A. Alien Sunset
暴力列舉答案即可。
#include<cstdio>
int n,i,mx;
struct P{
int h,r,t;
bool night(int x){
x%=h;
if(r<=t)return x<=r||x>=t;
return x<=r&&x>=t;
}
}a[50];
inline bool check(int x){
for(int i=0;i<n;i++)if(!a[i].night(x))return 0;
return 1;
}
int main(){
scanf("%d",&n);
for(i=0;i<n;i++){
scanf("%d%d%d",&a[i].h,&a[i].r,&a[i].t);
if(a[i].h>mx)mx=a[i].h;
}
for(i=0;i<1825*mx;i++)if(check(i))return printf("%d",i),0;
puts("impossible");
}
B. Breaking Biscuits
等價於選擇一對距離最小的平行線夾住所有點。
列舉一條邊，計算兩側所有點到這條直線的距離的最大值即可。
時間複雜度$O(n^3)$。
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
const int N=111;
struct P{
int x,y;
P(){}
P(int _x,int _y){x=_x,y=_y;}
P operator-(P b){return P(x-b.x,y-b.y);}
double len(){return hypot(x,y);}
}a[N];
int n,i,j,k;
double cross(P a,P b){return a.x*b.y-a.y*b.x;}
double dist(P p,P a,P b){
return cross(p-a,b-a)/(b-a).len();
}
int main(){
scanf("%d",&n);
for(i=1;i<=n;i++)scanf("%d%d",&a[i].x,&a[i].y);
double ans=1e100;
a[n+1]=a[1];
for(i=1;i<=n;i++)for(j=1;j<i;j++){
double l=1e100,r=-1e100;
for(k=1;k<=n;k++){
l=min(l,dist(a[k],a[i],a[j]));
r=max(r,dist(a[k],a[i],a[j]));
}
r-=l;
ans=min(ans,r);
}
printf("%.10f",ans);
}
C. Cued In
按題意模擬即可。
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
const int N = 3e5 + 10;
const int inf = 1e9;
int casenum, casei;
int c[2010], e[15];
int n;
map<string, int> mop;
int num[10];
char s[20];
int main()
{
mop["red"] = 1; mop["yellow"] = 2; mop["green"] = 3; mop["brown"] = 4;
mop["blue"] = 5; mop["pink"] = 6; mop["black"] = 7;
while(~scanf("%d", &n)){
for(int i = 1; i <= n; i ++){
scanf("%s", s);
num[mop[s]] ++;
}
int top = 1;
for(int i = 2; i <= 7; i ++){
if(num[i]) top = i;
}
if(top == 1) puts("1");
else{
int ans = 0;
ans = (1 + top) * num[1];
for(int i = 2; i <= 7; i ++) ans += num[i] * i;
printf("%d\n", ans);
}
}
return 0;
}
/*
*/
D. Deranging Hat
求出最終位置，然後貪心置換即可。
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
const int N = 1e5 + 10;
char s[N];
struct A
{
char ch;
int now;
bool operator < (const A & b)const
{
if(ch != b.ch)return ch < b.ch;
return now < b.now;
}
}a[N];
int pos_to_o[N];
int main()
{
while(~scanf("%s", s))
{
int n = strlen(s);
for(int i = 0; i < n; ++i)
{
a[i].ch = s[i];
a[i].now = i;
}
sort(a, a + n);
for(int i = 0; i < n; ++i)
{
pos_to_o[a[i].now] = i;
}
vector<pair<int, int> >ans;
for(int i = 0; i < n; ++i)
{
//我們要考慮移動，把位置為a[i].now的數，移動到位置i，那位置i的數的位置變成了a[i].now
if(a[i].now != i)
{
ans.push_back(make_pair(i, a[i].now));
int p = a[i].now;
int o = pos_to_o[i];
a[o].now = a[i].now;
pos_to_o[p] = o;
}
}
int g = ans.size() - 1;
for(int i = g; i >= 0; --i)
{
printf("%d %d\n", ans[i].second + 1, ans[i].first + 1);
}
}
