62 lines
1.6 KiB
Java
62 lines
1.6 KiB
Java
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import java.util.*;
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public class MonotonicApproximation {
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// finds array b that minimizes sum |a[i]-b[i]|
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public static long monotonicApproximation(int[] a) {
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int n = a.length;
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int[] t = new int[n];
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SortedMap<Integer, Integer> m = new TreeMap<>();
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for (int i = 0; i < n; i++) {
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Integer v = m.get(a[i]);
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if (v == null) v = 0;
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m.put(a[i], v + 2);
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int last = m.lastKey();
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t[i] = last;
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int count = m.get(last);
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if (count > 1)
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m.put(last, count - 1);
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else
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m.remove(last);
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}
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int[] b = new int[n];
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b[n - 1] = t[n - 1];
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for (int i = n - 2; i >= 0; i--)
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b[i] = Math.min(t[i], b[i + 1]);
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long res = 0;
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for (int i = 0; i < n; i++)
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res += Math.abs(a[i] - b[i]);
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return res;
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}
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// random test
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public static void main(String[] args) {
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Random rnd = new Random(1);
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for (int step = 0; step < 10000; step++) {
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int n = rnd.nextInt(100) + 1;
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int[] a = rnd.ints(n, 0, 1000).toArray();
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long res1 = monotonicApproximation(a);
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long res2 = slowMonotonicApproximation(a);
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if (res1 != res2)
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throw new RuntimeException(res1 + " " + res2);
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}
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}
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static long slowMonotonicApproximation(int[] a) {
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int n = a.length;
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int[] b = a.clone();
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Arrays.sort(b);
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long[] cur = new long[n];
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long[] next = new long[n];
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cur[0] = Math.abs(a[0] - b[0]);
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for (int i = 1; i < n; i++)
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cur[i] = Math.min(cur[i - 1], Math.abs(a[0] - b[i]));
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for (int i = 1; i < n; i++) {
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next[0] = Math.abs(a[i] - b[0]) + cur[0];
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for (int j = 1; j < n; j++)
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next[j] = Math.min(next[j - 1], Math.abs(a[i] - b[j]) + cur[j]);
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System.arraycopy(next, 0, cur, 0, n);
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}
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return cur[n - 1];
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}
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}
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