feat:Added Implementation of Split_Largest_Array_Sum Algorithm

Author: ARYPROGRAMMER

dynamic_programming/split_array_largest_sum.cpp

@@ -0,0 +1,131 @@
+/**
+ * @file
+ * @brief Given an integer array nums and an integer k, split nums into k
+ * non-empty subarrays such that the largest sum of any subarray is minimized.
+ * Return the minimized largest sum of the split.
+
+ * @details
+ * Example 1:
+
+    * Input: nums = [7,2,5,10,8], k = 2
+    * Output: 18
+    * Explanation: There are four ways to split nums into two subarrays.
+    * The best way is to split it into [7,2,5] and [10,8], where the largest sum
+    * among the two subarrays is only 18.
+  
+ * Example 2:
+
+    * Input: nums = [1,2,3,4,5], k = 2
+    * Output: 9
+    * Explanation: There are four ways to split nums into two subarrays.
+    * The best way is to split it into [1,2,3] and [4,5], where the largest sum
+    * among the two subarrays is only 9.
+
+ * @author [ARYA PRATAP SINGH](https://github.com/ARYPROGRAMMER)
+ * [Leetcode](https://leetcode.com/problems/split-array-largest-sum/description/?envType=problem-list-v2&envId=dynamic-programming)
+ */
+
+// header files
+#include <iostream>
+#include <iomanip>
+#include <cstdint>
+
+/**
+ * @namespace dynamic_programming
+ * @brief Dynamic Programming algorithms
+ */
+namespace dynamic_programming{
+    /**
+     * @namespace split_array_largest_sum
+     * @brief split_array_largest_sum algorithm
+     */
+    namespace split_array_largest_sum{
+
+        /**
+         * @brief This function calculates the minimum largest sum of the split
+         * @param nums integer array
+         * @param k integer
+         * @
+         */
+
+        int dp[1003][53];
+
+        int f(int i, int j, vector<int>& v) {
+            if (j < 0) {
+                if (i < 0)
+                    return -1;
+                return INT_MAX;
+            }
+            if (i < 0)
+                return INT_MAX;
+            if (dp[i][j] != -1)
+                return dp[i][j];
+
+            int res = INT_MAX, sum = 0;
+            for (int k = i; k >= 0; k--) {
+                sum += v[k];
+                res = min(res, max(sum, f(k - 1, j - 1, v)));
+            }
+
+            return dp[i][j] = res;
+            }
+
+        int splitArray(vector<int>& nums, int k) {
+            memset(dp, -1, sizeof(dp));
+            return f(nums.size() - 1, k - 1, nums);
+        }
+    }
+}
+
+/**
+ * Test Function
+ * @return void
+ */
+static void test() {
+    // custom input vector
+    std::vector<int> v{
+        7,2,5,10,8,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15
+    };
+    // custom value of k
+    int k = 5;
+   
+    //calling the function
+    int ans = dynamic_programming::split_array_largest_sum::splitArray(v, k);
+
+    // expected output
+    int expectedOutput = 30;
+    
+    // Testing implementation via assert function
+    // It will throw error if any of the expected test fails
+    // Else it will give nothing
+    assert(ans == expectedOutput);
+
+    std::cout << "All tests passed successfully!\n";
+    return;
+}
+
+/** Main function (driver code)*/
+int main() {
+    // test for implementation
+    test();
+
+    // user input
+    int n;
+    std::cout << "Enter the number of elements in the array : ";
+    std::cin >> n;
+    std::vector<int> v(n);
+    std::cout << "Enter the elements of the array : ";
+    for (int i = 0; i < n; i++) {
+        std::cin >> v[i];
+    }
+    int k;
+    std::cout << "Enter the value of k : ";
+    std::cin >> k;
+
+    int ans;
+
+    // user output
+    ans = dynamic_programming::split_array_largest_sum::splitArray(v, k);
+    std::cout << "The minimum largest sum of the split is : " << ans << std::endl;
+    return 0;
+}