2021.7.14提高B组模拟3T2 积木 （dp）

Posted 2021-08-13 SSL_LKJ

积木

输入样例

1.

3
-1 2 -1

2.

3
-1 -1 -1

3.

6
-1 -1 -1 2 -1 -1

输出样例

1.

0

2.

2

3.

3

解题思路

首先对于每个n

我们都可以求出积木的最高

n=7时，0 1 2 3 2 1 0 ，为3

n=8时，0 1 2 3 3 2 1 0 ，还是为3

那我们可以设 f [i][j]，为 i 位置的积木搭到 j 高度的方案数

如果当前点不知道，为-1

则有 $$f[i][j]=f[i-1][j-1]+f[i-1][j]+f[i-1][j+1]$$

知道则将 j 替换成 a [i]

注意：

用 滚动数组 + 玄学优化 ， 否则可能会炸

AC代码

// 下面可省略--------------------------------------------------------
#pragma GCC diagnostic error "-std=c++11"
#pragma GCC optimize("-fdelete-null-pointer-checks")
#pragma GCC optimize("inline-functions-called-once")
#pragma GCC optimize("-funsafe-loop-optimizations")
#pragma GCC optimize("-fexpensive-optimizations")
#pragma GCC optimize("-foptimize-sibling-calls")
#pragma GCC optimize("-ftree-switch-conversion")
#pragma GCC optimize("-finline-small-functions")
#pragma GCC optimize("inline-small-functions")
#pragma GCC optimize("-frerun-cse-after-loop")
#pragma GCC optimize("-fhoist-adjacent-loads")
#pragma GCC optimize("-findirect-inlining")
#pragma GCC optimize("-freorder-functions")
#pragma GCC optimize("no-stack-protector")
#pragma GCC optimize("-fpartial-inlining")
#pragma GCC optimize("-fsched-interblock")
#pragma GCC optimize("-fcse-follow-jumps")
#pragma GCC optimize("-fcse-skip-blocks")
#pragma GCC optimize("-falign-functions")
#pragma GCC optimize("-fstrict-overflow")
#pragma GCC optimize("-fstrict-aliasing")
#pragma GCC optimize("-fschedule-insns2")
#pragma GCC optimize("-ftree-tail-merge")
#pragma GCC optimize("inline-functions")
#pragma GCC optimize("-fschedule-insns")
#pragma GCC optimize("-freorder-blocks")
#pragma GCC optimize("-fwhole-program")
#pragma GCC optimize("-funroll-loops")
#pragma GCC optimize("-fthread-jumps")
#pragma GCC optimize("-fcrossjumping")
#pragma GCC optimize("-fcaller-saves")
#pragma GCC optimize("-fdevirtualize")
#pragma GCC optimize("-falign-labels")
#pragma GCC optimize("-falign-loops")
#pragma GCC optimize("-falign-jumps")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("-fsched-spec")
#pragma GCC optimize("-ffast-math")
#pragma GCC optimize("-fpeephole2")
#pragma GCC optimize("-ftree-pre")
#pragma GCC optimize("-ftree-vrp")
#pragma GCC optimize("-fgcse-lm")
#pragma GCC optimize("-fipa-sra")
#pragma GCC optimize("inline")
#pragma GCC optimize("-fgcse")
#pragma GCC optimize("Ofast")
#pragma GCC optimize(3)
#pragma GCC target("avx","sse2")
// 分界线 ---------------------------------------------------------
#include<cstring>
#include<cstdio>
using namespace std;
const long long Mod=1000000007;
int n,a[20005];
long long f[2][10005];
int high(int x)
{
	if(x<n/2+1)return x-1;
	return n-x;
}
int main()
{
	freopen("brick.in","r",stdin);
	freopen("brick.out","w",stdout);
	scanf("%d",&n);
	for(register int i=1;i<=n;i++)
	 scanf("%d",&a[i]);//输入
	f[0][0]=1;//预处理
	for(register int i=1;i<=n;i++)
	{
		int x=high(i),xx=high(i-1);
		if(a[i]!=-1)//两种情况
		{
			if(a[i]<=x)
			{
				f[1][a[i]]+=f[0][a[i]];
				if(a[i]>=1)f[1][a[i]]+=f[0][a[i]-1];
				if(a[i]+1<=xx)f[1][a[i]]+=f[0][a[i]+1];
				f[1][a[i]]%=Mod;
			}
		}
		else
		{
			for(register int j=0;j<=x;j++)
			{
				f[1][j]+=f[0][j];
				if(j>=1)f[1][j]+=f[0][j-1];
				if(j+1<=xx)f[1][j]+=f[0][j+1];
				f[1][j]%=Mod;
			}
		}
		memcpy(f[0],f[1],sizeof(f[1]));//这个是将f[1]的值全部转移到f[0]
		memset(f[1],0,sizeof(f[1]));
	}
	printf("%lld",f[0][0]%Mod);
	return 0;
}

谢谢