PKU ACM 1163-The Triangle

题目来源：http://acm.pku.edu.cn/JudgeOnline/problem?id=1163



解题报告：

难的DP不会做，先从简单的入手～

自底向上，f[k]保存从底部到a[k]的所有可能路径的和的最大值，那么f[k]=a[k]+a[k]下两个分支的f[]的最大值。

#include <iostream>
using namespace std;

int max(int a, int b)
{
	return a>b?a:b;
}

int main()
{
	int N;
	cin >> N;
	int total=(N+1)*N>>1;
	int *a=new int[total];
	int *f=new int[total];
	for(int i=0;i<total;i++)
		cin >> a[i];
	int k=total-1;
	for(int i=N;i>0;i--)
	{
		for(int j=i;j>0;j--)
		{
			if(i==N)
				f[k]=a[k];
			else
				f[k]=a[k]+max(f[k+i],f[k+i+1]);
			k--;
		}
	}
	cout << f[0] << endl;
}

附录：

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 19579		Accepted: 11412

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