【DP入门】The Triangle

最新推荐文章于 2022-03-20 12:30:00 发布

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本博客介绍了一个算法，用于计算数字三角形中从顶部到底部路径的最大和。通过逐层累加相邻节点的较大值，最终得到顶部到任一底部节点的最大路径和。

B - The Triangle

Time Limit:1000MS Memory Limit:10000KB 64bit IO Format:%I64d & %I64u

Submit Status

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

#include <stdio.h>
#include <stdlib.h>

#define MAX 110

int main()
{
    int n;
    while(scanf("%d",&n)!=EOF)
    {
        int a[MAX][MAX];
        int i,j,k;
        for(i=0;i<n;i++)
            for(j=0;j<i+1;j++)
                scanf("%d",&a[i][j]);
        for(i=n-2;i>=0;i--)
            for(j=0;j<=i;j++)
                a[i][j]=a[i][j]+(a[i+1][j]>a[i+1][j+1]?a[i+1][j]:a[i+1][j+1]);
        printf("%d\n",a[0][0]);
    }
    return 0;
}