Create weekly-contest-468-q2-maximum-total-subarray-value-i.java

Author: sanajitjana

Medium/weekly-contest-468-q2-maximum-total-subarray-value-i.java

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+/**
+ * Q2. Maximize Subarray Sum (Custom Variation)
+ * Medium - ? pt
+ *
+ * You are given an integer array nums of length n and an integer k.
+ * You must select exactly k distinct non-empty subarrays nums[l..r] of nums. 
+ * Subarrays may overlap, but the exact same subarray (same l and r) cannot be chosen more than once.
+ *
+ * The value of a subarray nums[l..r] is defined as:
+ *   max(nums[l..r]) - min(nums[l..r])
+ *
+ * The total value is the sum of the values of the selected subarrays.
+ *
+ * Return the maximum total value you can achieve.
+ *
+ * Example 1:
+ * Input: nums = [1,2,3], k = 2
+ * Output: 4
+ * Explanation: Choose [1,2] with value (2-1)=1 and [2,3] with value (3-2)=1, 
+ * but better is to pick [1,2,3] with value (3-1)=2 and then repeat logic to maximize → total = 4.
+ *
+ * ------------------------------------------------------------------
+ * Approach:
+ * - To maximize the total, the best difference comes from (global max - global min).
+ * - Since you must pick k subarrays, the optimal total is simply (max - min) * k.
+ * - This avoids the need to explicitly construct subarrays.
+ *
+ * ------------------------------------------------------------------
+ * Time Complexity: O(n)  
+ * (Single scan to compute max and min of nums)
+ *
+ * Space Complexity: O(1)  
+ * (Only a few variables used)
+ *
+ * ------------------------------------------------------------------
+ * LeetCode link: https://leetcode.com/problems/maximize-subarray-sum/
+ */
+
+class Solution {
+    public long maxTotalValue(int[] nums, int k) {
+        int max = 0, min = Integer.MAX_VALUE;
+        for (int num : nums) {
+            max = Math.max(max, num);
+            min = Math.min(min, num);
+        }
+        return (long)(max - min) * k;
+    }
+}