动态规划（1）1163 The Triangle

The Triangle

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 32266		Accepted: 19083

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

         最近要紧急学习动态规划，就打算从头学起，于是就有了这最最简单，最最基础的这道题，体现了最基础的动态规划思想，动态规划里的状态和状态转移是重点，这一题就开了一个好头，希望大家很快理解。本人也是菜鸟呃，感谢凤娇大神，希望有大神能不吝赐教，找找我的错误，不胜感激！

#include<stdio.h>
#include<string.h>
unsigned max(unsigned a,unsigned b)
{
return (a>b)?a:b;
};
int main()
{
unsigned int num[101][101],n;
int i,j;
memset(num,0,sizeof(num));
long ans = 0;
scanf("%u",&n);
for(i=0;i<n;i++)
for(j=0;j<i+1;j++)
scanf("%u",&num[i][j]);
for(i = n-2;i>=0;i--){
for(j = 0;j<=i;j++){
num[i][j] += max(num[i+1][j],num[i+1][j+1]) ;
}
}
ans = num[0][0];
printf("%ld",ans);
return 0;
}