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：


#include <bits/stdc++.h>
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;
}