欧拉项目第18题Maximum path sum I

By starting at the top of the triangle below and moving to adjacent numbers on the row below, the maximum total from top to bottom is 23.

3
7 4
2 4 6
8 5 9 3

That is, 3 + 7 + 4 + 9 = 23.

Find the maximum total from top to bottom of the triangle below:

75
95 64
17 47 82
18 35 87 10
20 04 82 47 65
19 01 23 75 03 34
88 02 77 73 07 63 67
99 65 04 28 06 16 70 92
41 41 26 56 83 40 80 70 33
41 48 72 33 47 32 37 16 94 29
53 71 44 65 25 43 91 52 97 51 14
70 11 33 28 77 73 17 78 39 68 17 57
91 71 52 38 17 14 91 43 58 50 27 29 48
63 66 04 68 89 53 67 30 73 16 69 87 40 31
04 62 98 27 23 09 70 98 73 93 38 53 60 04 23

NOTE: As there are only 16384 routes, it is possible to solve this problem by trying every route. However, Problem 67, is the same challenge with a triangle containing one-hundred rows; it cannot be solved by brute force, and requires a clever method! ;o)

从上到下，每次只能取相邻的数，求这些数和最大值。

思路如下，每一行看成一个数组，第一行是75，没啥说的，

到第二行，算出这个位数，线路最大值，放入数组里面，第二个是 75+95=170，64+75=139，

第三行， 170+17 = 187，MAX(170，139) + 47=217, 139 + 82= 221

第四行， 187 +18，  MAX(187，217) + 35,   MAX(217，221) + 87, 221+10

...

 static Map<Integer,Integer[]> x = new HashMap<Integer, Integer[]>();        static {        x.put(1, new Integer[]{75});         x.put(2, new Integer[]{95,64});        x.put(3, new Integer[]{17,47,82});        x.put(4, new Integer[]{18,35,87,10});        x.put(5, new Integer[]{20,4,82,47,65});        x.put(6, new Integer[]{19,1,23,75,3,34});        x.put(7, new Integer[]{88,2,77,73,7,63,67});        x.put(8, new Integer[]{99,65,4,28,6,16,70,92});        x.put(9, new Integer[]{41,41,26,56,83,40,80,70,33});        x.put(10, new Integer[]{41, 48, 72, 33, 47, 32, 37, 16, 94, 29});        x.put(11, new Integer[]{53,71, 44, 65, 25, 43, 91, 52, 97, 51, 14});        x.put(12, new Integer[]{70,11,33,28,77,73,17,78,39,68,17,57});        x.put(13, new Integer[]{91,71,52,38,17,14,91,43,58,50,27,29,48});        x.put(14, new Integer[]{63,66,4,68,89,53,67,30,73,16,69,87,40,31});        x.put(15, new Integer[]{4,62,98,27,23,9,70,98,73,93,38,53,60,4,23});    }        public static void main(String[] args) {        Integer[] y = new Integer[]{75};        for(int i=2;i<=15;i++) {            Integer[] t_x = x.get(i);            Integer[] on = new Integer[i];            for(int j=0;j<i;j++) {                if(j==0) {                    on[j] = y[0] + t_x[0];                } else if(j == i - 1) {                    on[j] = y[j-1] + t_x[j];                } else {                    on[j] = Math.max(y[j-1], y[j]) + t_x[j];                }            }            y = on;        }        Integer max =0;        for(Integer yy : y) {            if(max < yy) {                max = yy;            }        }        System.out.println(max);    }