10.11NOIP模拟题(3)

/*
可以看出，对于一段区间[L,R]如果统计了答案
若a[L]<a[R],那么当右端点往左移时答案不会更优，a[R]>a[L]同理
所以两个指针分别从头尾往中间扫那边小移哪边即可。
*/
#include<bits/stdc++.h>

#define N 1000007
#define ll long long

using namespace std;
ll a[N];
ll n,m,ans,cnt;

int main()
{
    freopen("w.in","r",stdin);
    freopen("w.out","w",stdout);
    scanf("%lld",&n);
    for(int i=;i<=n;i++) scanf("%lld",&a[i]);
    int L=,R=n;
    while(L<=R)
    {
        ll res=(R-L+)*min(a[L],a[R]);
        ans=max(ans,res);
        if(a[L]>=a[R]) R--;
        else L++;
    }
    cout<<ans<<endl;
    return ;
}

/*
发现算来算去所有数的二进制1的个数和位置不会变。
两个数and 或 or只是把他们的二进制位的1聚拢到一个数上。
若两个数为a，b，假设他们进行一次操作后变为(a+x),(b-x),则a>b
那么(a+x)^2+(b-x)^2=a^2+b^2+2x(x+a-b)>a^2+b^2
说明这种“聚拢”操作后平方和会变大
所以把所有数的二进制位1统计下来后尽可能的对分给一个数即可。
*/
#include<bits/stdc++.h>

#define mod 998244353
#define N 10005

using namespace std;
int n,x;
int cnt[N];

int main()
{
    freopen("s.in","r",stdin);
    freopen("s.out","w",stdout);
    scanf("%d",&n);
    for (int i=;i<=n;i++)
    {
        scanf("%d",&x);
        for (int j=;j<;j++) if (x & (<<j)) cnt[j]++;
    }
    unsigned long long ans=;
    for(int i=;i<n;i++)
    {
        x=;
        for(int j=;j<;j++) if (cnt[j]) x |=(<<j),cnt[j]--;
        ans+=(unsigned long long)(x)*x%mod;;
    }
    cout<<ans%mod;
    return ;
}

#include<bits/stdc++.h>

#define N 30
#define ll long long
#define mod 1000000007
#define opt 99999

using namespace std;
int n,m,k,lim;
ll ans;
int dx[]={,,,-};
int dy[]={,-,,};
int vis[N][N],f[N][N];

inline ll read()
{
    int x=,f=;char c=getchar();
    while(c>''||c<''){if(c=='-')f=-;c=getchar();}
    while(c>=''&&c<=''){x=x*+c-'';c=getchar();}
    return x*f;
}

bool can(int x,int y)
{
    if(vis[x][y]==-) return false;
    for(int i=max(,y-);i<=min(y+,m);i++)
      if(vis[x][i]>=opt) return false;
    for(int i=max(,x-);i<=min(n,x+);i++)
      if(vis[i][y]>=opt) return false;
    if(vis[x-][y-]>=opt || vis[x-][y+]>=opt) return false;
    if(vis[x+][y+]>=opt || vis[x+][y-]>=opt) return false;
    return true;
}

void update(int x,int y)
{
    vis[x][y]=opt;
    for(int i=max(,y-);i<=min(y+,m);i++)
      if(vis[x][i]!=-)vis[x][i]++;
    for(int i=max(,x-);i<=min(n,x+);i++)
      if(vis[i][y]!=-)vis[i][y]++;
    if(x- && y- && vis[x-][y-]!=-) vis[x-][y-]++;
    if(x- && y+<=m && vis[x-][y+]!=-) vis[x-][y+]++;
    if(x+<=n && y- && vis[x+][y-]!=-) vis[x+][y-]++;
    if(x+<=n && y+<=m && vis[x+][y+]!=-) vis[x+][y+]++;
}

