CodeForces 689D Friends and Subsequences （RMQ+二分）

Friends and Subsequences

题目链接：

http://acm.hust.edu.cn/vjudge/contest/121333#problem/H

Description

Mike and !Mike are old childhood rivals, they are opposite in everything they do, except programming. Today they have a problem they cannot solve on their own, but together (with you) — who knows?

Every one of them has an integer sequences a and b of length n. Being given a query of the form of pair of integers (l, r), Mike can instantly tell the value of while !Mike can instantly tell the value of .

Now suppose a robot (you!) asks them all possible different queries of pairs of integers (l, r)(1 ≤ l ≤ r ≤ n) (so he will make exactly n(n + 1) / 2 queries) and counts how many times their answers coincide, thus for how many pairs is satisfied.

How many occasions will the robot count?

Input

The first line contains only integer n (1 ≤ n ≤ 200 000).

The second line contains n integer numbers a1, a2, ..., an ( - 109 ≤ ai ≤ 109) — the sequence a.

The third line contains n integer numbers b1, b2, ..., bn ( - 109 ≤ bi ≤ 109) — the sequence b.

Output

Print the only integer number — the number of occasions the robot will count, thus for how many pairs max(al_ar)==min(blbr) is satisfied.

Sample Input

Input
6
1 2 3 2 1 4
6 7 1 2 3 2
Output
2
Input
3
3 3 3
1 1 1
Output
0

Hint

The occasions in the first sample case are:

1.l = 4,r = 4 since max{2} = min{2}.

2.l = 4,r = 5 since max{2, 1} = min{2, 3}.

There are no occasions in the second sample case since Mike will answer 3 to any query pair, but !Mike will always answer 1.

题意：

分别已知a b数组任意区间的最大值、最小值；
求有多少区间[l,r]满足max(al_ar)==min(blbr);

题解：

RMQ：O(nlgn)预处理 O(1)求出任意区间的min/max；

在固定区间左端点情况下：
由于最大值最小值均具有单调性；
用两次二分操作分别求出第一次和最后一次满足min==max的右端点，作差累加即可；
注意：两次二分操作的差别和意义.

代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <queue>
#include <map>
#include <set>
#include <vector>
#define LL long long
#define eps 1e-8
#define maxn 201000
#define mod 1000000007
#define inf 0x3f3f3f3f
#define IN freopen("in.txt","r",stdin);
using namespace std;

int n, A[maxn], B[maxn];
int d_min[maxn][30];
int d_max[maxn][30];

void RMQ_init() {
    for(int i=0; i<n; i++) d_max[i][0] = A[i], d_min[i][0] = B[i];
    for(int j=1; (1<<j)<=n; j++)
        for(int i=0; i+(1<<j)-1<n; i++) {
            d_min[i][j] = min(d_min[i][j-1], d_min[i+(1<<(j-1))][j-1]);
            d_max[i][j] = max(d_max[i][j-1], d_max[i+(1<<(j-1))][j-1]);
        }
}
int RMQ_min(int L, int R) {
    int k = 0;
    while((1<<(k+1)) <= R-L+1) k++;
    return min(d_min[L][k], d_min[R-(1<<k)+1][k]);
}
int RMQ_max(int L, int R) {
    int k = 0;
    while((1<<(k+1)) <= R-L+1) k++;
    return max(d_max[L][k], d_max[R-(1<<k)+1][k]);
}

int main(int argc, char const *argv[])
{
    //IN;

    while(scanf("%d",&n) != EOF)
    {
        for(int i=0; i<n; i++) scanf("%d",&A[i]);
        for(int i=0; i<n; i++) scanf("%d",&B[i]);
        RMQ_init();

        LL ans = 0;
        for(int i=0; i<n; i++) {
            if(A[i] > B[i]) continue;
            int first_r=-1, last_r=-1;
            int l=i,r=n-1,mid;

            while(l <= r) {
                mid = (l+r) / 2;
                if(RMQ_max(i,mid) == RMQ_min(i,mid)) first_r = mid;
                if(RMQ_max(i,mid) >= RMQ_min(i,mid)) r = mid-1;
                else l = mid+1;
            }
            if(first_r == -1) continue;

            l=i; r=n-1;
            while(l <= r) {
                mid = (l+r) / 2;
                if(RMQ_max(i,mid) > RMQ_min(i,mid))
                    r = mid-1;
                else l = mid+1, last_r = mid;
            }

            ans += last_r - first_r + 1;
        }

        printf("%I64d\n", ans);
    }

    return 0;
}