$NOIP2013$ 题解报告
目录
$Luogu\ P1965$ 转圈游戏$(\ √\ )$
$Luogu\ P1966$ 火柴排队$(\ √\ )$
$Luogu\ P1967$ 货车运输$(\ √\ )$
$Luogu\ P1969$ 积木大赛$(\ √\ )$
$Luogu\ P1970$ 花匠$(\ √\ )$
$Luogu\ P1979$ 华容道（ ）
$Luogu\ P1965$ 转圈游戏
快速幂$+$模拟
1 #include<bits/stdc++.h> 2 using namespace std; 3 int n,m,k,x,ans; 4 int quick(int a,int K){ 5 int A=a,res=1; 6 while(K){ 7 if(K&1) 8 res=res*A%n; 9 A=A*A%n; 10 K>>=1; 11 } 12 return res; 13 } 14 int main(){ 15 scanf("%d%d%d%d",&n,&m,&k,&x); 16 ans=(x%n+m%n*quick(10,k)%n)%n; 17 printf("%d",ans); 18 return 0; 19 }
$Luogu\ P1966$ 火柴排队
显然按大小匹配，求逆序对即可
1 #include<bits/stdc++.h> 2 #define ri register int 3 #define ll long long 4 #define rl register ll 5 #define go(i,a,b) for(ri i=a;i<=b;i++) 6 #define back(i,a,b) for(ri i=a;i>=b;i--) 7 #define g() getchar() 8 #define il inline 9 #define pf printf 10 #define mem(a,b) memset(a,b,sizeof(a)) 11 using namespace std; 12 il int fr(){ 13 ri w=0,q=1;char ch=g(); 14 while(ch<'0'||ch>'9'){if(ch=='-')q=-1;ch=g();} 15 while(ch>='0'&&ch<='9')w=(w<<1)+(w<<3)+ch-'0',ch=g(); 16 return w*q; 17 } 18 const int N=100002; 19 const int mod=99999997; 20 int n,to[N],ans; 21 struct node{ 22 int h,id; 23 }a[N],b[N]; 24 il bool cmp(node x,node y){return x.h<y.h;} 25 il void sol(ri l,ri r){ 26 if(l>=r)return; 27 ri mid=(l+r)>>1; 28 sol(l,mid);sol(mid+1,r); 29 ri i=l,j=mid+1,k=l; 30 int c[N]; 31 while(i<=mid&&j<=r){ 32 if(to[i]<=to[j]){c[k]=to[i];k++;i++;} 33 else{ 34 c[k]=to[j];k++;j++; 35 ans=(ans+mid-i+1)%mod; 36 } 37 } 38 while(i<=mid)c[k]=to[i],k++,i++; 39 while(j<=r)c[k]=to[j],k++,j++; 40 go(i0,l,r)to[i0]=c[i0];return; 41 } 42 int main(){ 43 //freopen(".in","r",stdin); 44 //freopen(".out","w",stdout); 45 n=fr(); 46 go(i,1,n)a[i].h=fr(),a[i].id=i; 47 go(i,1,n)b[i].h=fr(),b[i].id=i; 48 sort(a+1,a+1+n,cmp);sort(b+1,b+1+n,cmp); 49 go(i,1,n)to[a[i].id]=b[i].id; 50 sol(1,n);pf("%d\n",ans); 51 return 0; 52 }
$Luogu\ P1967$ 货车运输
求原图最大生成树，然后对于两个点，求$LCA$得到路径最小值
1 #include<bits/stdc++.h> 2 #define ri register int 3 #define ll long long 4 #define rl register ll 5 #define go(i,a,b) for(ri i=a;i<=b;i++) 6 #define back(i,a,b) for(ri i=a;i>=b;i--) 7 #define g() getchar() 8 #define il inline 9 #define pf printf 10 #define mem(a,b) memset(a,b,sizeof(a)) 11 #define E(i,x) for(ri i=hd[x];i;i=e[i].nxt) 12 #define t(i) e[i].to 13 using namespace std; 14 il int fr(){ 15 ri w=0,q=1;char ch=g(); 16 while(ch<'0'||ch>'9'){if(ch=='-')q=-1;ch=g();} 17 while(ch>='0'&&ch<='9')w=(w<<1)+(w<<3)+ch-'0',ch=g(); 18 return w*q; 19 } 20 const int M=50002; 21 const int N=10002; 22 const int INF=100002; 23 int n,m,q,fa[N],hd[N],ed,f[N][15],mn[N][15],dep[N]; 24 bool vis[N]; 25 struct node{ 26 int x,y,w; 27 }d[M]; 28 struct edge{ 29 int nxt,to,w; 30 }e[N<<1]; 31 il bool cmp(node a,node b){return a.w>b.w;} 32 il int find(ri a){return fa[a]==a?a:fa[a]=find(fa[a]);} 33 il void build(ri x,ri y,ri w){e[++ed]=(edge){hd[x],y,w};hd[x]=ed;return;} 34 il void Tree(ri x,ri ft){ 35 dep[x]=dep[ft]+1;f[x][0]=ft;vis[x]=1; 36 go(i,1,14){ 37 f[x][i]=f[f[x][i-1]][i-1]; 38 mn[x][i]=min(mn[f[x][i-1]][i-1],mn[x][i-1]); 39 } 40 E(i,x){ 41 if(t(i)==ft)continue; 42 mn[t(i)][0]=e[i].w;Tree(t(i),x); 43 } 44 return; 45 } 46 il int LCA(ri x,ri y){ 47 if(dep[x]<dep[y])swap(x,y); 48 ri as=INF; 49 back(i,14,0) 50 if(dep[f[x][i]]>=dep[y])as=min(as,mn[x][i]),x=f[x][i]; 51 if(x==y)return as; 52 back(i,14,0) 53 if(f[x][i]!