return 0;
}
/*
*/
E. Education
按人數從大到小考慮，每次選擇滿足條件的最便宜的房子。
#include<cstdio>
#include<algorithm>
using namespace std;
const int N=5010;
int n,m,i,a[N],b[N],c[N],q[N],ans[N];
bool cmp(int x,int y){return a[x]<a[y];}
int ask(int x){
int t=0,f=~0U>>1;
for(int i=1;i<=m;i++)if(b[i]>=x){
if(c[i]<f)f=c[i],t=i;
}
return t;
}
int main(){
scanf("%d%d",&n,&m);
for(i=1;i<=n;i++)scanf("%d",&a[i]),q[i]=i;
for(i=1;i<=m;i++)scanf("%d",&b[i]);
for(i=1;i<=m;i++)scanf("%d",&c[i]);
sort(q+1,q+n+1,cmp);
for(i=n;i;i--){
int x=ask(a[q[i]]);
if(!x)return puts("impossible"),0;
b[x]=0;
ans[q[i]]=x;
}
for(i=1;i<=n;i++)printf("%d ",ans[i]);
}
F. Flipping Coins
$f[i][j]$表示還需要操作$i$次，目前有$j$枚硬幣朝上時的最大期望正面向上的硬幣數。
時間複雜度$O(nk)$。
#include<cstdio>
#include<algorithm>
using namespace std;
const int N=444;
double f[N][N],ans;
int n,m,i,j;
int main(){
scanf("%d%d",&n,&m);
for(i=1;i<=n;i++)f[0][i]=i;
for(i=1;i<=m;i++)for(j=0;j<=n;j++){
if(j)f[i][j]=(f[i-1][j]+f[i-1][j-1])/2;
if(j<n)f[i][j]=max(f[i][j],(f[i-1][j]+f[i-1][j+1])/2);
}
printf("%.10f",f[m][0]);
}
G. GentleBots
設估價函式為兩點到終點的曼哈頓距離之和，每次選取使得估價函式最優的方向走，若不能走，則隨機抖動。
#include<cstdio>
#include<ctime>
#include<cstdlib>
#include<algorithm>
using namespace std;
const int dx[7]={1,-1,0,0,0,0,0},
dy[7]={0,0,-1,1,0,0,0},
dz[7]={0,0,0,0,1,-1,0};
struct P{
int x,y,z;
void read(){
scanf("%d%d%d",&x,&y,&z);
}
int dis(P b){
return abs(x-b.x)+abs(y-b.y)+abs(z-b.z);
}
void write(){
printf("(%d %d %d)",x,y,z);
}
P(){}
P(int _x,int _y,int _z){x=_x,y=_y,z=_z;}
P apply(int d){
return P(x+dx[d],y+dy[d],z+dz[d]);
}
}A,B,C,D;//A->B C->D
int main(){
A.read();
B.read();
C.read();
D.read();
while(1){
A.write();
putchar(' ');
C.write();
puts("");
int pre=A.dis(B)+C.dis(D);
if(!pre)return 0;
int best=~0U>>1;
int I=0,J=0;
for(int i=0;i<7;i++)for(int j=0;j<7;j++){
P NA=A.apply(i),NC=C.apply(j);
if(!NA.dis(C))continue;
if(!NA.dis(NC))continue;
if(!NC.dis(A))continue;
if(!NC.dis(NA))continue;
int now=NA.dis(B)+NC.dis(D);
if(now<best)best=now,I=i,J=j;
}
if(best>=pre){
while(1){
int i=rand()%7,j=rand()%7;
P NA=A.apply(i),NC=C.apply(j);
if(!NA.dis(C))continue;
if(!NA.dis(NC))continue;
if(!NC.dis(A))continue;
if(!NC.dis(NA))continue;
I=i,J=j;
break;
}
}
A=A.apply(I);
C=C.apply(J);
}
}
H. Hiker Safety
能走就走，用佇列維護所有可能走的人，時間複雜度$O(n^2)$。
#include<cstdio>
const int N=10010;
int B,m,i,n,d[N],a[N],pos[N],r;
int h,t,x,q[10000000];
int cnt,fin[3333333];
inline int abs(int x){return x>0?x:-x;}
inline bool check(int x){
if(pos[x]==m)return 0;
int pre=x-1,nxt=x+1;
if(nxt>r)nxt=0;
if(pre){
if(abs(d[pos[x]+1]-d[pos[pre]])>B)return 0;
if(abs(d[pos[x]+1]-d[pos[pre]])<a[x])return 0;
if(abs(d[pos[x]+1]-d[pos[pre]])<a[pre])return 0;
}
