POJ 1163 TRIANGLE

思路：动态规划，更新/记忆二维数组

可以进一步改进成一维数组，但是嫌麻烦没写。

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 52288		Accepted: 31580

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

5
7
3 8
8 1 0 
2 7 4 4
4 5 2 6 5

Sample Output

30

package POJ_1163;

//递推思想
//动态规划

import java.io.BufferedInputStream;
import java.io.BufferedReader;
import java.util.Scanner;

public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(new BufferedInputStream(System.in));
		int[][] arr = new int[100][100];
		
		int layer = sc.nextInt();
		for(int i = 0;i<layer;i++){
			for(int j = 0;j<=i;j++){
				arr[i][j] = sc.nextInt();
			}
		}
		for(int i = 1;i<layer;i++){
			for(int j = 0;j<=i;j++){
				if(j==0){
					arr[i][j] += arr[i-1][j];
				}else if(j==i){
					arr[i][j] += arr[i-1][j-1];
				}else
				arr[i][j] += arr[i-1][j-1] >= arr[i-1][j]?arr[i-1][j-1]:arr[i-1][j];
			}
		}
		int max = arr[0][0];
		for(int i = 0;i<layer;i++){
			if(arr[layer-1][i]>max){
				max = arr[layer-1][i];
			}
		}
		System.out.println(max);
		
	}
}