The Triangle
Time Limit: 1000MS | Memory Limit: 10000K | |
Total Submissions: 13904 | Accepted: 7977 |
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
此题解题的思路在于创建一个对应的三角结构,保存该层次的最大可能总和值。对于每一个值,需要按上一层左右两个值之中的较大者进行计算。
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); } }
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