算法競賽入門經典 例題 9-4

/*算法競賽入門經典 例題 9-4
 * 問題：求以c爲起點的邊權之和最大的路徑
 * 0-1揹包之物品無限   d[i]表示以i爲起點的最大路徑     d[i] = max{d[j] + w[i]}
 * */
import java.util.Arrays;
import java.util.Scanner;

public class PackageInfinite {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] v = new int[n + 1]; // v[i]物品i的體積
		int[] w = new int[n + 1];// w[i] 物品i的重量
		for (int i = 1; i <= n; i++) {
			v[i] = scanner.nextInt();
			w[i] = scanner.nextInt();
		}
		int c = scanner.nextInt();
		int[] d = new int[c + 1];
		Arrays.fill(d, -1);
		d[0] = 0;
		PackageInfinite pi = new PackageInfinite();

		// 記憶搜索法
		pi.dp(v, w, d, c);
		pi.print(v, w, d, c);
		System.out.println();

		// 遞推法
		int[] max = new int[c + 1];
		Arrays.fill(max, Integer.MIN_VALUE);
		max[0] = 0;
		for (int i = 1; i <= c; i++) {
			for (int j = 1; j <= n; j++) {
				if (i >= v[j]) {
					int temp = max[i - v[j]] + w[j];
					max[i] = max[i] < temp ? temp : max[i];
				}
			}
		}
		pi.print(v, w, max, c);
		System.out.println();
	}

	private int dp(int[] v, int[] w, int[] d, int c) {
		if (d[c] != -1)
			return d[c];
		d[c] = Integer.MIN_VALUE;
		for (int i = 1; i <= v.length - 1; i++) {
			if (c >= v[i]) {
				int temp = dp(v, w, d, c - v[i]) + w[i];
				d[c] = d[c] > temp ? d[c] : temp;
			}
		}
		return d[c];
	}

	private void print(int[] v, int[] w, int[] d, int c) {
		for (int i = 1; i <= v.length - 1; i++) {
			if (c >= v[i] && d[c] == d[c - v[i]] + w[i]) {
				System.out.printf("%d ", i);
				print(v, w, d, c - v[i]);
				break;
			}
		}
	}
}