POJ 1163 The Triangle

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本文介绍了一个关于寻找三角形网格中从顶点到底边的最大路径和的问题，并提供了一段Java代码实现。该算法通过动态规划逆向计算每一层的最大路径和，最终得出顶部节点的最大路径和。

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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

Code

import java.util.Scanner;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[][] data = new int[n][n];
        for (int i = 0; i < n; i++)
            for (int j = 0; j <= i; j++) {
                data[i][j] = sc.nextInt();
            }
        int[] dp = data[n - 1];
        for (int i = n - 2; i >= 0; i--)
            for (int j = 0; j <= i; j++) {
                dp[j] = Math.max(dp[j], dp[j + 1]) + data[i][j];
            }
        System.out.println(dp[0]);

        sc.close();
    }
}