feat: 添加P4170.cpp解决字符串最小染色问题

实现动态规划算法计算字符串的最小染色次数，用于解决P4170题目

src/10/1/P4170.cpp

@@ -0,0 +1,39 @@
+#include <algorithm>
+#include <cstdint>
+#include <iostream>
+#include <istream>
+#include <string>
+using ll = int64_t;
+
+const ll maxn=50+5,inf=1e9+7;
+std::string c;
+ll dp[maxn][maxn],n;
+
+int main(){
+    std::iostream::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin>>c;
+    n=c.size();
+    c=' '+c;
+    for(ll i=1;i<=n;i++){
+        for(ll j=1;j<=n;j++){
+            dp[i][j]=inf;
+        }
+    }
+    for(ll i=0;i<=n;i++){
+        dp[i][i]=1;
+    }
+    for(ll len=2;len<=n;len++){
+        for(ll i=1;i+len-1<=n;i++){
+            const ll j = i+len-1;
+            for(ll k=i;k<j;k++){
+                dp[i][j]=std::min(
+                    dp[i][j],
+                    dp[i][k]+dp[k+1][j]-(c[i]==c[j])
+                );
+            }
+        }
+    }
+    std::cout<<dp[1][n]<<"\n";
+}