結果

問題 No.913 木の燃やし方
ユーザー uwi
提出日時 2019-10-18 23:16:27
言語 Java
(openjdk 23)
結果
AC  
実行時間 1,338 ms / 3,000 ms
コード長 7,623 bytes
コンパイル時間 5,584 ms
コンパイル使用メモリ 82,632 KB
実行使用メモリ 77,184 KB
最終ジャッジ日時 2024-06-25 19:29:52
合計ジャッジ時間 44,490 ms
ジャッジサーバーID
(参考情報)
judge2 / judge4
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 34
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ソースコード

diff #
プレゼンテーションモードにする

package contest191018;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;
public class F {
InputStream is;
PrintWriter out;
String INPUT = "";
void solve()
{
// a, b
// (a+b+1)^2 + sa+sb+mine
// a^2+b^2+1+2a+2b+2ab+sa+sb+mine
// a^2+1+2a+sa+mine + b^2+2b + 2ab + sb
int n = ni();
long[] a = new long[n];
for(int i = 0;i < n;i++) {
a[i] = nl();
}
ans = new long[n];
vals = new long[n];
Arrays.fill(ans, Long.MAX_VALUE);
dfs(0, n, a);
for(long v : ans) {
out.println(v);
}
}
long[] ans;
long[] vals;
void dfs(int l, int r, long[] a)
{
if(r-l == 1) {
ans[l] = Math.min(ans[l], a[l]+1);
return;
}
int h = l+r>>1;
{
long sum = 0;
// EnvelopeLinear el = new EnvelopeLinear(r-h+1);
EnvelopeLinearDeque el = new EnvelopeLinearDeque(r-h+1);
long[][] si = new long[r-h][];
int p = 0;
for(int i = h;i < r;i++) {
sum += a[i];
si[p++] = new long[] {2L*(i-h+1), (long)(i-h+1)*(i-h+1) + sum};
}
for(int i = p-1;i >= 0;i--) {
el.add(si[i][0], si[i][1]);
}
// (l+r)^2 + sl + sr
// r^2 + 2lr + l^2
sum = 0;
for(int i = h-1;i >= l;i--) {
sum += a[i];
long val = sum + (long)(h-i)*(h-i) + el.get(h-i);
vals[i] = val;
}
for(int i = l+1;i < h;i++) {
vals[i] = Math.min(vals[i], vals[i-1]);
}
for(int i = l;i < h;i++) {
ans[i] = Math.min(ans[i], vals[i]);
}
}
{
long sum = 0;
// EnvelopeLinear el = new EnvelopeLinear(h-l);
EnvelopeLinearDeque el = new EnvelopeLinearDeque(h-l);
long[][] si = new long[h-l][];
int p = 0;
for(int i = h-1;i >= l;i--) {
sum += a[i];
si[p++] = new long[] {2L*(h-i), (long)(h-i)*(h-i) + sum};
}
for(int i = p-1;i >= 0;i--) {
el.add(si[i][0], si[i][1]);
}
// (l+r)^2 + sl + sr
// r^2 + 2lr + l^2
sum = 0;
for(int i = h;i < r;i++) {
sum += a[i];
long val = sum + (long)(i-h+1)*(i-h+1) + el.get(i-h+1);
vals[i] = val;
}
for(int i = r-2;i >= h;i--) {
vals[i] = Math.min(vals[i], vals[i+1]);
}
for(int i = r-1;i >= h;i--) {
ans[i] = Math.min(ans[i], vals[i]);
}
}
dfs(l, h, a);
dfs(h, r, a);
}
public static class EnvelopeLinearDeque {
public long[] slopes, intercepts;
public int f, b;
public EnvelopeLinearDeque(int n)
{
slopes = new long[n];
intercepts = new long[n];
f = b = 0;
}
public long f(long x, int ind)
{
return slopes[ind]*x+intercepts[ind];
}
public double f(double x, int ind)
{
return slopes[ind]*x+intercepts[ind];
}
public boolean strictLesser(int a, int b, long num, long den)
{
double x = (double)num/den;
double cha = f(x, a) - f(x, b);
if(Math.abs(cha) < 1e-9){
return (slopes[a]*num+intercepts[a]*den) - (slopes[b]*num+intercepts[b]*den) < 0;
}else{
return cha < 0;
}
}
public long get(long x)
{
while(f-b > 1 && f(x, b) > f(x, b+1))b++;
return f(x, b);
}
public void add(long slope, long intercept)
{
if(f-b > 0)assert slope <= slopes[f-1];
if(f-b > 0 && slope == slopes[f-1] && intercept >= intercepts[f-1])return;
// sl*x+in = lsl*x+lin
// (sl-lsl)*x = lin-in
