算法笔记/USACO Guide GOLD金组DP 3. Paths on Grids

今天学习背包DP（Knapsack DP) 

是USACO Guide的DP章节中第三点

What is grid DP? -Summary

DP problems often involve a 2D grid where paths are analyzed. Movement is restricted to one direction on the x-axis and y-axis, typically starting from one corner and ending at another. The goal may be to count paths or find max/min values. Sub-problems are sub-rectangles of the grid. For instance, to count paths from 1,1 to N,M moving positively, we define dp[x][y] as the number of paths to x,y. The recurrence relation is dp[x][y] = dp[x-1][y] + dp[x][y-1], with dp[1][1] = 1. Understanding cell appending aids in forming the correct recurrence.

简单来说，DP 问题通常涉及分析路径的时候使用2D的数组。移动仅限于 x 轴和 y 轴上的一个方向，通常从一个角开始并在另一个角结束。目标可能是对路 径进行计数或查找最大/最小值。子问题是网格的子矩形。例如，为了计算从 1,1 到 N,M 正向移动的路径，我们将 dp[x][y] 定义为到 x,y 的路径数。递推关系为 dp[x][y] = dp[x-1][y] + dp[x][y-1]，其中 dp[1][1] = 1。理解单元格附加有助于形成正确的规律。

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