if(nxt){
if(abs(d[pos[x]+1]-d[pos[nxt]])>B)return 0;
if(abs(d[pos[x]+1]-d[pos[nxt]])<a[x])return 0;
if(abs(d[pos[x]+1]-d[pos[nxt]])<a[nxt])return 0;
}
return 1;
}
inline void gao(int x){
//printf("->%d\n",x);
pos[x]++;
fin[++cnt]=x;
while(r&&pos[r]==m)r--;
if(x>1)q[++t]=x-1;
if(x<r)q[++t]=x+1;
if(x<=r)q[++t]=x;
}
int main(){
scanf("%d%d",&B,&m);
for(i=1;i<=m;i++)scanf("%d",&d[i]);
for(i=1;i<m;i++)if(d[i]>d[i+1])while(1);
scanf("%d",&n);
for(i=1;i<=n;i++){
scanf("%d%d",&a[i],&pos[i]);
}
for(i=1;i<=n;i++){
if(pos[i]<m)r=i;
}
//[1,r]
h=1,t=0;
for(i=1;i<=r;i++)q[++t]=i;
while(h<=t){
x=q[h++];
if(check(x)){
gao(x);
}
}
for(i=1;i<=n;i++)if(pos[i]<m)return puts("impossible"),0;
for(i=1;i<=cnt;i++)printf("%d ",fin[i]);
}
I. I Work All Day
按題意模擬即可。
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
const int N = 3e5 + 10;
const int inf = 1e9;
int casenum, casei;
int c[15], e[15];
int n;
int main()
{
while(~scanf("%d", &n))
{
for(int i = 0; i < n; ++i)scanf("%d", &c[i]);
int T; scanf("%d", &T);
int ans = c[0]; int val = T % c[0];
for(int i = 1; i < n; ++i)
{
if(T % c[i] < val)
{
val = T % c[i];
ans = c[i];
}
}
printf("%d\n", ans);
}
return 0;
}
/*
*/
J. Just A Minim
按題意模擬即可。
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
const int N = 3e5 + 10;
const int inf = 1e9;
int casenum, casei;
int c[2010], e[15];
int n;
int main()
{
while(~scanf("%d", &n))
{
for(int i = 0; i < n; ++i)scanf("%d", &c[i]);
double ans = 0;
for(int i = 0; i < n; i ++){
if(c[i] == 0) ans += 2;
else if(c[i] == 1) ans += 1;
else if(c[i] == 2) ans += 0.5;
else if(c[i] == 4) ans += 0.25;
else if(c[i] == 8) ans += 0.125;
else if(c[i] == 16) ans += 0.0625;
}
printf("%.8f\n", ans);
}
return 0;
}
/*
*/
K. Knightsbridge Rises
拆點求最大流。
#include<stdio.h>
#include<iostream>
#include<string.h>
#include<string>
#include<ctype.h>
#include<math.h>
#include<set>
#include<map>
#include<vector>
#include<queue>
#include<bitset>
#include<algorithm>
#include<time.h>
using namespace std;
const int N = 305, M = N * N * 8;
const int inf = 0x3f3f3f3f;
#define MS(x, y) memset(x, y, sizeof(x))
int n;
int L[N], W[N];
int ST, ED;
int first[N], ID;
int w[M], cap[M], nxt[M];
void ins(int x, int y, int cap_)
{
w[++ID] = y;
cap[ID] = cap_;
nxt[ID] = first[x];
first[x] = ID;
w[++ID] = x;
cap[ID] = 0;
nxt[ID] = first[y];
first[y] = ID;
}
int d[N];
bool bfs()
{
MS(d, -1);
queue<int>q; q.push(ST); d[ST] = 0;
while(!q.empty())
{
int x = q.front(); q.pop();
for(int z = first[x]; z; z = nxt[z])if(cap[z])
{
int y = w[z];
if(d[y] == -1)
{
d[y] = d[x] + 1;
q.push(y);
if(y == ED)return 1;
}
}
}
return 0;
}
int dfs(int x, int all)
{
if(x == ED)return all;
int use = 0;