while(f-1-b > 0 && strictLesser(f-2, f-1, intercept-intercepts[f-1], slopes[f-1] - slope)){
f--;
}
slopes[f] = slope;
intercepts[f] = intercept;
f++;
}
}
public static class EnvelopeLinear {
public static final long INF = Long.MIN_VALUE;
public long[] xs;
public long[] intercepts, slopes;
public int p;
public EnvelopeLinear(int n)
{
xs = new long[n];
intercepts = new long[n];
slopes = new long[n];
p = 0;
}
public void clear()
{
p = 0;
}
public void add(long slope, long intercept)
{
assert p == 0 || slopes[p-1] >= slope;
while(p > 0){
int i = p-1;
if(p > 1 && intercept+xs[i]*slope <= intercepts[i]+xs[i]*slopes[i]){ // x=xs[i]
p--;
continue;
}
if(slope == slopes[i]){
if(intercept >= intercepts[i]){
return;
}else{
p--;
continue;
}
}
// y=sx+i vs y=Sx+I
// sx+i=Sx+I
// x=(i-I)/(S-s)
long num = intercept-intercepts[i];
long den = slopes[i]-slope;
long nx = num < 0 ? num/den : (num+den-1)/den;
xs[p] = nx;
intercepts[p] = intercept;
slopes[p] = slope;
p++;
return;
}
xs[p] = INF;
intercepts[p] = intercept;
slopes[p] = slope;
p++;
}
public int argmin(int x)
{
if(p <= 0)return -1;
int ind = Arrays.binarySearch(xs, 0, p, x);
if(ind < 0)ind = -ind-2;
return ind;
}
public long min(long x)
{
if(p <= 0)return Long.MIN_VALUE;
int ind = Arrays.binarySearch(xs, 0, p, x);
if(ind < 0)ind = -ind-2;
return slopes[ind]*x + intercepts[ind];
}
}
void run() throws Exception
{
is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);
long s = System.currentTimeMillis();
solve();
out.flush();
if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){
// @Override
// public void run() {
// long s = System.currentTimeMillis();
// solve();
// out.flush();
// if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
// }
// };
// t.start();
// t.join();
}
public static void main(String[] args) throws Exception { new F().run(); }
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
private int readByte()
{
if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}
private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
private double nd() { return Double.parseDouble(ns()); }
private char nc() { return (char)skip(); }
private String ns()
{
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
sb.appendCodePoint(b);
b = readByte();
}
return sb.toString();
}
private char[] ns(int n)
{
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
b = readByte();
}
return n == p ? buf : Arrays.copyOf(buf, p);
}
private int[] na(int n)
{
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}
private long[] nal(int n)
{
long[] a = new long[n];
for(int i = 0;i < n;i++)a[i] = nl();
return a;
}
private char[][] nm(int n, int m) {
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}
private int[][] nmi(int n, int m) {
int[][] map = new int[n][];
for(int i = 0;i < n;i++)map[i] = na(m);
return map;
}
private int ni() { return (int)nl(); }
private long nl()
{
long num = 0;
int b;
boolean minus = false;
while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
b = readByte();
}
while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
b = readByte();
}
}
private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); }
}
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