DP-Algo

Algorithm/DP-DynamicProgramming/Linear-DP/Interval-DP/UVa11584划分回文串.cpp

@@ -0,0 +1,54 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+int main(){
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+    
+    int T;
+    if(!(cin >> T)) return 0;
+    while(T--){
+        string s;
+        cin >> s;
+        int n = s.size();
+        if(n == 0){
+            cout << 0 << "\n";
+            continue;
+        }
+        // isPal[i][j] whether s[i..j] is palindrome
+        vector<vector<char>> isPal(n, vector<char>(n, 0));
+        // center expand to fill isPal (or use DP)
+        for(int center = 0; center < n; ++center){
+            // odd length
+            int l = center, r = center;
+            while(l >= 0 && r < n && s[l] == s[r]){
+                isPal[l][r] = 1;
+                --l; ++r;
+            }
+            // even length
+            l = center; r = center + 1;
+            while(l >= 0 && r < n && s[l] == s[r]){
+                isPal[l][r] = 1;
+                --l; ++r;
+            }
+        }
+        
+        // dp[i] = min cuts for s[0..i]
+        const int INF = 1e9;
+        vector<int> dp(n, INF);
+        for(int i = 0; i < n; ++i){
+            if(isPal[0][i]){
+                dp[i] = 0;
+            } else {
+                for(int j = 0; j < i; ++j){
+                    if(isPal[j+1][i]){
+                        dp[i] = min(dp[i], dp[j] + 1);
+                    }
+                }
+            }
+        }
+        cout << dp[n-1] << "\n";
+    }
+    return 0;
+}
+