2021年csp认证题解
202109
T1-数组推导
简单贪心
import java.util.Scanner;
public class Maincsp2 {//202109-1 数组推导 100
static int n,sum1,sum2;
static int [] a,b = new int[1000];
public static void main(String[] args){
Scanner in = new Scanner(System.in);
n = in.nextInt();
for(int i = 1;i <= n;i ++){
b[i] = in.nextInt();
sum1 += b[i];
if(b[i] != b[i - 1])sum2 += b[i];
}
System.out.println(sum1);
System.out.println(sum2);
}
}
T2-非零段划分
一道很有意思的差分题。
考虑会出现非零段的条件，当 \(a_{i - 1} < a_i\)，\(a_{i - 1}\le x < a_i\) 时,会贡献一个非零段
当 \(x \ge a_i\) 时此非零段消失，所以通过差分可以实现此操作。
import java.util.Scanner;
import java.util.Vector;
public class Maincsp4 {//202109-2 非零段划分
static int n,ans,tmp;
static int [] a = new int[500100];
static int [] b = new int[10101];
public static void main(String[] args){
Scanner in = new Scanner(System.in);
n = in.nextInt();
for(int i = 1;i <= n;i ++) {
a[i] = in.nextInt();
if(a[i - 1] < a[i]){
b[a[i - 1]] ++ ;
b[a[i]] --;
}
}
for(int i = 0;i <= 10000;i ++){
tmp += b[i];
ans = Math.max(ans,tmp);
}
System.out.println(ans);
}
}
T3-脉冲神经网络
大模拟。这利用邻接表进行建图，对于当前时间下对\(N - 1\)~\(N + P - 1\)的子节点传递脉冲，利用一个二维数组来记录延迟后的时间和子节点对应的脉冲值。
考虑延迟的时间最多为1000，所以可以用循环数组来减少空间。
重点是读清题意，注意小坑。
//import java.util.ArrayList;
import java.util.Scanner;
public class Maincsp6 {//202109-3 脉冲神经网络
static long next = 1;
static int N,P,S,T,l;
static double deltT,ans1,ans2;
static double [] u = new double[1010];
static double [] v = new double[1010];
static double [] a = new double[1010];
static double [] b = new double[1010];
static double [] c = new double[1010];
static double [] d = new double[1010];
static double [][] I = new double[2110][1010];
static double [] w = new double[1010];
static int [] pre = new int[1010];
static int [] last = new int[2010];
static int [] other = new int[1010];
static int [] len = new int[1010];
static int [] r = new int[1010];
static int [] cnt = new int[1010];
static int myrand() {
next = next * 1103515245 + 12345;
return (int)((Long.divideUnsigned(next, 65536)) % 32768);
}
static void add(int x,int y,double z,int t){
l ++;
pre[l] = last[x];
last[x] = l;
other[l] = y;
w[l] = z;
len[l] = t;
}
public static void main(String[] args){
Scanner in = new Scanner(System.in);
N = in.nextInt();S = in.nextInt();
P = in.nextInt();T = in.nextInt();
deltT = in.nextDouble();
int tmpsum = 0;
while(true){
if(tmpsum == N)break;
int R = in.nextInt();
double V = in.nextDouble(),U = in.nextDouble(),A = in.nextDouble();
double B = in.nextDouble(),C = in.nextDouble(),D = in.nextDouble();
for(int i = tmpsum;i <= tmpsum + R;i ++){
u[i] = U;v[i] = V;a[i] = A;b[i] = B;c[i] = C;d[i] = D;
}
tmpsum += R;
}
for(int i = 0;i < P;i ++){
r[i] = in.nextInt();
}
for(int i = 1;i <= S;i ++){
int s = in.nextInt(),t = in.nextInt();
double W = in.nextDouble();int D = in.nextInt();
add(s,t,W,D);
}
for(int i = 1;i <= T;i ++){
for(int j = 0;j < P;j ++){
int ff = myrand();
if(r[j] > ff){
for(int p = last[j + N];p != 0;p = pre[p]){
int v1 = other[p];
if(i + len[p] <= T)I[(i + len[p]) % 2000][v1] += w[p];
}
}
}
for(int j = 0;j < N;j ++){
double tmp1 = v[j],tmp2 = u[j];
v[j] = tmp1 + deltT * (0.04 * tmp1 * tmp1 + 5 * tmp1 + 140 - tmp2) + I[i % 2000][j];
