CodeForces 446A DZY Loves Sequences (DP+暴力)

Posted 2020-08-15 dwtfukgv

题意：给定一个序列，让你找出一个最长的序列，使得最多改其中的一个数，使其变成严格上升序列。

析：f[i] 表示以 i 结尾的最长上升长度，g[i] 表示以 i 为开始的最长上升长度，这两个很容易就求得，最后枚举中间值即可。

代码如下：

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include <cstdio>
#include <string>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <cstring>
#include <set>
#include <queue>
#include <algorithm>
#include <vector>
#include <map>
#include <cctype>
#include <cmath>
#include <stack>
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
//#include <tr1/unordered_map>
#define freopenr freopen("in.txt", "r", stdin)
#define freopenw freopen("out.txt", "w", stdout)
using namespace std;
//using namespace std :: tr1;

typedef long long LL;
typedef pair<int, int> P;
const int INF = 0x3f3f3f3f;
const double inf = 0x3f3f3f3f3f3f;
const LL LNF = 0x3f3f3f3f3f3f;
const double PI = acos(-1.0);
const double eps = 1e-8;
const int maxn = 1e5 + 5;
const LL mod = 10000000000007;
const int N = 1e6 + 5;
const int dr[] = {-1, 0, 1, 0, 1, 1, -1, -1};
const int dc[] = {0, 1, 0, -1, 1, -1, 1, -1};
const char *Hex[] = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};
inline LL gcd(LL a, LL b){  return b == 0 ? a : gcd(b, a%b); }
int n, m;
const int mon[] = {0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
const int monn[] = {0, 31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
inline int Min(int a, int b){ return a < b ? a : b; }
inline int Max(int a, int b){ return a > b ? a : b; }
inline LL Min(LL a, LL b){ return a < b ? a : b; }
inline LL Max(LL a, LL b){ return a > b ? a : b; }
inline bool is_in(int r, int c){
    return r >= 0 && r < n && c >= 0 && c < m;

}
int f[maxn], g[maxn], a[maxn];

int main(){
    while(scanf("%d", &n) == 1){
        a[0] = 0;
        memset(f, 0, sizeof f);
        memset(g, 0, sizeof g);
        for(int i = 1; i <= n; ++i)  scanf("%d", a+i);
        f[0] = 0;  f[1] = 1;
        for(int i = 2; i <= n; ++i)
            if(a[i] > a[i-1]) f[i] = f[i-1] + 1;
            else f[i] = 1;
        g[n] = 1;
        for(int i = n-1; i > 0; --i)
            if(a[i] < a[i+1]) g[i] = g[i+1] + 1;
            else g[i] = 1;
        int ans = 0;
        for(int i = 1; i <= n; ++i){
            ans = Max(ans, f[i]+g[i]-1);
            if(i < n) ans = Max(ans, f[i]+1);
            if(i > 1) ans = Max(ans, g[i]+1);
            if(i > 1 && a[i] > a[i-1])  ans = Max(ans, f[i-1]+g[i]);
            if(i < n && a[i] < a[i+1])  ans = Max(ans, f[i]+g[i+1]);
            if(i > 1 && i < n && a[i+1] - a[i-1] > 1)  ans = Max(ans, f[i-1]+g[i+1]+1);
        }
        printf("%d\n", ans);
    }
    return 0;
}