Project Euler Problem 18 Maximum path sum I

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 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)

C++:

#include <iostream>
#include <cstring>
#include <cstdlib>

using namespace std;

const int MAXN = 15;

int grid[MAXN][MAXN];
int max;

inline int mymax(int left, int right)
{
    return left > right ? left : right;
}

int setmax(int n)
{
    for(int i=1; i<n; i++)
        for(int j=0; j<=i; j++)
            if(j == 0)
                grid[i][j] += grid[i-1][j];
            else
                grid[i][j] = mymax(grid[i][j] + grid[i-1][j-1], grid[i][j] + grid[i-1][j]);

    int max = 0;
    for(int i=n-1, j=0; j<n; j++)
        if(grid[i][j] > max)
            max = grid[i][j];

    return max;
}

int main()
{
    int n;

    while(cin >> n && n<=MAXN) {
        memset(grid, 0, sizeof(grid));

        for(int i=0; i<n; i++) {
            for(int j=0; j<=i; j++)
                cin >> grid[i][j];
        }

        int max = setmax(n);

        cout << max << endl;
    }

    return 0;
}

参考链接：Project Euler Problem 67 Maximum path sum II