//動態規劃數塔問題
#include<iostream>
using namespace std;
const int n = 5;
int d[n][n] = { {8},
				{12,15},
				{3,9,6},
				{8,10,5,12},
				{16,4,18,10,9} };
int DataTower(int d[n][n]) {
	int maxAdd[n][n] = { 0 };
	int path[n][n] = { 0 };
	int i, j;
	for (j = 0; j < n; j++) {
		maxAdd[n - 2][j] =
 
 d[n - 2][j];
	}
	for (i = n - 2; i >= 0; i--) {
		for (j = 0; j <= i; j++) {
			if (maxAdd[i + 1][j] > maxAdd[i + 1][j + 1]) {
				maxAdd[i][j] = d[i][j] + maxAdd[i + 1][j];
				path[i][j] = j;
			}
			else
			{
				maxAdd[i][j] = d[i][j] + maxAdd[i + 1][j+1];
				path[i][j] = j+1;
			}
		}
	}
 

	cout << "The path is : " <<d[0][0];
	j = path[0][0];
	for (int i = 1; i < n; i++) {
		cout << " ---> " << d[i][j];
		j = path[i][j];
	}
	return maxAdd[0][0];
}
int main()
{
	cout << "maxAdd = " << DataTower(d)<<endl;
	//system("pause");
	return 0;
}