u[j] = tmp2 + deltT * a[j] * (b[j] * tmp1 - tmp2);
if(v[j] >= 30){
v[j] = c[j];u[j] += d[j];
cnt[j] ++;
for(int p = last[j];p != 0;p = pre[p]){
int v1 = other[p];
if(i + len[p] <= T)I[(i + len[p]) % 2000][v1] += w[p];
}
}
I[i % 2000][j] = 0;
}
}
ans2 = ans1 = v[0];
int ans3 = cnt[0],ans4 = cnt[0];
for(int i = 0;i < N;i ++) {
ans1 = Math.max(ans1,v[i]);
ans2 = Math.min(ans2,v[i]);
ans3 = Math.max(ans3,cnt[i]);
ans4 = Math.min(ans4,cnt[i]);
}
System.out.printf("%.3f %.3f\n",ans2,ans1);
System.out.print(ans4 + " " + ans3);
}
}
T4-收集卡牌
import java.util.Scanner;
public class Maincsp5 {//202109-4 收集卡牌
static int n,k;
static double ans;
static double [] p = new double[20];
static double [][] dp = new double[65550][100];
public static void main(String[] args){
Scanner in = new Scanner(System.in);
n = in.nextInt();k = in.nextInt();
for(int i = 1;i <= n;i ++){
p[i] = in.nextDouble();
}
dp[0][0] = 1;
for(int s = 0;s < (1 << n);s ++){
for(int i = 0;i <= n * k;i ++){
int cnt = 0;
for(int j = 0;j < n;j ++)if((s & (1 << j)) != 0)cnt ++;
if(cnt + i / k >= n){
ans += dp[s][i] * (cnt + i);
continue;
}
for(int j = 0;j < n;j ++){
if((s & (1 << j)) != 0) {
dp[s][i + 1] += dp[s][i] * p[j + 1];
// System.out.println(dp[s][i]);
}
else dp[s|(1 << j)][i] += dp[s][i] * p[j + 1];
}
}
}
System.out.printf("%.10f",ans);
}
}
202104
T1-灰度直方图
简单模拟
import java.util.Scanner;
public class Maincsp1 {//202104-1 灰度直方图
static int n,m,l;
static int [][] a = new int[510][510];
static int [] h = new int [300];
public static void main(String[] args){
Scanner in = new Scanner(System.in);
n = in.nextInt();
m = in.nextInt();l = in.nextInt();
for(int i = 1;i <= n;i ++){
for(int j = 1;j <= m;j ++){
a[i][j] = in.nextInt();
h[a[i][j]] ++;
}
}
for(int i = 0;i < l;i ++){
System.out.print(h[i] + " ");
}
}
}
T2-邻域均值
简单二维前缀和
import java.util.Scanner;
public class Maincsp3 {//202104-2 邻域均值
static int n,l,t,r,ans;
static int [][] a = new int[610][610];
static int [][] sum = new int[610][610];
public static void main(String[] args){
Scanner in = new Scanner(System.in);
n = in.nextInt();l = in.nextInt();
r = in.nextInt();t = in.nextInt();
for(int i = 1;i <= n;i ++){
for(int j = 1;j <= n;j ++) {
a[i][j] = in.nextInt();
sum[i][j] = sum[i][j - 1] + sum[i - 1][j] + a[i][j] - sum[i - 1][j - 1];
}
}
for(int i = 1;i <= n;i ++){
for(int j = 1;j <= n;j ++){
int x = Math.max(i - r,1);
int y = Math.max(j - r,1);
int xx = Math.min(i + r,n);
int yy = Math.min(j + r,n);
int tmp = sum[xx][yy] - sum[xx][y - 1] - sum[x - 1][yy] + sum[x - 1][y - 1];
if(t * (xx - x + 1) * (yy - y + 1) >= tmp)ans ++;
}
}
System.out.println(ans);
}
}
T3-DHCP服务器
import java.util.*;
public class Maincsp11 {//202104-3 DHCP服务器
static int N,Tdef,Tmax,Tmin,n;
static String H;
static Map<String,Integer> map = new HashMap<>();
static Map<Integer,String> mp = new HashMap<>();
static int [] vis = new int[10110];// 0 - 未分配 1 - 待分配 2 - 占用 3 - 过期
static int [] iplast = new int[10010];//地址过期时刻
static String [] ipnow = new String[10010];//地址占用者
static int find(int x) {
for(int i = 1;i <= N;i ++) {
if(vis[i] == x) {
return i;
}
}
return 0;
}
static int cale(int last,int t) {
if(last == 0) return t + Tdef;
