【19.11.9】雅礼集团联考

题目 

*一个不是很好理解的DP

*考虑过数学和DP，感觉应该是数学但推不出，所以DP没怎么想，但这题的DP的状态转移不是很好想

#include<bits/stdc++.h>
#define ri register int
#define ll long long
#define For(i,l,r) for(ri i=l;i<=r;i++)
#define Dfor(i,r,l) for(ri i=r;i>=l;i--)
using namespace std;
const int M=1e5+5;
int n,a[M],b[M];
ll f[M][2];
ll p=1000000007;
inline ll read(){
    ll f=1,sum=0;
    char ch=getchar();
    while(!isdigit(ch)){if(ch=='-')f=-1;ch=getchar();}
    while(isdigit(ch)){sum=(sum<<1)+(sum<<3)+(ch^48);ch=getchar();}
    return f*sum;
}
int main(){
    freopen("choose.in","r",stdin);
    freopen("choose.out","w",stdout);
    n=read();
    For(i,1,n){
        a[i]=read();
    }
    For(i,1,n-1){
        b[i]=read();
    }
    f[0][0]=1;
    For(i,1,n){
        f[i][1]=(f[i-1][0]*b[i]%p+f[i-1][1]*b[i]%p)%p;
        f[i][0]=((f[i-1][1]*((a[i]+b[i-1]-1)%p)%p)+(f[i-1][0]*((a[i]+b[i-1])%p)%p))%p;
    }
    printf("%lld
",(f[n][0]+p)%p);
    return 0;
}

 

*

#include<bits/stdc++.h>
using namespace std;
#define MAXN 100010
#define int long long
int n,ans,cur,sets[MAXN];

inline int read(){
    int x=0, f=1;
    char ch=getchar();
    while(ch<'0' || ch>'9'){
        if(ch=='-') f=-1;
        ch=getchar();
    }
    while(ch>='0' && ch<='9'){
        x=x*10+ch-48;
        ch=getchar();
    }
    return x*f;
}

struct EData{
    int a, b, w;
}es[10*MAXN];

struct Node{
    int id, x, y, z;
}a[MAXN];

bool cmp1(Node a, Node b){
    return a.x < b.x;
}

bool cmp2(Node a, Node b){
    return a.y < b.y;
}

bool cmp3(Node a, Node b){
    return a.z < b.z;
}

bool cmp4(EData a, EData b){
    return a.w < b.w;
}

void add_e(int a, int b, int w){
    cur++;
    es[cur].a = a;
    es[cur].b = b;
    es[cur].w = w;
}

int find_root(int x){
    if(sets[x] == x) return x;
    int root = find_root(sets[x]);
    sets[x] = root;
    return root;
}

bool sets_union(int x, int y){
    int x_root = find_root(x);
    int y_root = find_root(y);
    if(x_root == y_root) return 0;
    sets[x_root] = y_root;
    return 1;
}

signed main(){
    freopen("planet.in","r",stdin);
    freopen("planet.out","w",stdout);
    n=read();
    for(int i=1; i<=n; i++){
        a[i].id = i;
        a[i].x = read();
        a[i].y = read();
        a[i].z = read();
    }
    sort(a+1,a+n+1,cmp1);
    for(int i=1; i<n; i++){
        add_e(a[i].id, a[i+1].id, abs(a[i].x-a[i+1].x));
    }
    sort(a+1,a+n+1,cmp2);
    for(int i=1; i<n; i++){
        add_e(a[i].id, a[i+1].id, abs(a[i].y-a[i+1].y));
    }
    sort(a+1,a+n+1,cmp3);
    for(int i=1; i<n; i++){
        add_e(a[i].id, a[i+1].id, abs(a[i].z-a[i+1].z));
    }
    sort(es+1,es+cur+1,cmp4);
    for(int i=1; i<=n; i++){
        sets[i] = i;
    }
    for(int i=1; i<=cur; i++){
        if(sets_union(es[i].a, es[i].b)) ans += es[i].w;
    }
    printf("%lld",ans);
    return 0;
}

 

