ACM ICPC 1163 The Triangle

最新推荐文章于 2021-08-13 09:43:03 发布

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本文介绍了一个关于寻找三角形网格中从顶部到底部的最大路径和的问题，并提供了一段C++代码实现。通过动态规划的方法，该算法能有效地解决这一问题。适用于初学者实践和理解动态规划思想。

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Description

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.

Input

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.

Output

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

Sample Input

Sample Output

【说明】简单的题目，适合练手

#include<iostream>
using namespace std;

int main()
{
	int triangle[5050];
	int row;
	cin >> row;
	for (int i = 1; i <= row; ++i)
	{
		for (int j = 1; j <= i; ++j)
		{
			cin >> triangle[(i-1)*i/2+j-1];
		}
	}
	for (int k = row-1; k > 0; --k)
	{
		for (int j = 1; j <= k; ++j)
		{
			triangle[(k-1)*k/2+j-1] += (triangle[k*(k+1)/2+j-1] > triangle[k*(k+1)/2+j]) ? triangle[k*(k+1)/2+j-1] : triangle[k*(k+1)/2+j];
		}
	}
	cout << triangle[0] << endl;
	return 0;
}

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