USACO 1.5 Number Triangles (numtri)

最新推荐文章于 2025-01-30 23:05:35 发布

DamonHao

最新推荐文章于 2025-01-30 23:05:35 发布

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分类专栏： USACO USACO 题解文章标签： Algorithm

本文链接：https://blog.youkuaiyun.com/damonhao/article/details/19616443

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USACO 题解

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本文介绍了一个关于寻找三角形网格中从顶部到底部的最大路径和的问题，并提供了一段使用C++实现的代码示例。该算法通过动态规划从底部向上逐层计算每个节点上的最大路径和。

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/*
ID: haolink1
PROG: numtri
LANG: C++
*/

//Note: the key point of this problem is you shoud add the vlaue of number
//triangle from bottom to top, then you can see the optimal substructure.
//So you can try DP(dynamic programming),and that's it!

//#include <iostream>
#include <fstream>

using namespace std;
const short max_row = 1000;
int numbers[max_row][max_row];

int Max(int first,int second){
    if(first >= second)
        return first;
    return second;
}

int main(){
    ifstream fin("numtri.in");
    short row_num = 0;
    fin >> row_num;
    for(short i = 0; i < row_num; i++){
        for(short j = 0; j <= i; j++){
            fin >> numbers[i][j];
        }  
    }
    for(int i = row_num-2; i >=0; i--){
        for(int j = 0; j <= i; j++){
            //optimal substucture
            numbers[i][j] = Max(numbers[i+1][j],numbers[i+1][j+1])+numbers[i][j]; 
        }
    }
    ofstream fout("numtri.out");
    fout<<numbers[0][0]<< endl;
    return 0;
}