for(int z = first[x]; z; z = nxt[z])if(cap[z])
{
int y = w[z];
if(d[y] == d[x] + 1)
{
int tmp = dfs(y, min(cap[z], all - use));
cap[z] -= tmp;
cap[z ^ 1] += tmp;
use += tmp;
if(use == all)break;
}
}
if(use == 0)d[x] = -1;
return use;
}
int dinic()
{
int ret = 0;
while(bfs())ret += dfs(ST, inf);
return ret;
}
vector<int>vt[N];
void go(int o, int x)
{
for(int z = first[x]; z; z = nxt[z])if((z & 1) && cap[z])
{
x = w[z];
break;
}
if(x == 0)
{
//for(auto it : vt[o])
/*
int cnt = 0;
for(int ii = 0; ii < vt[o].size(); ++ii)
{
int it = vt[o][ii];
if(++cnt == 1)printf("%d", it);
else printf(" %d", it);
}
puts("");
*/
return;
}
vt[o].push_back(x - n);
go(o, x - n);
}
int main()
{
while(~scanf("%d", &n))
{
MS(first, 0); ID = 1;
ST = 0;
for(int i = 1; i <= n; ++i)
{
scanf("%d%d", &W[i], &L[i]);
if(W[i] == 0)
{
ins(ST, i, 1);
}
ins(i, n + i, 1);
}
for(int i = 1; i <= n; ++i)
{
for(int j = 1; j <= n; ++j)if(j != i && L[i] >= W[j])
{
ins(n + i, j, 1);
}
}
int m;
scanf("%d", &m);
ED = n + n + m + 1;
for(int i = 1; i <= m; ++i)
{
int x;
scanf("%d", &x);
ins(n + n + i, ED, 1);
for(int j = 1; j <= n; ++j)if(L[j] >= x)
{
ins(n + j, n + n + i, 1);
}
}
if(dinic() != m)
{
puts("impossible");
}
else
{
for(int z = first[ED]; z; z = nxt[z])if((z & 1) && cap[z])
{
vt[w[z] - n - n].clear();
go(w[z] - n - n, w[z]);
}
for(int o = 1; o <= m; ++o)
{
int cnt = 0;
for(int ii = vt[o].size() - 1; ii >= 0; --ii)
{
int it = vt[o][ii];
if(++cnt == 1)printf("%d", it);
else printf(" %d", it);
}
puts("");
}
}
}
return 0;
}
/*
5
0 1
1 2
2 3
3 4
0 2
2
4 2
7
0 1
1 4
0 3
0 1
2 5
2 5
1 2
3
5 4 5
2
0 1
5 3
2
2 1
*/
L. Lounge Lizards
將所有點到原點的方向向量約分後分組，每組按距離從小到大排序，然後求LIS。
時間複雜度$O(n\log n)$。
#include<cstdio>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1000010;
int n,i,j,k,m,f[N],ans;
struct P{int x,y,h;ll w;}a[N],O;
ll sqr(ll x){return x*x;}
int gcd(int a,int b){return b?gcd(b,a%b):a;}
inline bool cmp(const P&a,const P&b){
if(a.x!=b.x)return a.x<b.x;
if(a.y!=b.y)return a.y<b.y;
return a.w<b.w;
}
inline void ins(int x){
if(!m||x>f[m]){
f[++m]=x;
return;
}
int l=1,r=m,mid,t;
while(l<=r){
mid=(l+r)>>1;
if(f[mid]>=x)r=(t=mid)-1;else l=mid+1;
}
f[t]=x;
}
int main(){
scanf("%d%d",&O.x,&O.y);
scanf("%d",&n);
for(i=1;i<=n;i++){
scanf("%d%d%d",&a[i].x,&a[i].y,&a[i].h);
a[i].x-=O.x;
a[i].y-=O.y;
a[i].w=sqr(a[i].x)+sqr(a[i].y);
//sgn gcd
int d=gcd(abs(a[i].x),abs(a[i].y));
a[i].x/=d,a[i].y/=d;
//printf("%d %d %lld\n",a[i].x,a[i].y,a[i].w);
}
sort(a+1,a+n+1,cmp);
for(i=1;i<=n;i=j){
for(j=i;j<=n&&a[i].x==a[j].x&&a[i].y==a[j].y;j++);
m=0;
for(k=i;k<j;k++){
ins(a[k].h);
}
ans+=m;
}
printf("%d",ans);
}
/*
0 0
6
0 -1 2
0 -2 2
0 -3 3
0 1 1
0 2 2
0 3 1
*/