《程序设计与算法（二）算法基础》《第六周 分治》动态规划

1163:The Triangle

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总时间限制: 

1000ms

 

内存限制: 

65536kB

描述

Figure 1 shows a number triangle. Write a program that calculates the highest sum of numbers passed on a route that starts at the top and ends somewhere on the base. Each step can go either diagonally down to the left or diagonally down to the right.

输入

Your program is to read from standard input. The first line contains one integer N: the number of rows in the triangle. The following N lines describe the data of the triangle. The number of rows in the triangle is > 1 but <= 100. The numbers in the triangle, all integers, are between 0 and 99.

输出

Your program is to write to standard output. The highest sum is written as an integer.

样例输入

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

样例输出

30

/*
http://bailian.openjudge.cn/practice/1163/
1163:The Triangle
递归解法2：数字三角形的记忆递归型动归程序
*/
#include<iostream>
#include<algorithm>
#define MAX 101
using namespace std;
int D[MAX][MAX];
int sum[MAX][MAX];
int n;
int MaxSum(int i, int j)
{
    if (sum[i][j] != -1)/*说明这个路径的最大和已经算过了*/
    {
        return sum[i][j];
    }
    if (i == n)
    {
        sum[i][j] = D[i][j];
    }
    else
    {
        int x = MaxSum(i + 1, j);
        int y = MaxSum(i + 1, j + 1);
        sum[i][j] = max(x, y) + D[i][j];
    }
    return sum[i][j];
}
int main()
{
    int i, j;
    cin >> n;
    for (i = 0; i < n; i++)
    {
        for (j = 0; j <= i; j++)
        {
            cin >> D[i][j];
            sum[i][j] = -1;
        }
    }
    cout << MaxSum(0, 0) << endl;
    return 0;

}