南阳理工oj_The Triangle

最新推荐文章于 2021-12-06 19:14:28 发布

原创最新推荐文章于 2021-12-06 19:14:28 发布 · 779 阅读

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#数字三角形 #动态规划

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本文介绍了一种算法解决方案，用于计算数列三角形中从顶点到基底的最大路径和。通过动态规划方法，实现高效求解路径优化问题。

The Triangle
时间限制：1000 ms | 内存限制：65535 KB
难度：4
描述
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5
(Figure 1)
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
上传者
苗栋栋

#include <iostream>
#include <cstdio> 
#include <algorithm>
#include <string>
#include <cstring>
#include <cstdlib>
using namespace std;

int a[110][110], dp[110][110];
#define mem(a) memset(a, 0, sizeof(a))

int main() {
    int n;
    while (cin >> n) {
        mem(a);     mem(dp);
        for (int i = 0; i<n; i++) {
            for (int j = 0; j<=i; j++) {
                cin >> a[i][j];
            }
        }
        for (int i = 0; i<n; i++)   dp[n-1][i] = a[n-1][i];
        for (int i = n-2; i>=0; i--) {
            for (int j = i; j>=0; j--) {
                dp[i][j] = max(a[i][j] + dp[i+1][j], a[i][j] + dp[i+1][j+1]);
            }
        }
        cout << dp[0][0] << endl;
    }
    return 0;
}