From 70b5de109d854aaf28f81b1119b43b79e7b83eba Mon Sep 17 00:00:00 2001
From: Zengtudor <zengtudor@outlook.com>
Date: Thu, 17 Oct 2024 13:46:37 +0800
Subject: [PATCH] update

---
 README.md           | 19 +++++++++++++++++++
 src/P7414/P7414.cpp | 26 ++++++++++++++++++++++++++
 2 files changed, 45 insertions(+)
 create mode 100644 src/P7414/P7414.cpp

diff --git a/README.md b/README.md
index 80fb707..2507327 100755
--- a/README.md
+++ b/README.md
@@ -74,4 +74,23 @@ void bfs(){
             l=mid+1;
         }
     }
+```
+### [P7414](https://www.luogu.com.cn/problem/P7414)
+
+#### 区间DP思路
+```cpp
+/*
+区间动态规划解题步骤：
+1.根据问题推测dp[i][j]的含义
+问题：将第1个到第Ｎ个位置涂上指定颜色的最小次数
+dp[i][j]的含义：将第i个到第j个位置涂上指定颜色的最小次数
+
+2.根据规则推出dp[i][j]的状态转移公式
+在i-j之间找一个中间值k，将i-j这一段分成两段i-k和k+1~j）
+dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j]);
+
+3.边界问题（比如设定dp[0][0],dp[0][j],dp[i][0]初始值）
+dp[i][j]=dp[i][j-1]+(a[i]!=a[j]);
+dp[i][i]=1;
+*/
 ```
\ No newline at end of file
diff --git a/src/P7414/P7414.cpp b/src/P7414/P7414.cpp
new file mode 100644
index 0000000..43eff09
--- /dev/null
+++ b/src/P7414/P7414.cpp
@@ -0,0 +1,26 @@
+#include <bits/stdc++.h>
+
+using ll = long long;
+using namespace std;
+
+const ll max_n=3e2+5;
+ll n, a[max_n], dp[max_n][max_n];
+
+int main(){
+    cin>>n;
+    for(ll i{1};i<=n;i++){
+        cin>>a[i];
+    }
+
+    for(ll i{n};i>=1;i--){
+        dp[i][i]=1;
+        for(ll j{i+1};j<=n;j++){
+            dp[i][j]=dp[i][j-1]+(a[i]==a[j]?0:1);
+            for(ll k{i};k<j;k++){
+                dp[i][j]=min(dp[i][j],dp[i][k]+dp[k+1][j]);
+            }
+        }
+    }
+
+    cout<<dp[1][n]<<'\n';
+}   
\ No newline at end of file