[Project Euler] Problem 18

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)

按照下面的提示，如果把所有的路线的和求出了，会有16384种情况。

我们从三角形顶向下计算无法剪枝了，我们换一种思路来计算。从下往上计算，把小的结果直接舍去。

3 3 3 23
7 4 7 4 20 19
2 4 6 -> 10 13 15 -> ->
8 5 9 3

可以看出，只要简单的阅历一遍

我们用同样的思路来解决那个15层的三角形

#include <iostream>
usingnamespace std;

int main(){
int item[120]={
75,
95,64,
17,47,82,
18,35,87,10,
20, 4,82,47,65,
19, 1,23,75, 3,34,
88, 2,77,73, 7,63,67,
99,65, 4,28, 6,16,70,92,
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, 4,68,89,53,67,30,73,16,69,87,40,31,
4,62,98,27,23, 9,70,98,73,93,38,53,60, 4,23
};
int step =15;
int tmp1,tmp2;
for(int i=14; i>0; i--){
tmp1 = i*(i-1)/2-1;
tmp2 = i*(i+1)/2-1;
for(int j=i; j>0; j--){
item[tmp1+j] += item[tmp2+j]>item[tmp2+j+1]?item[tmp2+j]:item[tmp2+j+1];
}
}
cout << item[0] << endl;
}