1010.Number Triangles

题目大意：给出数字金字塔，找出从上到下的一条路，使得总和最大，且只能从上往左下或右下走。

Description

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.

 

Input

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.

Output

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

Sample Input

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

Sample Output

30

Hint

Huge input, scanf is recommended if you are using C++.

Source

USACO

// 1010_NumberTriangles.cpp : 定义控制台应用程序的入口点。//#include "stdafx.h"#include<iostream>#include<string.h>//#include<math.h>using namespace std;int str[1100][1100], dir[1010][1010];int max(int a, int b){return (a > b) ? a : b;}int main(){int n, i, j;while (cin >> n){for (i = 1; i <= n; i++){for (j = 1; j <= i; j++){cin >> str[i][j];}}memset(dir, 0, sizeof(dir));for (i = n; i >= 1; i--){for (j = 1; j <= i; j++){dir[i][j] = max(dir[i + 1][j], dir[i + 1][j + 1]) + str[i][j]; //从底层开始寻找最大的数据}}cout << dir[1][1] << endl;}return 0;}