POJ1163 The Triangle

当前这个点可以由它的左上方的点和正上方的点走到
dp[i][j]的含义是走到[i,j]这个点的最大值
所以状态转移方程就是 dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - 1]) + nums[i][j];

#include <iostream>
using namespace std;
const int maxn = 105;
int nums[maxn][maxn];
int dp[maxn][maxn];
int main()
{
    int n;
    cin >> n;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= i; j++) {
            cin >> nums[i][j];
        }
    }
    dp[0][0] = 0;
    int ans = 0;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= n; j++) {
            dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - 1]) + nums[i][j];
            ans = max(ans, dp[i][j]);
        }
    }
    cout << ans;
}