Maximum path sum I
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
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)
Answer:
1074
Completed on Thu, 27 Oct 2016, 05:44
题解：dp。dp[i][j]+=max(dp[i-1][j-1],dp[i-1][j])。搞定....
代码：
using namespace std;
int dp[16][15];
int main()
{
int maxn=0;
memset(dp,0,sizeof(dp));
int dp[15][15] = {
{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},
};
for(int i=1;i<=15;i++)
{
for(int j=1;j<=i;j++)
{
dp[i][j]+=max(dp[i-1][j-1],dp[i-1][j]);
maxn=max(maxn,dp[i][j]);
}
}
cout<<maxn<<endl;
return 0;
}