POJ ACM习题【No.3176】

最新推荐文章于 2021-05-22 02:29:05 发布

最新推荐文章于 2021-05-22 02:29:05 发布 · 122 阅读

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本文介绍了一种名为CowBowling的算法问题，该问题要求在给定的三角形数字阵列中找出从顶到底的最大路径和。通过动态规划的方法，文章提供了一个高效的解决方案，并给出了示例说明。

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Cow Bowling

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 4594		Accepted: 2973

Description

The cows don't use actual bowling balls when they go bowling. They each take a number (in the range 0..99), though, and line up in a standard bowling-pin-like triangle like this:

          7



        3   8



      8   1   0



    2   7   4   4



  4   5   2   6   5

Then the other cows traverse the triangle starting from its tip and moving "down" to one of the two diagonally adjacent cows until the "bottom" row is reached. The cow's score is the sum of the numbers of the cows visited along the way. The cow with the highest score wins that frame.

Given a triangle with N (1 <= N <= 350) rows, determine the highest possible sum achievable.

Input

Line 1: A single integer, N

Lines 2..N+1: Line i+1 contains i space-separated integers that represent row i of the triangle.

Output

Line 1: The largest sum achievable using the traversal rules

Sample Input

Sample Output

Hint

Explanation of the sample:

          7

         *

        3   8

       *

      8   1   0

       *

    2   7   4   4

       *

  4   5   2   6   5

The highest score is achievable by traversing the cows as shown above.

此题与1163雷同

import java.util.*;

public class Main {

	public static void main(String[] args) {
		Scanner cin = new Scanner(System.in);
		int height = cin.nextInt();
		int[][] tree = new int[height][height]; 
		int[][] max = new int[height][height];
		int maxValue = 0;
		int left, right = 0;
		
		for(int i = 0; i < height; i++)
		{
			for(int j = 0; j <= i; j++)
			{
				tree[i][j] = cin.nextInt();
//				System.out.print(tree[i][j] + " ");
			}
//			System.out.println("\n");
		}
		
		max[0][0] = tree[0][0];
		

		
		for(int i = 1; i < height; i++)
		{
			for(int j = 0; j <= i; j++)
			{
				if(j == 0)
					max[i][j] = max[i-1][j] + tree[i][j];
				else if(j == i)
					max[i][j] = max[i-1][j-1] + tree[i][j];
				else
				{
					if(max[i-1][j-1] >= max[i-1][j])
						max[i][j] = max[i-1][j-1] + tree[i][j];
					else
						max[i][j] = max[i-1][j] + tree[i][j];
				}
			}
		}
		
		for(int j = 0; j < height; j++)
		{
			if(max[height-1][j] > maxValue)
				maxValue = max[height-1][j];
		}
		
		System.out.println(maxValue);
		

	}

}