算法实践篇-钢条切割问题-动态规划

来源：互联网发布：管线机什么牌子好知乎编辑：程序博客网时间：2024/04/29 16:34

问题描述：给定一个钢条的长度，求最大效益和切割方法

长度和价格的关系如下：

length  1  2  3  4  5  6  7  8  9  10

price   1  5  8  9  10 17 17 20 24 30

package com.dynamic;public class CutRod {private int []price;private int length;private int []r;private int []s;public CutRod(int []price){this.price=price;}/** *自顶向下递归  * @param length * @return */public int momoizedCutRod(int length){r=new int[length+1];for(int i=0;i<=length;i++){r[i]=-1;}return memoizedCutRodAux(length,r);}private int memoizedCutRodAux(int length,int []r){if(r[length]>=0){return r[length];}int q;if(length==0){q=0;}else{if(length>=price.length){q=price[price.length-1];}else{q=price[length];}if(length>price.length){for(int i=1;i<=price.length-1;i++){q=Math.max(q, price[i]+memoizedCutRodAux(length-i,r));}}else{for(int i=1;i<=length-1;i++){q=Math.max(q, price[i]+memoizedCutRodAux(length-i,r));}}}r[length]=q;return q;}public int bottomUpCutRod(int length){r=new int[length+1];r[0]=0;for(int j=1;j<=length;j++){int q=0;if(j>=price.length){q=price[price.length-1];}else{q=price[j];}for(int i=1;i<=j;i++){q=Math.max(q, price[i]+r[j-i]);}r[j]=q;}return r[length];}public int extendBottomUpCutRod(int length){r=new int[length+1];s=new int[length+1];r[0]=0;for(int j=1;j<=length;j++){int q=0;if(j>=price.length){q=price[price.length-1];}else{q=price[j];}for(int i=1;i<=j;i++){if(q<=price[i]+r[j-i]){q=price[i]+r[j-i];s[j]=i;}}r[j]=q;}return r[length];}public void printSolution(int length){extendBottomUpCutRod(length);int n=length;while(n>0){System.out.print(s[n]+" ");n=n-s[n];}System.out.println();}public static void main(String[] args) {int []price=new int[]{0,1,5,8,9,10,17,17,20,24,30};CutRod cut=new CutRod(price);System.out.println(cut.extendBottomUpCutRod(3));cut.printSolution(3);System.out.println(cut.extendBottomUpCutRod(4));cut.printSolution(4);System.out.println(cut.extendBottomUpCutRod(5));cut.printSolution(5);System.out.println(cut.extendBottomUpCutRod(10));cut.printSolution(10);System.out.println("===========");System.out.println(cut.bottomUpCutRod(5));System.out.println("===========");System.out.println(cut.momoizedCutRod(4));}}

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