动态规划-数字三角形

 

 

#include <iostream>
using namespace std;

const int N = 550, INF = 1e9;

int n;
int a[N][N], f[N][N];

int main()
{
    cin >> n;
    for (int i = 1; i <= n; ++ i)
        for (int j = 1; j <= i; ++ j)
            cin >> a[i][j];
            
    for (int i = 0; i <= n; ++ i)
        for (int j = 0; j <= i + 1; ++ j)   // 注意，边界全部初始化为负无穷
            f[i][j] = -INF;
    
    f[1][1] = a[1][1];
    for (int i = 2; i <= n; ++ i)
        for (int j = 1; j <= i; ++ j)
            f[i][j] = max(f[i - 1][j - 1] + a[i][j], f[i - 1][j] + a[i][j]);
    
    int res = -INF; // 初始化为负无穷，防止都是负数
    for (int i = 1; i <= n; ++ i)   res = max(res, f[n][i]);
    
    cout << res << endl;
    
    return 0;
}