 *预处理每个点与最近的树木的距离

#include<bits/stdc++.h>
using namespace std;
#define MAXN 2010
const int bas=1000;
int hang,lie,cnt,mp[MAXN][MAXN],d[MAXN][MAXN],dist[MAXN][MAXN],vis[MAXN][MAXN],sx,sy,tx,ty;
const int INF=10000000;
int dirx[5]={0,0,-1,1}, diry[5]={1,-1,0,0};
char s[MAXN];
inline int read(){
    int x=0,f=1;
    char ch=getchar();
    while(ch<'0'||ch>'9'){
        if(ch=='-') f=-1;
        ch=getchar();
    }
    while(ch>='0'&&ch<='9'){
        x=x*10+ch-48;
        ch=getchar();
    }
    return x*f;
}
struct Tree{
    int x, y;
}tr[MAXN*MAXN];
struct FData{
    int x,y,g,h;
    bool operator < (const FData &t) const{
        return g+h>t.g+t.h;
    }
}fs[MAXN][MAXN];
priority_queue <FData> q;
int check(int x,int y,int r){
    int minx=min(2000,x+r);
    int miny=min(2000,y+r);
    int maxx=max(1,x-r);
    int maxy=max(1,y-r);
    return d[maxx][maxy]-d[maxx][miny-1]-d[minx-1][maxy]+d[minx-1][miny-1];
}
int Deal(int x, int y){
    int l=0,r=2000,rt=0;
    while(l<=r){
        int mid=l+r>>1;
        if(check(x,y,mid)){
            rt=mid;
            r=mid-1;
        }else{
            l=mid+1;
        }
    }
    return rt;
}
int H(int x, int y){
    return abs(x-tx)+abs(y-ty);
}
int D_min_dist(int lim){
    memset(vis,0,sizeof(vis));
    for(int i=1;i<=hang;i++){
        for(int j=1;j<=lie;j++){
            fs[i][j].x=i;
            fs[i][j].y=j;
            fs[i][j].g=INF;
            fs[i][j].h=0;
        }
    }
    fs[sx][sy].g=0;
    fs[sx][sy].h=H(sx,sy);
    q.push(fs[sx][sy]);
    while(!q.empty()){
        int x=q.top().x;
        int y=q.top().y;
        q.pop();
        if(vis[x][y]) continue;
        vis[x][y]=1;
        for(int i=0;i<4;i++){
            int cx=x+dirx[i];
            int cy=y+diry[i];
            if(cx<1||cx>hang||cy<1||cy>lie) continue;
            if(dist[cx][cy]<lim) continue;
            if(vis[cx][cy]) continue;
            int dis=fs[x][y].g+1;
            if(fs[cx][cy].g>dis){
                fs[cx][cy].g=dis;
                fs[cx][cy].h=H(cx,cy);
                q.push(fs[cx][cy]);
            }
        }
    }
    if(fs[tx][ty].g==INF) return 0;
    else return 1;
}
int main(){
    freopen("path.in","r",stdin);
    freopen("path.out","w",stdout);
    hang=read();lie=read();
    for(int i=1;i<=hang;i++){
        scanf("%s",s+1);
        for(int j=1;j<=lie;j++){
            if(s[j]=='V'){
                sx=i,sy=j;
                mp[i][j]=2;
            }
            else if(s[j]=='J'){
                tx=i,ty=j;
                mp[i][j]=3;
            }
            else if(s[j]=='+'){
                cnt++;
                tr[cnt].x=i+j+bas;
                tr[cnt].y=i-j+bas;
                d[i+j+bas][i-j+bas]=1;
                mp[i][j]=-1;
            }
        }
    }
    for(int i=1;i<=2000;i++){
        for(int j=1;j<=2000;j++){
            d[i][j]+=d[i][j-1]+d[i-1][j]-d[i-1][j-1];
        }
    }
    for(int i=1;i<=hang;i++){
        for(int j=1;j<=lie;j++){
            dist[i][j]=Deal(i+j+bas,i-j+bas)-1;
            if(mp[i][j]==-1) dist[i][j]++;
        }
    }
    int l=0,r=dist[sx][sy],rt=0;
    while(l<=r){
        int mid=l+r>>1;
        if(D_min_dist(mid)){
            rt=mid;
            l=mid+1;
        }else{
            r=mid-1;
        }
    }
    printf("%d",rt);
    return 0;
}