Merge branch '7oSkaaa:main' into main

06- June/24- Tallest Billboard/24- Tallest Billboard (Ahmed Hossam).cpp

@@ -0,0 +1,45 @@
+// Author: Ahmed Hossam
+
+class Solution {
+public:
+
+    int n; // Number of rods
+    static constexpr int MAXN = 5000, INF = 1e9; // Constants for array size and infinite value
+    vector < int > rods; // Vector to store the lengths of the rods
+    vector < vector < int > > dp; // Dynamic programming array
+
+    // Function to calculate the maximum score
+    int max_score(int idx, int diff) {
+        // Base case: If all rods have been processed, return 0 if the difference is 0, or -INF otherwise
+        if (idx == n) return (!diff ? 0 : -INF);
+
+        // Reference to the maximum score at current index and difference
+        int& ret = dp[idx][diff + MAXN];
+
+        // If the maximum score has already been calculated, return it 
+        if (~ret) return ret; 
+
+        // Scenario 1: Exclude the current rod
+        ret = max_score(idx + 1, diff); 
+
+        // Scenario 2: Include the current rod as positive difference
+        ret = max(ret, rods[idx] + max_score(idx + 1, diff + rods[idx]));
+
+        // Scenario 3: Include the current rod as negative difference
+        ret = max(ret, max_score(idx + 1, diff - rods[idx]));
+
+        // Return the maximum score
+        return ret;
+    }
+
+    int tallestBillboard(vector<int>& rods) {
+        this -> rods = rods; // Assign the input rods to the member variable
+        this -> n = rods.size(); // Set the number of rods
+
+        // Initialize the dynamic programming array with -1
+        this -> dp = vector < vector < int > > (n, vector < int > (2 * MAXN + 5, -1));
+
+        // Return the maximum score starting from index 0 and with 0 difference
+        return max_score(0, 0);
+    }
+};

06- June/README.md

@@ -45,6 +45,7 @@
 1. **[Minimum Cost to Make Array Equal](#21--minimum-cost-to-make-array-equal)**
 1. **[Best Time to Buy and Sell Stock with Transaction Fee](#22--best-time-to-buy-and-sell-stock-with-transaction-fee)**
 1. **[Longest Arithmetic Subsequence](#23--longest-arithmetic-subsequence)**
+1. **[Tallest Billboard](#24--tallest-billboard)**
 
 <hr>
 <br><br>
@@ -1380,4 +1381,66 @@ public:
     }
 };
 ```
+
+<hr>
+<br><br>
+
+## 24)  [Tallest Billboard](https://leetcode.com/problems/tallest-billboard/)
+
+### Difficulty
+
+![](https://img.shields.io/badge/Hard-red?style=for-the-badge)
+
+### Related Topic
+
+`Array` `Dynamic Programming`
+
+### Code
+
+
+```cpp
+class Solution {
+public:
+
+    int n; // Number of rods
+    static constexpr int MAXN = 5000, INF = 1e9; // Constants for array size and infinite value
+    vector < int > rods; // Vector to store the lengths of the rods
+    vector < vector < int > > dp; // Dynamic programming array
+
+    // Function to calculate the maximum score
+    int max_score(int idx, int diff) {
+        // Base case: If all rods have been processed, return 0 if the difference is 0, or -INF otherwise
+        if (idx == n) return (!diff ? 0 : -INF);
+        
+        // Reference to the maximum score at current index and difference
+        int& ret = dp[idx][diff + MAXN];
+        
+        // If the maximum score has already been calculated, return it 
+        if (~ret) return ret; 
+
+        // Scenario 1: Exclude the current rod
+        ret = max_score(idx + 1, diff); 
+        
+        // Scenario 2: Include the current rod as positive difference
+        ret = max(ret, rods[idx] + max_score(idx + 1, diff + rods[idx]));
+        
+        // Scenario 3: Include the current rod as negative difference
+        ret = max(ret, max_score(idx + 1, diff - rods[idx]));
+
+        // Return the maximum score
+        return ret;
+    }
+
+    int tallestBillboard(vector<int>& rods) {
+        this -> rods = rods; // Assign the input rods to the member variable
+        this -> n = rods.size(); // Set the number of rods
+
+        // Initialize the dynamic programming array with -1
+        this -> dp = vector < vector < int > > (n, vector < int > (2 * MAXN + 5, -1));
+        
+        // Return the maximum score starting from index 0 and with 0 difference
+        return max_score(0, 0);
+    }
+};
+```