动态规划之钢条切割问题

/*
 * 钢条切割方案自底向上
 */
public class CutRodBottom2Up {
	//钢条价格表
	private final int[] price={1,5,8,9,10,17,17,20,24,30};
	public static void main(String[] args) {
		new CutRodBottom2Up().start();
	}

	private void start() {
		for(int i=1;i<=10;i++) {
			//打印一种最优方案
			printCutRodSolution(i);
		}
	}

	private CutRodSolution bottomUpCutRod(int n) {
		CutRodSolution crsl = new CutRodSolution(price.length+1);
		crsl.r[0] = 0;
		for(int j=1;j<=n;j++) {
			//因为钢条价格非负，因此-1可以看做-OO
			int q=-1;
			for(int i=1;i<=j;i++) {
				if(q < price[i-1]+crsl.r[j-i]) {
					//存储最优收益值
					q = price[i-1]+crsl.r[j-i];
					//存储最优切割方法(第一次切割长度)
					crsl.s[j] = i;
				}
			}
			crsl.r[j] = q;
		}
		return crsl;
	}

	//打印输出钢条长度为n的完整切割方案
	private void printCutRodSolution(int n) {
		CutRodSolution sl = bottomUpCutRod(n);
		System.out.print("长度为"+n+"的钢条最优收益为："+sl.r[n]+" ");
		System.out.print("切割方案为：");
		while(n > 0) {
			System.out.print(sl.s[n]+" ");
			n = n-sl.s[n];
		}
		System.out.println();
	}

	//内部类存储最优切割方案信息
	private static class CutRodSolution {
		//存储最优收益值数组r[0..n]
		int[] r = null;
		//存储最优切割方案数组s[0..n]
		int[] s = null;
		public CutRodSolution(int capacity) {
			r = new int[capacity];
			s = new int[capacity];
		}
	}
}