USACO19JAN Gold题解
噩梦的回忆。。
上周日在机房打的模拟赛，结果十分惨烈，就最后一题yy出了正解结果玄学的只拿了80
考试结果：0+0+80=80
订正时对着T3打了2hours结果还是90
订正结果：100+100+90=290
我太弱了QAQ
T1 Luogu P5196 [USACO19JAN]Cow Poetry
思路：dp+神奇的数学推导
快速幂一开始还写锅了，受到了ftq大佬的嘲笑
code
#include<bits/stdc++.h>
using namespace std;
const int MOD=1e9+7,MAXN=5000+10;
int f[5010][MAXN],s[MAXN],c[MAXN],g[MAXN],num[35],n,m,k;
long long ans,re=1;
long long pow(int b, int p) {
if (p == 0) {
return 1;
}
long long x = b;
long long ans = 1;
while (p > 0) {
if (p % 2 == 1) {
ans = ans * x % MOD;
}
x = x * x % MOD;
p = p >> 1;
}
return ans % MOD;
}
void debug()
{
for(int i=1;i<=5;++i){
cout<<f[k][i]<<" ";
}
cout<<endl;
for(int i=0;i<=5;++i){
cout<<num[i]<<" ";
}
cout<<endl;
}
signed main()
{
// freopen(".in","r",stdin);
// freopen(".out","w",stdout);
cin>>n>>m>>k;
for(int i=1;i<=n;++i){
cin>>s[i]>>c[i];
}
g[0]=1;
for(int i=1;i<=k;i++){
for(int j=1;j<=n;j++){
if(i-s[j]>=0){
(f[i][c[j]]+=g[i-s[j]])%=MOD;
(g[i]+=g[i-s[j]])%=MOD;
}
}
}
for(int i=1;i<=m;++i){
char ch;
cin>>ch;
num[ch-'A']++;
}
// debug();
for(int i=0;i<26;++i){
if(num[i]){
ans=0;
for(int j=1;j<=n;++j){
if(f[k][j]){
(ans+=pow(f[k][j],num[i]))%=MOD;
// cout<<ans<<endl;
}
}
(re*=ans)%=MOD;
}
}
cout<<re<<endl;
return 0;
}
T2 Luogu P5200 [USACO19JAN]Sleepy Cow Sorting
思路：神奇的推导+树状数组
code
#include<bits/stdc++.h>
using namespace std;
const int MAXN=1e5+10;
inline int lowbit(int x){return x&(-x);}
int ans[MAXN],num[MAXN],tree[MAXN],n,sum,k;
void add(int x)
{
for(int i=x;i<=n;i+=lowbit(i)){
tree[i]++;
}
}
int query(int x)
{
int re=0;
for(int i=x;i;i-=lowbit(i)){
re+=tree[i];
}
return re;
}
int main()
{
// freopen(".in","r",stdin);
// freopen(".out","w",stdout);
cin>>n;
for(int i=1;i<=n;++i){
cin>>num[i];
}
sum=n,k=0;
while(num[n-k]>num[n-k-1]){
add(num[n-k]);
sum--,k++;
}
add(num[n-k]);
sum--;
for(int i=1;i<=sum;++i){
add(num[i]);
ans[i]=sum-i+query(num[i]-1);
}
cout<<sum<<endl;
for(int i=1;i<=sum;++i){
cout<<ans[i]<<" ";
}
return 0;
}
T3 Luogu P5201 [USACO19JAN]Shortcut
思路：dij+最短路树
code
#include<bits/stdc++.h>
#define int long long
#define ll long long
using namespace std;
const int MAXN=1e5+10,INF=0x3f3f3f3f;
inline int read()
{
int s=0,f=1;
char ch=getchar();
while(ch<'0'||ch>'9'){
if(ch=='-')
f=-1;
ch=getchar();
}
while(ch>='0'&&ch<='9'){
s=s*10+ch-'0';
ch=getchar();
}
return s*f;
}
struct NODE {
int first,second;
bool operator<(NODE b) const { return (b.first==first)?b.second<second:b.first < first; }
};
int cnt,Cnt,m,n,T;
int head[MAXN],Head[MAXN],from[MAXN],siz[MAXN],v[MAXN];
ll dist[MAXN],ans=0;
priority_queue <NODE > q;
bool vis[MAXN],vi[MAXN];
void debug()
{
puts("head Head from siz dist");
for(int i=1;i<=n;++i){
cout<<head[i]<<" "<<Head[i]<<" "<<from[i]<<" "<<siz[i]<<" "<<dist[i]<<endl;
}
}
struct node{
int to,next,l;
}edge[MAXN];
void addedge(int x,int y,int l)
{
edge[++cnt].to=y;
edge[cnt].l=l;
edge[cnt].next=head[x];
head[x]=cnt;
}
struct Node{
int to,next;
}Edge[MAXN];
void Addedge(int x,int y)
{
Edge[++Cnt].to=y;
Edge[Cnt].next=Head[x];
Head[x]=Cnt;
}
void dij()
{
memset(dist,INF,sizeof(dist));
dist[1]=0;
NODE a;
a.first=0,a.second=1;
q.push(a);
while(!q.empty()){
NODE now=q.top();q.pop();
int x=now.second;
// if(vi[x])continue;
// vi[x]=1;
// cout<<x<<"while\n";
for(int i=head[x];i;i=edge[i].next){
// cout<<i<<"i\n";
int y=edge[i].to;
// cout<<y<<" y\n";
if(dist[x]+edge[i].l<dist[y]){
// cout<<y<<"y\n";
NODE aa;
aa.second=y,aa.first=dist[y];
dist[y]=dist[x]+edge[i].l;
from[y]=x;
// cout<<"to"<<y<<endl;
q.push(aa);
}
}
}
}
void build()
{
for(int i=1;i<=n;++i){
Addedge(i,from[i]);
Addedge(from[i],i);
}
}
int dfs(int x,int fa)
{
vis[x]=1;
siz[x]+=v[x];
for(int i=Head[x];i;i=Edge[i].next){
int y=Edge[i].to;
if(!vis[y]&&y!=fa){
siz[x]+=dfs(y,x);
}
}
return siz[x];
}
signed main()
{
// freopen("test08.in","r",stdin);
// freopen("1.out","w",stdout);
cin>>n>>m>>T;
for(int i=1;i<=n;++i){
v[i]=read();
}
for(int i=1;i<=m;++i){
int x=read(),y=read(),t=read();
addedge(x,y,t);
addedge(y,x,t);
}
dij();
build();
dfs(1,0);
// debug();
for(int i=1;i<=n;++i){
ans=max(ans,siz[i]*(dist[i]-T));
}
cout<<ans<<endl;
return 0;
}
