数字三角形POJ1163 program7.1.4.cpp-优快云博客

本文介绍了一个经典的算法问题——数字三角形的最高路径求和。问题要求从三角形顶部开始，到达底部的过程中找到一条路径，使得路径上数字之和最大。文中提供了一段C++代码实现，通过动态规划的方法解决了这个问题。

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1163:The Triangle

总时间限制:

1000ms

内存限制:

65536kB

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

样例输出

来源

IOI 1994

//数字三角形POJ1163 program7.1.4.cpp
#include<iostream>
#include<algorithm>
using namespace std;
const int maxN = 101;
int d[maxN][maxN];
int n;
int *maxSum;

int main(void)
{
    int i, j;
    cin >> n;
    for(i = 1; i <= n; i++)
    {
        for(j = 1; j <= i; j++)
        {
            cin >> d[i][j];
        }
    }

    maxSum = d[n];

    for(int i = n - 1; i >= 1; --i)
    {
        for(int j = 1; j <= i; ++j)
        {
            maxSum[j] = max(maxSum[j], maxSum[j + 1]) + d[i][j];
        }
    }

    cout << maxSum[1] << endl;

    return 0;
}