Educational Codeforces Round 23 D. Imbalanced Array-优快云博客

本文链接：https://blog.youkuaiyun.com/weixin_45714303/article/details/125783340

这篇博客介绍了两种解决数组区间和问题的算法，sol1 和 sol2。它们分别处理正数和负数数组，通过维护单调栈来计算左右边界，然后更新区间乘积的贡献。算法适用于处理大规模数据，有效地计算了每个元素区间内的乘积之和。

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#include<bits/stdc++.h>

using namespace std;

#define X first
#define Y second
#define eps  1e-2
#define gcd __gcd
#define pb push_back
#define PI acos(-1.0)
#define lowbit(x) (x)&(-x)
#define bug printf("!!!!!\n");
#define mem(x,y) memset(x,y,sizeof(x))

typedef long long LL;
typedef long double LD;
typedef pair<int,int> pii;
typedef unsigned long long uLL;

#define int long long 
const int maxn = 1e5+2;
const int INF  = 1<<30;
const int mod  = 1e9+7;

int n,a[maxn],l[maxn],r[maxn]; 

int ans=0;

void sol1(){
    a[0]=a[n+1]=1e9;
    std::vector<int> v;
    v.push_back(0);
    for(int i=1;i<=n;i++){
        while(a[v.back()]<=a[i]) v.pop_back();
        l[i]=i-v.back()-1;
        v.push_back(i);
    }
    v.clear();
    v.push_back(n+1);
    for(int i=n;i>=1;i--){
        while(a[v.back()]<a[i]) v.pop_back();
        r[i]=v.back()-i-1;
        v.push_back(i);
    }
    for(int i=1;i<=n;i++){
        ++r[i];++l[i];
        // cout<<r[i]<<" "<<l[i]<<endl;
        int cnt=r[i]*l[i];
        ans+=cnt*a[i];
    }
}
void sol2(){
    a[0]=a[n+1]=-1;
    std::vector<int> v;
    v.push_back(0);
    for(int i=1;i<=n;i++){
        while(a[v.back()]>a[i]) v.pop_back();
        l[i]=i-v.back()-1;
        v.push_back(i);
    }
    v.clear();
    v.push_back(n+1);
    for(int i=n;i>=1;i--){
        while(a[v.back()]>=a[i]) v.pop_back();
        r[i]=v.back()-i-1;
        v.push_back(i);
    }
    for(int i=1;i<=n;i++){
        ++r[i];++l[i];
        int cnt=r[i]*l[i];
        // cout<<l[i]<<" "<<r[i]<<endl;
        ans-=cnt*a[i];
    }
}

void solve(){
    scanf("%lld",&n);
    for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
    sol1();
    sol2();
    cout<<ans<<endl;
    return;
}

int32_t main()
{
//    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
//    ios::sync_with_stdio(false);
    int t = 1;
    //scanf("%d",&t);
    while(t--){
    //    printf("Case %d: ",cas++);
        solve();
    }
    return 0;
}