feat: 添加P3146题目的动态规划解法实现

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/P1775.cpp

@@ -0,0 +1,39 @@
+#include <algorithm>
+#include <cstdint>
+#include <iostream>
+
+using ll = int64_t;
+
+const ll maxn = 300 + 5, inf = 1e18;
+
+ll m[maxn], s[maxn];
+ll n, dp[maxn][maxn];
+
+int main() {
+    std::ios::sync_with_stdio(false);
+    std::cin.tie(nullptr);
+
+    std::cin >> n;
+    for (ll i = 1; i <= n; ++i) {
+        std::cin >> m[i];
+        s[i] = s[i - 1] + m[i];
+        dp[i][i] = 0;
+    }
+
+    for (ll i = 1; i <= n; ++i) {
+        for (ll j = i + 1; j <= n; ++j) {
+            dp[i][j] = inf;
+        }
+    }
+
+    for (ll len = 2; len <= n; ++len) {
+        for (ll i = 1; i + len - 1 <= n; ++i) {
+            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] + s[j] - s[i - 1]);
+            }
+        }
+    }
+
+    std::cout << dp[1][n] << "\n";
+}

src/10/1/P3146.cpp

@@ -0,0 +1,34 @@
+#include <algorithm>
+#include <iostream>
+#include <istream>
+
+using namespace std;
+
+const int MAXN = 250;
+int n;
+int a[MAXN];
+int dp[MAXN][MAXN];
+
+int main() {
+    iostream::sync_with_stdio(false);
+    cin.tie(nullptr);
+    cin >> n;
+    for (int i = 1; i <= n; i++) {
+        cin >> a[i];
+        dp[i][i] = a[i];
+    }
+    int ans = 0;
+    for (int len = 2; len <= n; len++) {
+        for (int i = 1; i + len - 1 <= n; i++) {
+            int j = i + len - 1;
+            for (int k = i; k < j; k++) {
+                if (dp[i][k] != 0 && dp[k + 1][j] != 0 && dp[i][k] == dp[k + 1][j]) {
+                    dp[i][j] = max(dp[i][j], dp[i][k] + 1);
+                }
+            }
+            ans = max(ans, dp[i][j]);
+        }
+    }
+
+    cout << ans << endl;
+}

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";
+}

src/8/30/P1063.cpp

@@ -1,6 +1,6 @@
 /*
 
-dp[i][j]=将[1,j]合并为一堆时的最大总能量
+dp[i][j]=将[i,j]合并为一堆时的最大总能量
 dp[i][j]=max(
     dp[i][j],
     dp[i][k]+dp[k+1][j]+i.m*k.n*j.n