else {
if(last - t >= Tmin) {
if(last - t <= Tmax)return last;
else return t + Tmax;
}
else return t + Tmin;
}
}
static int check(String x) {
for(int i = 1;i <= N;i ++) {
if(ipnow[i].equals(x)) {
return i;
}
}
return 0;
}
static void clear(int x) {
for(int i = 1;i <= N;i ++) {
if(iplast[i] <= x) {
if(vis[i] == 1) {
vis[i] = 0;ipnow[i] = "A";iplast[i] = 0;
}
else if(vis[i] == 2) {
vis[i] = 3;iplast[i] = 0;
}
else iplast[i] = 0;
}
}
}
static void init() {
for(int i = 1;i <= N;i ++)ipnow[i] = "A";
}
public static void main(String[] args) {
Scanner in = new Scanner(System.in);
N = in.nextInt();Tdef = in.nextInt();Tmax = in.nextInt();Tmin = in.nextInt();
H = in.next();
n = in.nextInt();
init();
for(int i = 1;i <= n;i ++) {
int t = in.nextInt();
clear(t);
String send = in.next(),receive = in.next(),type = in.next();
int ip = in.nextInt(),last = in.nextInt();
if(!receive.equals(send) && !receive.equals("*")) {
if(!type.equals("REQ"))continue;
}
if(!type.equals("DIS") && !type.equals("REQ"))continue;
if(receive.equals("*") && !type.equals("DIS"))continue;
if(receive.equals(send) && type.equals("DIS"))continue;
int nowip,nowlast;
if(type.equals("DIS")) {
int pd = check(send);
if(pd != 0) {
nowip = pd;
vis[nowip] = 1;
}//dis 1.1
else {
int tmp = find(0);//dis1.2
if(tmp == 0) {
tmp = find(3);//dis1.3
if(tmp == 0)continue;//dis1.4
else vis[tmp] = 1;
}
else {
vis[tmp] = 1;
}//dis 1
nowip = tmp;
}//dis1
ipnow[nowip] = send;//dis2
nowlast = cale(last,t);//dis 3
iplast[nowip] = nowlast;
System.out.println(H + " " + send + " OFR " + nowip + " " +nowlast);//ofr
}
else {
if(!receive.equals(H)) {
for(int j = 1;j <= N;j ++) {
if(ipnow[j].equals(send) && vis[j] == 1) {
vis[j] = 0;
ipnow[j] = "A";
iplast[j] = 0;
}
}
}
else {
// System.out.println(ipnow[ip]);
if(ip <= N && ip >= 1 && ipnow[ip].equals(send)) {
nowlast = cale(last,t);
vis[ip] = 2;
iplast[ip] = nowlast;
System.out.println(H + " " + send + " ACK " + ip + " " + nowlast);//ack
}
else{
nowlast = 0;
System.out.println(H + " " + send + " NAK " + ip + " " + nowlast);//nak
}
}
}
}
}
}
T4-校门外的树
import java.util.ArrayList;
import java.util.Scanner;
public class Maincsp7 {//202104-4 校门外的树
static int n;
static final long mo = 1000000007;
static int [] a = new int[1010];
static int [] vis = new int[100010];
static long [] dp = new long[1010];
static ArrayList<Integer> p[];
static long solve(int x,int y){
long cnt = 0;
int len = a[x] - a[y];
// System.out.println(x + " " + y);
vis[len] = 1;
for(Integer i:p[len]){
if(vis[i] == 1){
continue;
}
else {
cnt ++;vis[i] = 1;
}
}
//System.out.println(cnt);
return cnt;
}
public static void main(String[] args){
Scanner in = new Scanner(System.in);
n = in.nextInt();
for(int i = 1;i <= n;i ++){
a[i] = in.nextInt();
}
p = new ArrayList[100010];
for(int i = 1;i <= a[n];i ++){
p[i] = new ArrayList<Integer>();
p[i].add(1);
for(int j = 2;j <= Math.sqrt(i);j ++){
if(i % j == 0){
p[i].add(j);
if(j != i / j)p[i].add(i / j);
}
}
}
dp[1] = 1;
for(int i = 2;i <= n;i ++){
for(int j = i - 1;j >= 1;j --){
dp[i] = (dp[i] + dp[j] * solve(i,j) % mo) % mo;
}
for(int j = 1;j <= a[n];j ++)vis[j] = 0;
}
System.out.println(dp[n]);
}
}