103 lines
2.4 KiB
Java
103 lines
2.4 KiB
Java
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import java.util.Random;
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public class Coloring {
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int minColors;
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int[] bestColoring;
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public int minColors(boolean[][] graph) {
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int n = graph.length;
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bestColoring = new int[n];
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int[] id = new int[n + 1];
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int[] deg = new int[n + 1];
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for (int i = 0; i <= n; i++)
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id[i] = i;
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bestColoring = new int[n];
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int res = 1;
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for (int from = 0, to = 1; to <= n; to++) {
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int best = to;
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for (int i = to; i < n; i++) {
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if (graph[id[to - 1]][id[i]])
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++deg[id[i]];
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if (deg[id[best]] < deg[id[i]])
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best = i;
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}
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int t = id[to];
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id[to] = id[best];
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id[best] = t;
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if (deg[id[to]] == 0) {
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minColors = n + 1;
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dfs(graph, id, new int[n], from, to, from, 0);
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from = to;
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res = Math.max(res, minColors);
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}
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}
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return res;
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}
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void dfs(boolean[][] graph, int[] id, int[] coloring, int from, int to, int cur, int usedColors) {
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if (usedColors >= minColors)
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return;
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if (cur == to) {
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for (int i = from; i < to; i++)
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bestColoring[id[i]] = coloring[i];
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minColors = usedColors;
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return;
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}
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boolean[] used = new boolean[usedColors + 1];
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for (int i = 0; i < cur; i++)
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if (graph[id[cur]][id[i]])
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used[coloring[i]] = true;
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for (int i = 0; i <= usedColors; i++) {
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if (!used[i]) {
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int tmp = coloring[cur];
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coloring[cur] = i;
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dfs(graph, id, coloring, from, to, cur + 1, Math.max(usedColors, i + 1));
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coloring[cur] = tmp;
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}
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}
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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(10) + 1;
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boolean[][] g = new boolean[n][n];
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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][j] = true;
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g[j][i] = true;
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}
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int res1 = new Coloring().minColors(g);
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int res2 = colorSlow(g);
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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 colorSlow(boolean[][] g) {
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int n = g.length;
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for (int allowedColors = 1; ; allowedColors++) {
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long colors = 1;
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for (int i = 0; i < n; i++)
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colors *= allowedColors;
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m1:
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for (long c = 0; c < colors; c++) {
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int[] col = new int[n];
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long cur = c;
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for (int i = 0; i < n; i++) {
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col[i] = (int) (cur % allowedColors);
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cur /= allowedColors;
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}
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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 (g[i][j] && col[i] == col[j])
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continue m1;
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return allowedColors;
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}
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}
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}
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}
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