67 lines
1.9 KiB
Java
67 lines
1.9 KiB
Java
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import java.util.*;
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// https://en.wikipedia.org/wiki/Bron–Kerbosch_algorithm
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public class BronKerbosh {
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public static int BronKerbosch(long[] g, long cur, long allowed, long forbidden, int[] weights) {
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if (allowed == 0 && forbidden == 0) {
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int res = 0;
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for (int u = Long.numberOfTrailingZeros(cur); u < g.length; u += Long.numberOfTrailingZeros(cur >> (u + 1)) + 1)
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res += weights[u];
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return res;
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}
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if (allowed == 0)
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return -1;
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int res = -1;
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int pivot = Long.numberOfTrailingZeros(allowed | forbidden);
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long z = allowed & ~g[pivot];
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for (int u = Long.numberOfTrailingZeros(z); u < g.length; u += Long.numberOfTrailingZeros(z >> (u + 1)) + 1) {
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res = Math.max(res, BronKerbosch(g, cur | (1L << u), allowed & g[u], forbidden & g[u], weights));
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allowed ^= 1L << u;
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forbidden |= 1L << u;
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}
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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 < 1000; step++) {
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int n = rnd.nextInt(16) + 1;
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long[] g = new long[n];
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int[] weights = new int[n];
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for (int i = 0; i < n; i++)
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weights[i] = rnd.nextInt(1000);
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for (int i = 0; i < n; i++)
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for (int j = 0; j < i; j++)
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if (rnd.nextBoolean()) {
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g[i] |= 1L << j;
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g[j] |= 1L << i;
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}
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int res1 = BronKerbosch(g, 0, (1L << n) - 1, 0, weights);
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int res2 = maxCliqueSlow(g, weights);
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if (res1 != res2)
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throw new RuntimeException();
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}
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}
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static int maxCliqueSlow(long[] g, int[] weights) {
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int res = 0;
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int n = g.length;
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for (int set = 0; set < 1 << n; set++) {
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boolean ok = true;
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for (int i = 0; i < n; i++)
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for (int j = 0; j < i; j++)
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ok &= (set & (1 << i)) == 0 || (set & (1 << j)) == 0 || (g[i] & (1L << j)) != 0;
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if (ok) {
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int cur = 0;
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for (int i = 0; i < n; i++)
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if ((set & (1 << i)) != 0)
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cur += weights[i];
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res = Math.max(res, cur);
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}
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}
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return res;
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}
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}
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