poj1163 数字三角形

最新推荐文章于 2019-10-06 23:01:54 发布

原创最新推荐文章于 2019-10-06 23:01:54 发布 · 376 阅读

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本文介绍了一个算法问题，即计算从三角形顶部到底部的最大路径和，路径只能沿对角线向下移动。通过逆向从底部向上计算的方式，利用动态规划思想高效地解决了该问题。

The Triangle

            Time Limit: 1000MS      Memory Limit: 10000K
            Total Submissions: 53441        Accepted: 32282

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

这里写图片描述

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;
int n;
int a[100][100];
int b[100];
void f(int t[],int x){
    for(int i = 0;i < x; ++i){
        b[i] = max(t[i] + b[i] , t[i] + b[i+1]);
    }

}
int main(){
    cin >> n;
        for(int i = 0;i < n;++i){
            for(int j = 0;j <= i; ++j){
                cin >> a[i][j];
            }
        }
    memset(b,0,sizeof(b));
    for(int i = n;i > 0; --i){
        f(a[i-1],i);
    }
    cout << b[0] << endl;
    return 0;
}