void _update(int x,int y)
{
    vis[x][y]=;
    for(int i=max(,y-);i<=min(y+,m);i++)
      if(vis[x][i]>)vis[x][i]--;
    for(int i=max(,x-);i<=min(n,x+);i++)
      if(vis[i][y]>)vis[i][y]--;
    if(vis[x-][y-]>)vis[x-][y-]--;
    if(vis[x-][y+]>)vis[x-][y+]--;
    if(vis[x+][y-]>)vis[x+][y-]--;
    if(vis[x+][y+]>)vis[x+][y+]--;
    f[x][y]=;
}

void dfs(int x,int y,int L)
{
    if(L==)
    {
        ans++;ans%=mod;
        return;
    }
    for(int xx=x;xx<=n;xx++) for(int yy=;yy<=m;yy++)
    {
        if(f[xx][yy]) continue;
        if(vis[xx][yy]<opt && can(xx,yy) && !f[xx][yy])
        {
            update(xx,yy);
            f[xx][yy]=;
            dfs(xx,yy,L-);
            _update(xx,yy);//dfs(xx,yy,L);
        }
    }
}

int main()
{
    freopen("l.in","r",stdin);
    freopen("l.out","w",stdout);
    int x,y;ans=;
    n=read();m=read();k=read();
    for(int i=;i<=n;i++)
    {
        x=read();y=read();
        vis[x][y]=-;
    }
    lim=n*m-k;
    while(lim--)
    {
        memset(f,,sizeof f);
        f[][]=;
        dfs(,,lim);
    }
    ans%=mod;cout<<ans<<endl;
    return ;
}

没调出来的dfs

#include <cstdio>
#include <cstring>
#include <vector>

const int MAXN = ;
const int MOD = 1e9 + ;

int m;

inline unsigned int getBit(int i) {
    return 1u << i;
}

inline bool isValidLine(unsigned int s) {
    return !((s & (s << )) || (s & (s << )));
}

inline bool isValidTwoLines(unsigned int a, unsigned int b) {
    return !((a & (b << )) || (a & (b >> )) || (a & b));
}

inline bool isValidThreeLines(unsigned int a, unsigned int b, unsigned int c) {
    return !(a & c) && isValidTwoLines(a, b)/* && isValidTwoLines(b, c)*/;
}

int main() {
    freopen("l.in", "r", stdin);
    freopen("l.out", "w", stdout);

    int n, k;
    scanf("%d %d %d", &n, &m, &k);

    unsigned int ban[n + ];
    memset(ban, , sizeof(ban));
    while (k--) {
        int i, j;
        scanf("%d %d", &i, &j);
        ban[i] |=  << (j - );
    }

    std::vector<unsigned int> validStates;

    unsigned int maxS =  << m;
    for (int i = ; i < maxS; i++) {
        if (isValidLine(i)) {
            validStates.push_back(i);
        }
    }

    // f[i][state of line i - 1][state of line i] = count
    long long f[n + ][validStates.size()][validStates.size()];

    memset(f, , sizeof(f));
    for (int a = ; a < (int)validStates.size(); a++) f[][][a] = ;

    long long ans = ;
    for (int i = ; i <= n; i++) {
        for (int c = ; c < (int)validStates.size(); c++) {
            if (ban[i] & validStates[c]) continue;
            for (int b = ; b < (i <=  ?  : (int)validStates.size()); b++) {
                if (!isValidTwoLines(validStates[b], validStates[c])) continue;
                if (ban[i - ] & validStates[b]) continue;

                for (int a = ; a < (i <=  ?  : (int)validStates.size()); a++) {
                    if (!isValidThreeLines(validStates[a], validStates[b], validStates[c])) continue;
                    if (a && (ban[i - ] & validStates[a])) continue;

                    (f[i][b][c] += f[i - ][a][b]) %= MOD;
                }

                if (i == n) (ans += f[i][b][c]) %= MOD;
            }
        }
    }

    printf("%lld\n", ans);
}

std

暂时放弃  先做完互不侵犯king再来写这道题