【Project Euler 8】Largest product in a series

題目要求是：

The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product?　　　　

看到這題目的那一刻，感受有點棘手，可是仔細分析起來也還好，並非很難。

題目給出的序列是一個很規矩的數字組合。咱們能夠考慮把它存放到等長的二維數組裏面，固然也能夠直接存放到一位數組。這裏我存放到二維數組裏面了。

首先，我先把序列進行簡化來講明。假設我有如下序列，並存放到二維數組裏面。

我從上到下依次給每一個數組元素進行編號。

假設咱們要找相連的T個數字的乘積最大值，咱們能夠設置標記從1號位置開始，直到36號位置結束（爲何是36號位置結束呢？這個應該不用解釋吧）。固然這裏不是每一個位置都須要咱們處理，稍後我會說咱們怎麼跳過部分不須要處理的位置。

可是這裏還有一個問題就是：咱們使用的是二維數組存放，咱們須要把咱們的位置編號計算成二維數組的行號和列號。由於是數組是規矩的，因此咱們計算起來仍是挺方便的。

假設咱們的標記位置爲i，數組的二維長度是n（這裏是10），則

行號rowIndex=i/n，而列號columnIndex=i%n;

好了，下一步咱們來講如何跳過某些位置。咱們知道0乘以任何數都得0，因此在0的位置以及0前面T-1個位置都是能夠不用計算的，能夠直接跳過。

例如：當前位置爲i，數字0的位置爲j（j-i<T），則下一次開始計算位置應該爲j+1。下面是用java寫出來的簡單代碼。

 1 int[][] numbers=new int[][]{
 2            {7,3,1,6,7,1,7,6,5,3,1,3,3,0,6,2,4,9,1,9,2,2,5,1,1,9,6,7,4,4,2,6,5,7,4,7,4,2,3,5,5,3,4,9,1,9,4,9,3,4},
 3            {9,6,9,8,3,5,2,0,3,1,2,7,7,4,5,0,6,3,2,6,2,3,9,5,7,8,3,1,8,0,1,6,9,8,4,8,0,1,8,6,9,4,7,8,8,5,1,8,4,3},
 4            {8,5,8,6,1,5,6,0,7,8,9,1,1,2,9,4,9,4,9,5,4,5,9,5,0,1,7,3,7,9,5,8,3,3,1,9,5,2,8,5,3,2,0,8,8,0,5,5,1,1},
 5            {1,2,5,4,0,6,9,8,7,4,7,1,5,8,5,2,3,8,6,3,0,5,0,7,1,5,6,9,3,2,9,0,9,6,3,2,9,5,2,2,7,4,4,3,0,4,3,5,5,7},
 6            {6,6,8,9,6,6,4,8,9,5,0,4,4,5,2,4,4,5,2,3,1,6,1,7,3,1,8,5,6,4,0,3,0,9,8,7,1,1,1,2,1,7,2,2,3,8,3,1,1,3},
 7            {6,2,2,2,9,8,9,3,4,2,3,3,8,0,3,0,8,1,3,5,3,3,6,2,7,6,6,1,4,2,8,2,8,0,6,4,4,4,4,8,6,6,4,5,2,3,8,7,4,9},
 8            {3,0,3,5,8,9,0,7,2,9,6,2,9,0,4,9,1,5,6,0,4,4,0,7,7,2,3,9,0,7,1,3,8,1,0,5,1,5,8,5,9,3,0,7,9,6,0,8,6,6},
 9            {7,0,1,7,2,4,2,7,1,2,1,8,8,3,9,9,8,7,9,7,9,0,8,7,9,2,2,7,4,9,2,1,9,0,1,6,9,9,7,2,0,8,8,8,0,9,3,7,7,6},
10            {6,5,7,2,7,3,3,3,0,0,1,0,5,3,3,6,7,8,8,1,2,2,0,2,3,5,4,2,1,8,0,9,7,5,1,2,5,4,5,4,0,5,9,4,7,5,2,2,4,3},
11            {5,2,5,8,4,9,0,7,7,1,1,6,7,0,5,5,6,0,1,3,6,0,4,8,3,9,5,8,6,4,4,6,7,0,6,3,2,4,4,1,5,7,2,2,1,5,5,3,9,7},
12            {5,3,6,9,7,8,1,7,9,7,7,8,4,6,1,7,4,0,6,4,9,5,5,1,4,9,2,9,0,8,6,2,5,6,9,3,2,1,9,7,8,4,6,8,6,2,2,4,8,2},
