DP-Algo

Algorithm/DP-DynamicProgramming/Linear-DP/Interval-DP/UVa10003CuttingSticks.cpp

@@ -0,0 +1,38 @@
+#include <iostream>
+#include <vector>
+using namespace std;
+int main(){
+	int len, n;
+	cin >> len >> n;
+	vector<int> a(n + 2);
+	vector<vector<int>> dp(n + 2, vector<int>(n + 2, 0));
+	//<2F><><EFBFBD><EFBFBD>dp[i][j]Ϊ<>и<EFBFBD>ľ<EFBFBD><C4BE>[i, j]<5D><> 0|---1|-----2|----3|--4| <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ķ<EFBFBD><C4B7><EFBFBD> a[0] = 0 a[1] = x,,, a[n + 1] = len
+	a[0] = 0; a[n + 1] = len;
+	for(int i = 1; i <= n; i++){
+		cin >> a[i];
+	}
+	//a[i]<5D>Ƿֵ<C7B7>
+	/*<2A><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 
+	for(int i = 0; i <= n + 1; i++){
+		for(int j = i; j <= n + 1 ;j++){
+			dp[i][j] = 114514;
+			for(int k = i + 1; k < j; k++){
+				dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]);
+			}
+			if(dp[i][j] == 114514) dp[i][j] = 0;
+		}
+	} */
+	// <20><><EFBFBD><EFBFBD> DP<44><50><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ȵ<EFBFBD><C8B5><EFBFBD>
+    for(int l = 2; l <= n + 1; l++){ // <20><><EFBFBD>䳤<EFBFBD><E4B3A4><EFBFBD><EFBFBD><EFBFBD><EFBFBD>2
+        for(int i = 0; i + l <= n + 1; i++){
+            int j = i + l;
+            dp[i][j] = INT_MAX;
+            for(int k = i + 1; k < j; k++){
+                dp[i][j] = min(dp[i][j], dp[i][k] + dp[k][j] + a[j] - a[i]);
+            }
+            if(dp[i][j] == INT_MAX) dp[i][j] = 0;
+        }
+    }
+	cout << dp[0][n + 1] << endl;
+	return 0;
+}

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;
+}
+

Algorithm/DP-DynamicProgramming/Linear-DP/Interval-DP/UVa1626括号序列.cpp

@@ -0,0 +1,31 @@
+#include <iostream>
+#include <string>
+#include <vector>
+using namespace std;
+const int INF = 1e9;
+bool match(char a, char b){
+	return (a == '(' && b == ')') || (a == '[' && b == ']');
+}
+int main(){
+    string s;
+    cin >> s;
+    int n = s.size();
+    vector<vector<int>> dp(s.size() + 2, vector<int>(s.size() + 2, 1));
+    for(int l = 2; l <= n; l++){
+    	for(int i = 0; i < n - l + 1; i++){
+    		int j = i + l - 1;
+    		dp[i][j] = INF; 
+    		for(int k = i; k < j; k++){
+    			dp[i][j] = min(dp[i][j], dp[i][k] + dp[k + 1][j]);
+			}
+			if(match(s[i], s[j])) {
+				if (i + 1 <= j - 1)
+                    dp[i][j] = min(dp[i][j], dp[i+1][j-1]);
+                else
+                    dp[i][j] = 0; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD><EFBFBD><EFBFBD>ֱ<EFBFBD><D6B1>ƥ<EFBFBD><C6A5>
+            }
+		}
+	}
+	cout << dp[0][n - 1] << endl;
+    return 0;
+}