Project Euler Problem 67 Maximum path sum II

Maximum path sum II

Problem 67

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 in triangle.txt (right click and 'Save Link/Target As...'), a 15K text file containing a triangle with one-hundred rows.

NOTE: This is a much more difficult version ofProblem 18. It is not possible to try every route to solve this problem, as there are 2⁹⁹ altogether! If you could check one trillion (10¹²) routes every second it would take over twenty billion years to check them all. There is an efficient algorithm to solve it. ;o)

C++:

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

using namespace std;

const int MAXN = 100;

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 18 Maximum path sum I