13            {8,3,9,7,2,2,4,1,3,7,5,6,5,7,0,5,6,0,5,7,4,9,0,2,6,1,4,0,7,9,7,2,9,6,8,6,5,2,4,1,4,5,3,5,1,0,0,4,7,4},
14            {8,2,1,6,6,3,7,0,4,8,4,4,0,3,1,9,9,8,9,0,0,0,8,8,9,5,2,4,3,4,5,0,6,5,8,5,4,1,2,2,7,5,8,8,6,6,6,8,8,1},
15            {1,6,4,2,7,1,7,1,4,7,9,9,2,4,4,4,2,9,2,8,2,3,0,8,6,3,4,6,5,6,7,4,8,1,3,9,1,9,1,2,3,1,6,2,8,2,4,5,8,6},
16            {1,7,8,6,6,4,5,8,3,5,9,1,2,4,5,6,6,5,2,9,4,7,6,5,4,5,6,8,2,8,4,8,9,1,2,8,8,3,1,4,2,6,0,7,6,9,0,0,4,2},
17            {2,4,2,1,9,0,2,2,6,7,1,0,5,5,6,2,6,3,2,1,1,1,1,1,0,9,3,7,0,5,4,4,2,1,7,5,0,6,9,4,1,6,5,8,9,6,0,4,0,8},
18            {0,7,1,9,8,4,0,3,8,5,0,9,6,2,4,5,5,4,4,4,3,6,2,9,8,1,2,3,0,9,8,7,8,7,9,9,2,7,2,4,4,2,8,4,9,0,9,1,8,8},
19            {8,4,5,8,0,1,5,6,1,6,6,0,9,7,9,1,9,1,3,3,8,7,5,4,9,9,2,0,0,5,2,4,0,6,3,6,8,9,9,1,2,5,6,0,7,1,7,6,0,6},
20            {0,5,8,8,6,1,1,6,4,6,7,1,0,9,4,0,5,0,7,7,5,4,1,0,0,2,2,5,6,9,8,3,1,5,5,2,0,0,0,5,5,9,3,5,7,2,9,7,2,5},
21            {7,1,6,3,6,2,6,9,5,6,1,8,8,2,6,7,0,4,2,8,2,5,2,4,8,3,6,0,0,8,2,3,2,5,7,5,3,0,4,2,0,7,5,2,9,6,3,4,5,0}
22        };
23        int number=13;
24        int total=numbers.length*numbers[0].length-1; //Total numbers subtract 1
25        int k=0;
26        long temp=1;
27        long result=1;
28        for(int i=0;i<=(total-number+1);){
29            
30            temp=1;
31            k=i+number-1;
32            
33            for(int j=i;j<=k;j++){
34                int oneIndex= j/numbers[0].length;               
35                int twoIndex= j%numbers[0].length;
36                
37                temp*=numbers[oneIndex][twoIndex];
38                
39                if(numbers[oneIndex][twoIndex]==0)
40                {
41                    i=j+1;
42                    break;
43                }
44            }
45            if(temp!=0)
46            {
47                if(temp>result)
48                {
49                    //System.out.printf("%3d %d\r\n",i,temp);
50                    result=temp;
51                }
52                i++;
53            }
54        }
55        
56        System.out.println(result);

Project Euler 8