算法学习之路：动态规划-钢条切割-java实现

public class SteelCutting {

public static void main(String[] args) {
SteelCutting s = new SteelCutting();
int[] p = new int[] { 0, 1, 5, 8, 9, 10, 17, 17, 20, 24, 25};
System.out.println(s.extendedBottomUpCutRod(p, 4));
}

/**
* 递归实现钢铁切割
* @param 下标p
* @param 下标n
* @return
*/
int cutRod(int[] p, int n) {
if (n == 0) {
return 0;
}
int q = Integer.MIN_VALUE;
for (int i = 1; i <= n; i++) {
q = max(q, p[i] + cutRod(p, n - i));
System.out.println("执行i="+i+" n="+n+" q="+q);
if (i==n){
System.out.println("子问题规模为 "+n+" 的最优值 = "+q);
}
}
return q;
}

/**
* 备忘切割
* @param 数组p
* @param 下标n
* @return
*/
int memoizedCutRod(int[] p, int n){
int[] r = new int[n + 1];
for (int i = 0; i <= n; i++) {
r[i] = Integer.MIN_VALUE;
}
return memoizedCutRodAux(p, n, r);
}

/**
* 备忘切割
* @param 数组p
* @param 下标n
* @param 下标r
* @return
*/
int memoizedCutRodAux(int[] p, int n, int r[]){
if(r
>= 0){
return r
;
}
int q = Integer.MIN_VALUE;
if(n == 0){
q = 0;
}else {
for (int i = 1; i <= n; i++) {
q = max(q, p[i] + memoizedCutRodAux(p, n - i, r));
System.out.println("执行i="+i+" n="+n+" q="+q);
if (i==n){
System.out.println("子问题规模为 "+n+" 的最优值 = "+q);
}
}
}
//将每一次求的长度为 n 的最优值保存在数组 r 里面
r
= q;
return q;
}

/**
* 自顶向下切割
* @param 数组p
* @param 下标n
* @return
*/
int bottomUpCutRod(int[] p, int n){
int[] r = new int[n + 1];
r[0] = 0;
int q = Integer.MIN_VALUE;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= i; j++) {
q = max(q, p[j] + r[i - j]);
System.out.println("执行i="+i+" j="+j+" q="+q);
}
r[i] = q;
System.out.println("子问题规模为 "+i+" 的最优值 = "+q);
}
return r
;
}

/**
* 自顶向下切割（扩展）
* @param 数组p
* @param 下标n
* @return
*/
int extendedBottomUpCutRod(int[] p, int n){
int[] r = new int[n + 1];
int[] s = new int[n + 1];
r[0] = 0;
int q = Integer.MIN_VALUE;
for (int i = 1; i <= n; i++) {
for (int j = 1; j <= i; j++) {
if(q < p[j] + r[i - j]){
q = p[j] + r[i - j];
s[i] = j;
}
System.out.println("执行i="+i+" j="+j+" q="+q);
}
r[i] = q;
System.out.println("子问题规模为 "+i+" 的最优值 = "+q);
}
System.out.println(s
);
return r
;
}

public int max(int a, int b) {
return a > b ? a : b;
}

}