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
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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()
    {
        // 左a, 右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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