2017 ACM/ICPC Asia Regional Shenyang Online 1004 array array array 最長上升子序列（板子可以更新啦，複雜度nlog2(n)）

題目鏈接：array array array
題意：從給定n個元素的數組中刪除k個元素，如果剩下的數組元素是一個非遞增序列或者是一個非遞減序列，則輸出“A is a magic array.”，否則，輸出“A is not a magic array.”
思路：等於求至少得刪除幾個元素使得原序列要麼是個遞增序列，要麼是個遞減序列，它等於 (n - max(最長遞增子序列長度，最長遞減子序列長度)),最後再和k比較就行了。
本題主要是複雜度n*n求最長上升子序列會被卡，n*log（n）才能過。

#include <iostream>
#include <cstdio>
#include <fstream>
#include <algorithm>
#include <cmath>
#include <deque>
#include <vector>
#include <queue>
#include <string>
#include <cstring>
#include <map>
#include <stack>
#include <set>
#define Max(a,b) a>b?a:b
#define Min(a,b) a>b?b:a
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
typedef long long ll;
int dir[4][2]= {{1,0},{-1,0},{0,1},{0,-1}};
const double eps = 1e-6;
const double Pi = acos(-1.0);
const int INF=0x3f3f3f3f;

const int maxn = 1e5+10;
int a[maxn];

int dp1[maxn];
int dp2[maxn];
int tmp1,tmp2;
int n;
int find1(int tag,int rr,int* dp1){
    int l = 1, r = rr,mid;
    while(l <= r){
        mid = (l + r)/2;
        if(dp1[mid] == tag){
            l = mid;
            break;
        }else if(dp1[mid] < tag){
            l = mid + 1;
        }else{
            r = mid - 1;
        }
    }
    return l;
}

int find2(int tag,int rr,int *dp2){
    int l = 1, r = rr, mid;
    while(l <= r){
        mid = (r + l)/2;
        if(dp2[mid] == tag){
            l = mid;
            break;
        }else if(dp2[mid] < tag){
            r = mid - 1;
        }else{
            l = mid + 1;
        }
    }
    return l;
}

void LIS(){
    tmp1 = 0,tmp2 = 0;
    memset(dp1,INF,sizeof(dp1));
    memset(dp2,0,sizeof(dp2));
    dp1[0] = 0,dp2[0] = INF;
    for(int i = 1; i <= n; i++){
        int p = find1(a[i],tmp1,dp1);
        if(p > tmp1) tmp1++;
        dp1[p] = min(dp1[p],a[i]);//以上爲求最長遞增子序列

        p = find2(a[i],tmp2,dp2);
        if(p > tmp2) tmp2++;
        dp2[p] = max(dp2[p],a[i]);//以上爲求最長遞減子序列
    }
}


int main()
{
    int T,k;
    scanf("%d",&T);
    while(T--){
        scanf("%d%d",&n,&k);
        for(int i = 1 ; i <= n; i++)
        {
            scanf("%d",&a[i]);
        }
        LIS();

        if(min(n - tmp1,n - tmp2) <= k){
            printf("A is a magic array.\n");
        }else{
            printf("A is not a magic array.\n");
        }
    }
    return 0;
}

必須多做點DP題纔行…