USACO 1.5.1 —— DP

Number Triangles

Consider the number triangle shown below. Write a program that calculates the highest sum of numbers that can be 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.

7

3   8

8   1   0

2   7   4   4

4   5   2   6   5

In the sample above, the route from 7 to 3 to 8 to 7 to 5 produces the highest sum: 30.

PROGRAM NAME: numtri

INPUT FORMAT

The first line contains R (1 <= R <= 1000), the number of rows. Each subsequent line contains the integers for that particular row of the triangle. All the supplied integers are non-negative and no larger than
100.

SAMPLE INPUT (file numtri.in)

5
7
3 8
8 1 0
2 7 4 4
4 5 2 6 5

OUTPUT FORMAT

A single line containing the largest sum using the traversal specified.

SAMPLE OUTPUT (file numtri.out)

30

经典的DP模型。从下往上推即可。

/*
ID: XMzhou
LANG: C++
TASK: numtri
*/
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <iostream>
#include <cstring>
#include <map>
#include <string>
#include <stack>
#include <cctype>
#include <vector>
#include <queue>
#include <set>
#include <utility>
#include <cassert>
#include <numeric>
using namespace std;
#define Online_Judge
#define outstars cout << "***********************" << endl;
#define clr(a,b) memset(a,b,sizeof(a))
#define lson l , mid  , rt << 1
#define rson mid + 1 , r , rt << 1 | 1
#define mk make_pair

const int MAXN = 1000 + 50;
const int MAXS = 10000 + 50;
const int sigma_size = 26;
const long long LLMAX = 0x7fffffffffffffffLL;
const long long LLMIN = 0x8000000000000000LL;
const int INF = 0x7fffffff;
const int IMIN = 0x80000000;
const int inf = 1 << 30;
#define eps 1e-10
const long long MOD = 1000000000 + 7;
const int mod = 10007;
typedef long long LL;
const double PI = acos(-1.0);
typedef double D;
typedef pair<int , int> pii;
typedef vector<int> vec;
typedef vector<vec> mat;

#define Bug(s) cout << "s = " << s << endl;
///#pragma comment(linker, "/STACK:102400000,102400000")
int a[MAXN][MAXN];
int main()
{
//ios::sync_with_stdio(false);
#ifdef Online_Judge
freopen("numtri.in","r",stdin);
freopen("numtri.out","w",stdout);
#endif // Online_Judge
int n;
while(~scanf("%d" , &n))
{
for(int i = 0 ; i < n ; i++)
{
for(int j = 0 ; j <= i ; j++)
{
scanf("%d" , &a[i][j]);
}
}
for(int i = n - 1 ;i >= 0 ; i--)
{
for(int j = 0 ;j <= i ;j++)
{
a[i][j] += max(a[i + 1][j] , a[i + 1][j + 1]);
}
}
printf("%d\n" , a[0][0]);
}
return 0;
}