From 77cbf36358c787d1cc6a11750b5292a866dbae26 Mon Sep 17 00:00:00 2001 From: CyC2018 Date: Fri, 30 Oct 2026 20:18:04 +0800 Subject: [PATCH] =?UTF-8?q?Update=2047.=20=E7=A4=BC=E7=89=A9=E7=9A=84?= =?UTF-8?q?=E6=9C=80=E5=A4=A7=E4=BB=B7=E5=80=BC.md?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit 补充动态规划状态转移方程与滚动数组优化的推导说明,并补充一维数组滚动更新的示意配图。 --- notes/47. 礼物的最大价值.md | 6 +++++- notes/pics/offer47-rolling-dp.png | Bin 0 -> 145293 bytes 2 files changed, 5 insertions(+), 1 deletion(-) create mode 100644 notes/pics/offer47-rolling-dp.png diff --git a/notes/47. 礼物的最大价值.md b/notes/47. 礼物的最大价值.md index 96aac6f5..ed943dce 100644 --- a/notes/47. 礼物的最大价值.md +++ b/notes/47. 礼物的最大价值.md @@ -17,7 +17,11 @@ ## 解题思路 -应该用动态规划求解,而不是深度优先搜索,深度优先搜索过于复杂,不是最优解。 +深度优先搜索要枚举所有路径,路径数随棋盘大小指数增长;用动态规划每个格子只需计算一次。 + +设 dp[i][j] 为走到格子 (i, j) 时拿到的最大价值。只能从上方或左方到达,因此 dp[i][j] = max(dp[i - 1][j], dp[i][j - 1]) + 礼物价值。按行计算时只用到上一行,代码用一维数组滚动:更新 dp[i] 之前,dp[i] 是上方格子的结果,dp[i - 1] 是左方格子刚更新的结果。以上面棋盘的第二行为例: + +

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