[suf[i]]+1ll*a[i]*(suf[i]-i),gl[i]=gl[i+1]+fl[i];

    int l,r,p;
    while(m--){
        in>>l>>r;
        p=ask(l,r);
        out<<(ll)(gr[r]-gr[p]-1ll*fr[p]*(r-p)+1ll*a[p]*(p-l+1)*(r-p+1)+gl[l]-gl[p]-1ll*fl[p]*(p-l))<<ln;
    }
}
LG 3246 [HNOI2016]序列
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