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POJ 1163 The Triangle

2024-07-18 14:39:21   210人阅读

来源:http://poj.org/problem?id=1163



The Triangle
Time Limit: 1000MS Memory Limit: 10000K
Total Submissions: 37660 Accepted: 22611

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

Source

IOI 1994

题意:  找一条从顶节点到底部的路径，使该路径上点之和最大，求最大值。

题解: 动态规划解决之


AC代码:

#include<cstdio>
#include<cstring>
const int Max=105;
int max[Max][Max],sum[Max][Max],n;
int DP(int i,int j){
	if(~sum[i][j])
	return sum[i][j];
	if(i==n-1)
	sum[i][j]=max[i][j];
	else 
	sum[i][j]=max[i][j]+(DP(i+1,j)>DP(i+1,j+1) ? DP(i+1,j):DP(i+1,j+1));
	return sum[i][j];
}
int main()
{
	memset(sum,-1,sizeof(sum));
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	for(int j=0;j<=i;j++)
	scanf("%d",&max[i][j]);
	printf("%d\n",DP(0,0));
	return 0;
}





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