一道动态规划 在线coding 题目
测试结束后，辗转反侧，夜不能寐，还是想再试试看能否解出正确答案。
花了将近3小时，总算解出来了，虽然是答案是正确的，但还是有很多可以优化的地方，比如：其实DP方程是可以降维的。
下面把题目和代码放在文章里，欢迎大家一起讨论优化。
【题目：】
现在有abcdef六种颜色的球，集齐其中满足一定组合的三个可以抽一次奖，这样的组合有：3a,
2a1b, 1a2b, 2a1d, 1a2d, 2a1c, 2a1e, f可以充当任何类型，给出六种球的个数，如何找出最大的抽奖次数。
我的代码如下：
import java.io.*;
import java.util.*;
import java.util.Map.Entry;
class Solution {
/**
* 利用动态规划方法
* 【分析】：
* 想要中奖的话，在a方向上，上一步到这一步的步长可以有4种{0,1,2,3};
* 想要中奖的话，在b方向上，上一步到这一步的步长可以有3种{0,1,2};
* 想要中奖的话，在c方向上，上一步到这一步的步长可以有2种{0,1};
* 想要中奖的话，在d方向上，上一步到这一步的步长可以有3种{0,1,2};
* 想要中奖的话，在e方向上，上一步到这一步的步长可以有2种{0,1};
* 想要中奖的话，在e方向上，上一步到这一步的步长可以有4种{0,1,2,3};
*/
public static int getMaxValue(int[] num) {
int aN=num[0];//a的个数
int bN=num[1];
int cN=num[2];
int dN=num[3];
int eN=num[4];
int fN=num[5];
HashMap maxTable=new HashMap();
for(int a=0;a<=aN;a++)
for(int b=0;b<=bN;b++)
for(int c=0;c<=cN;c++)
for(int d=0;d<=dN;d++)
for(int e=0;e<=eN;e++)
for(int f=0;f<=fN;f++)
{
int max=0;
int isBonus=0;
//C方向 :2a1c
if(c-1>=0){
if(a+f-2>=0)
{
if(a-2>=0)
{
String key=a-2+","+b+","+(c-1)+","+d+","+e+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-2>=0)
{
String key=a+","+b+","+(c-1)+","+d+","+e+","+(f-2);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if((f-1>=0)&&(a-1>=0)){
String key=(a-1)+","+b+","+(c-1)+","+d+","+e+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
}
//E方向: 2a1e
if(e-1>=0){
if(a+f-2>=0)
{
if(a-2>=0)
{
String key=a-2+","+b+","+c+","+d+","+(e-1)+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-2>=0)
{
String key=a+","+b+","+c+","+d+","+(e-1)+","+(f-2);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if((f-1>=0)&&(a-1>=0)){
String key=(a-1)+","+b+","+c+","+d+","+(e-1)+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
}
//d方向: 1a2d
if(d-2>=0){
if(a+f-1>=0)
{
if(a-1>=0)
{
String key=a-1+","+b+","+c+","+(d-2)+","+e+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-1>=0)
{
String key=a+","+b+","+c+","+(d-2)+","+e+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
}
//d方向: 2a1d
if(d-1>=0){
if(a+f-2>=0)
{
if(a-2>=0)
{
String key=a-2+","+b+","+c+","+(d-1)+","+e+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-2>=0)
{
String key=a+","+b+","+c+","+(d-1)+","+e+","+(f-2);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if((f-1>=0)&&(a-1>=0)){
String key=(a-1)+","+b+","+c+","+(d-1)+","+e+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
}
//b方向: 1a2b
if(b-2>=0){
if(a+f-1>=0)
{
if(a-1>=0)
{
String key=a-1+","+(b-2)+","+c+","+d+","+e+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-1>=0)
{
String key=a+","+(b-2)+","+c+","+d+","+e+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
}
//b方向: 2a1b
if(b-1>=0){
if(a+f-2>=0)
{
if(a-2>=0)
{
String key=a-2+","+(b-1)+","+c+","+d+","+e+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-2>=0)
{
String key=a+","+(b-1)+","+c+","+d+","+e+","+(f-2);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if((f-1>=0)&&(a-1>=0)){
String key=(a-1)+","+(b-1)+","+c+","+d+","+e+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
}
//a方向 3a
if(a+f-3>=0){
if(a-3>=0)
{
String key=(a-3)+","+b+","+c+","+d+","+e+","+f;
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if((a-2>=0)&&(f-1>=0)){
String key=(a-2)+","+b+","+c+","+d+","+e+","+(f-1);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if((a-1>=0)&&(f-2>=0)){
String key=(a-1)+","+b+","+c+","+d+","+e+","+(f-2);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
if(f-3>=0){
String key=a+","+b+","+c+","+d+","+e+","+(f-3);
if(maxTable.get(key)>max){
max=maxTable.get(key);
}
isBonus=1;
}
}
String key=a+","+b+","+c+","+d+","+e+","+f;
maxTable.put(key, max+isBonus);
}
return maxTable.get(aN+","+bN+","+cN+","+dN+","+eN+","+fN);
}
public static void main(String[] args) {
int[] num=new int[]{7,4,2,2,1,8};
System.out.println(getMaxValue(num));
}
}