From 91e8a1f75145fba2f5251de08bf1778d4105f693 Mon Sep 17 00:00:00 2001
From: Ren Baoshuo <i@baoshuo.ren>
Date: Sun, 15 Nov 2020 15:12:33 +0800
Subject: [PATCH] =?UTF-8?q?P7074=20=E6=96=B9=E6=A0=BC=E5=8F=96=E6=95=B0?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

R41944428
---
 problem/P7074/P7074.cpp   | 35 +++++++++++++++++++++++++++++++++++
 problem/P7074/solution.md | 11 +++++++++++
 2 files changed, 46 insertions(+)
 create mode 100644 problem/P7074/P7074.cpp
 create mode 100644 problem/P7074/solution.md

diff --git a/problem/P7074/P7074.cpp b/problem/P7074/P7074.cpp
new file mode 100644
index 00000000..fbb4784f
--- /dev/null
+++ b/problem/P7074/P7074.cpp
@@ -0,0 +1,35 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+int       n, m;
+long long w[1005][1005], f[1005][1005][2];
+
+long long dfs(int x, int y, int from) {
+    if (x < 1 || x > n || y < 1 || y > m) {
+        return -0x3f3f3f3f;
+    }
+    if (f[x][y][from] != -0x3f3f3f3f) {
+        return f[x][y][from];
+    }
+    if (from == 0) {
+        f[x][y][from] = max({dfs(x + 1, y, 0), dfs(x, y - 1, 0), dfs(x, y - 1, 1)}) + w[x][y];
+    }
+    else {
+        f[x][y][from] = max({dfs(x - 1, y, 1), dfs(x, y - 1, 0), dfs(x, y - 1, 1)}) + w[x][y];
+    }
+    return f[x][y][from];
+}
+
+int main() {
+    cin >> n >> m;
+    for (int i = 1; i <= n; i++) {
+        for (int j = 1; j <= m; j++) {
+            cin >> w[i][j];
+            f[i][j][0] = f[i][j][1] = -0x3f3f3f3f;
+        }
+    }
+    f[1][1][0] = f[1][1][1] = w[1][1];
+    cout << dfs(n, m, 1) << endl;
+    return 0;
+}
diff --git a/problem/P7074/solution.md b/problem/P7074/solution.md
new file mode 100644
index 00000000..a3fe48af
--- /dev/null
+++ b/problem/P7074/solution.md
@@ -0,0 +1,11 @@
+## 思路
+
++ 算法：记忆化搜索
+
+设 $F_{i,j,0}$ 表示从一个格子上方走到该格子的路径最大和，$F_{i,j,1}$ 表示从一个格子下方走到该格子的路径最大和。
+
+若搜到以前搜过的状态则直接返回搜过的最大和（也就是 $F$ 中的值），否则继续搜索到达该格时的最大和。
+
+## 代码
+
+见 `P7074.cpp` 。