http://projecteuler.net/problem=18

動的計画法。

{{{#!highlight c++
#include <iostream>

using namespace std;

int data[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},
};
int dp[15][15];

void debug() {
    for (int i = 0; i < 15; i++) {
        for (int j = 0; j <= i; j++) {
            cout << dp[i][j] << ' ';
        }
        cout << endl;
    }
}

int main() {
    dp[0][0] = data[0][0];
    for (int i = 1; i < 15; i++) {
        dp[i][0] = dp[i-1][0] + data[i][0];
        for (int j = 1; j < i; j++) {
            dp[i][j] = max(dp[i-1][j-1], dp[i-1][j]) + data[i][j];
        }
        dp[i][i] = dp[i-1][i-1] + data[i][i];
    }
    int ans = 0;
    for (int i = 0; i < 15; i++) {
        ans = max(ans, dp[14][i]);
    }
    cout << ans << endl;
    return 0;
}
}}}