记忆化搜索

#include <bits/stdc++.h>
using namespace std;
int r;
int a[1005][1005];

// 走到 (x,y) 的最大值
int book[1005][1005];
int f(int x, int y)
{
    if (book[x][y] != -1)
        return book[x][y];
    if (x == 1 && y == 1)
        return book[x][y] = a[x][y];
    if (y == 1)
        return book[x][y] = f(x - 1, y) + a[x][y];
    if (y == x)
        return book[x][y] = f(x - 1, y - 1) + a[x][y];
    return book[x][y] = max(f(x - 1, y), f(x - 1, y - 1)) + a[x][y];
}
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> r;
    for (int i = 1; i <= r; i++)
        for (int j = 1; j <= i; j++)
        {
            cin >> a[i][j];
            book[i][j] = -1;
        }
    int ans = 0;
    for (int j = 1; j <= r; j++)
        ans = max(ans, f(r, j));
    cout << ans;
    return 0;
}

自己找到顺序递推

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int n, ans;
int a[1005][1005];
//dp[i][j] 从(1,1)走到(i,j)位置和的最大值
int dp[1005][1005];
int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    cin >> n;
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= i; j++)
            cin >> a[i][j];
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= i; j++)
            if (i == 1)
                dp[i][j] = a[i][j];
            else if (j == 1)
                dp[i][j] = dp[i - 1][j] + a[i][j];
            else if (j == i)
                dp[i][j] = dp[i - 1][j - 1] + a[i][j];
            else
                dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - 1]) + a[i][j];
    ans = -1;
    for (int j = 1; j <= n; j++)
        ans = max(ans, dp[n][j]);
    cout << ans << endl;
    return 0;
}