CodeForces 447C DZY Loves Sequences DP

题目：click here

题意：求给定序列更改其中一个元素后的最长连续上升子序列的长度

分析：最长的连续子序列有2种，一种是严格上升(没有更改元素)的长度加1，一种是两段严格上升的加起来。

 

#include <bits/stdc++.h>
using namespace std;
#define F first
#define S second
#define pb push_back
#define power(a) ((a)*(a))
#define ENTER printf("\n");
typedef unsigned long long ll;
const int INF = 0x3f3f3f3f;
const double EPS = 1e-8;
const int M = 1e5+5;

int n, ret;
int a[M]; 
int dps[M];     // dps[i]保存以i开头的最长连续上升子序列
int dpe[M];     // dpe[i]保存以i结束的最长连续上升子序列
void solve()    {
    ret = dpe[0] = dps[n-1] = 1;
    for( int i=1; i<n; i++ )
        if( a[i] > a[i-1] ) dpe[i] = dpe[i-1] + 1;
        else dpe[i] = 1;
    for( int i=n-2; i>=0; i-- )
        if( a[i] < a[i+1] ) dps[i] = dps[i+1] + 1;
        else dps[i] = 1;
    for( int i=0; i<n; i++ )
        if( a[i+1]-a[i-1] >= 2 ) ret = max( ret, dps[i+1]+dpe[i-1]+1 );
        else ret = max( ret, max( dps[i+1]+1, dpe[i-1]+1 ) );
    printf("%d\n", ret);
}

int main()  {
    while( ~scanf("%d", &n ) )  {
        for( int i=0; i<n; i++ )    
            scanf("%d", a+i);
        solve();
    }
    return 0;
}