=f[y][i]){ 54 as=min(as,min(mn[x][i],mn[y][i])); 55 x=f[x][i];y=f[y][i]; 56 } 57 as=min(as,min(mn[x][0],mn[y][0]));return as; 58 } 59 int main(){ 60 //freopen(".in","r",stdin); 61 //freopen(".out","w",stdout); 62 n=fr();m=fr(); 63 go(i,1,n)fa[i]=i; 64 go(i,1,m)d[i]=(node){fr(),fr(),fr()}; 65 sort(d+1,d+1+m,cmp);ri num=0; 66 go(i,1,m){ 67 ri x=d[i].x,y=d[i].y,w=d[i].w; 68 ri fx=find(x),fy=find(y); 69 if(fx==fy)continue; 70 fa[fx]=fy;build(x,y,w);build(y,x,w); 71 num++;if(num==n-1)break; 72 } 73 mem(mn,0x3f);Tree(1,0); 74 go(i,1,n)if(!vis[i])Tree(i,0); 75 q=fr(); 76 while(q--){ 77 ri x=fr(),y=fr(); 78 ri fx=find(x),fy=find(y); 79 if(fx!=fy){puts("-1");continue;} 80 pf("%d\n",LCA(x,y)); 81 } 82 return 0; 83 }
$Luogu\ P1969$ 积木大赛
大水题，递归模拟即可
1 #include<bits/stdc++.h> 2 #define ri register int 3 #define ll long long 4 #define rl register ll 5 #define go(i,a,b) for(ri i=a;i<=b;i++) 6 #define back(i,a,b) for(ri i=a;i>=b;i--) 7 #define g() getchar() 8 #define il inline 9 #define pf printf 10 #define mem(a,b) memset(a,b,sizeof(a)) 11 using namespace std; 12 il int fr(){ 13 ri w=0,q=1;char ch=g(); 14 while(ch<'0'||ch>'9'){if(ch=='-')q=-1;ch=g();} 15 while(ch>='0'&&ch<='9')w=(w<<1)+(w<<3)+ch-'0',ch=g(); 16 return w*q; 17 } 18 const int N=100002; 19 const int INF=10001; 20 int n,h[N],ans; 21 il void work(ri l,ri r){ 22 if(l>r)return; 23 if(l==r){ans+=h[l];h[l]=0;return;} 24 ri mn=INF,L=l; 25 go(i,l,r)mn=min(mn,h[i]);ans+=mn; 26 go(i,l,r){ 27 h[i]-=mn; 28 if(!h[i])work(L,i-1),L=i+1; 29 } 30 work(L,r);return; 31 } 32 int main(){ 33 //freopen(".in","r",stdin); 34 //freopen(".out","w",stdout); 35 n=fr();go(i,1,n)h[i]=fr(); 36 work(1,n);pf("%d\n",ans); 37 return 0; 38 }
$Luogu\ P1970$ 花匠
有个类似贪心的思想，对于要求下降的，显然越小越优；对于要求上升的，显然越大越优，直接$O(N)$贪心即可
1 #include<bits/stdc++.h> 2 #define ri register int 3 #define ll long long 4 #define rl register ll 5 #define go(i,a,b) for(ri i=a;i<=b;i++) 6 #define back(i,a,b) for(ri i=a;i>=b;i--) 7 #define g() getchar() 8 #define il inline 9 #define pf printf 10 #define mem(a,b) memset(a,b,sizeof(a)) 11 using namespace std; 12 il int fr(){ 13 ri w=0,q=1;char ch=g(); 14 while(ch<'0'||ch>'9'){if(ch=='-')q=-1;ch=g();} 15 while(ch>='0'&&ch<='9')w=(w<<1)+(w<<3)+ch-'0',ch=g(); 16 return w*q; 17 } 18 const int N=1e5+2; 19 int n,h[N]; 20 int main(){ 21 //freopen(".in","r",stdin); 22 //freopen(".out","w",stdout); 23 n=fr(); 24 go(i,1,n)h[i]=fr(); 25 ri t1=1,t2=1; 26 go(i,2,n){ 27 if(t1&1){if(h[i]>h[i-1])t1++;} 28 else if(h[i]<h[i-1])t1++; 29 if(t2&1){if(h[i]<h[i-1])t2++;} 30 else if(h[i]>h[i-1])t2++; 31 } 32 pf("%d\n",max(t1,t2)); 33 return 0; 34 }
$Luogu\ P1979$ 华容道
