HDU暑假多校第八场J-Taotao Picks Apples

Posted 2020-12-30 六花的邪王真眼

一、题意

给定一个序列，之后给出若干个修改，修改的内容为在原序列的基础上，将某一位元素的值改成给定的值<每次修改相互独立，不保存修改后的结果>。之后询问，在选择第一位元素的情况下，最长递增子序列的长度是多少。

二、题解

考虑不经修改的情况，应当设dp[i]为选取当前位情况下的最长递增子串的长度。则对于这道题，应当认为对于修改a为b，设l_pos为a左边最大的元素的位置，r_pos为a右边大于max(b,r_pos)的元素的位置。则有ans = dp[1] - dp[l_pos] + 1 + dp[r_pos];对于b本身大于位于l_pos的元素，应当给结果+1。

 

#include<bits/stdc++.h>
using namespace std;

#define ll long long 

const int MAXN = 1000233;

class Node{
    public:
        int l,r,lc,rc,maxx;
};
Node nodes[MAXN];
int nodes_num;
int t,n,m;

int arr[MAXN];
int dp[MAXN];

void tree_init(int a,int b){
    int now = nodes_num++;
    nodes[now].l = a;
    nodes[now].r = b;
    if(a == b-1){
        nodes[now].maxx = arr[a];
        return ;
    }
    int mid = (a+b)/2;
    nodes[now].lc = nodes_num;
    tree_init(a,mid);
    nodes[now].rc = nodes_num;
    tree_init(mid,b);
    nodes[now].maxx = max(nodes[nodes[now].lc].maxx,nodes[nodes[now].rc].maxx);
}

int find_max(int now){
    int l = nodes[now].l;
    int r = nodes[now].r;
    if(l == r-1)return l;
    int maxx = nodes[now].maxx;
    int lc = nodes[now].lc;
    int rc = nodes[now].rc;
    if(maxx == nodes[lc].maxx)return find_max(lc);
    else return find_max(rc);
}

int find_biggest(int now,int a,int b){
    int l = nodes[now].l;
    int r  =nodes[now].r;
    if(l == a&&r == b){
        return find_max(now);
    }
    int mid = (l+r)/2;
    int ret ;
    int lc = nodes[now].lc;
    int rc = nodes[now].rc;
    if(a<mid){
        ret = find_biggest(lc,a,min(b,mid));
        if(b>mid){
            int tmp = find_biggest(rc,mid,b);
            ret = arr[ret] >= arr[tmp] ? ret:tmp;
        }
    }else ret = find_biggest(rc,a,b);
    return ret;
}

int find_left(int now,int key){
    int l = nodes[now].l;
    int r = nodes[now].r;
    if(l == r-1)return l;
    int lc = nodes[now].lc;
    int rc = nodes[now].rc;
    if(nodes[lc].maxx > key)return find_left(lc,key);
    else return find_left(rc,key);
}

int find_first(int now,int pos, int key){
    int l = nodes[now].l;
    int r = nodes[now].r;
    if(l >= pos){
        return find_left(now,key);
    }
    int mid = (l+r)/2;

    int lc = nodes[now].lc;
    int rc = nodes[now].rc;
    int ret ;
    if(pos < mid && nodes[lc].maxx > key){
        ret = find_first(lc,pos,key);
        if(ret >= pos && arr[ret] > key)return ret;
    }
    if(nodes[rc].maxx <= key)return r-1;
    return find_first(rc,pos,key);
    
}

void init(){
    scanf("%d %d",&n,&m);
    nodes_num = 0;
    arr[0] = -100233;
    arr[n+1] = INT_MAX;
    for(int i=1;i<=n;++i)scanf("%d",&arr[i]);
    tree_init(0,n+2);
    memset(dp,0,sizeof(dp));
    for(int i=n;i>=1;--i){
        dp[i] = dp[find_first(0,i+1,arr[i])]+1;
    }
    dp[0] = dp[1]+1;
    for(int i=0;i<m;++i){
        int a,b;
        scanf("%d %d",&a,&b);
        int l_pos = find_biggest(0,0,a);
        int key = max(b,arr[l_pos]);
        int r_pos = find_first(0,a+1,max(b,arr[l_pos]));
        int ans = dp[1] - dp[l_pos] + 1 + dp[r_pos];
        if(b > arr[l_pos] )ans++;
        cout<<ans<<‘
‘;
    }

}

int main(){
    
    cin>>t;
    while(t--)init();

    return 0;
}