/*
* 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];
}
}
}
运行结果为:
长度为1的钢条最优收益为:1 切割方案为:1
长度为2的钢条最优收益为:5 切割方案为:2
长度为3的钢条最优收益为:8 切割方案为:3
长度为4的钢条最优收益为:10 切割方案为:2 2
长度为5的钢条最优收益为:13 切割方案为:2 3
长度为6的钢条最优收益为:17 切割方案为:6
长度为7的钢条最优收益为:18 切割方案为:1 6
长度为8的钢条最优收益为:22 切割方案为:2 6
长度为9的钢条最优收益为:25 切割方案为:3 6
长度为10的钢条最优收益为:30 切割方案为:10