Create Minimal Cost.java

Hacktoberfest contribution

Author: Prakhar-Sinha16

src/main/java/com/thealgorithms/dynamicprogramming/Minimal Cost.java

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+// This is a famoush problem asked in interview rounds.
+// It was Asked to me also
+
+Ques: 
+There is an array arr of heights of stone and Geek is standing at the first stone and can jump to one of the following: Stone i+1, i+2, ... i+k stone, where k is the maximum number of steps that can be jumped and cost will be |hi-hj| is incurred, where j is the stone to land on. Find the minimum possible total cost incurred before the Geek reaches the last stone.
+
+Example:
+
+Input: k = 3, arr[]= [10, 30, 40, 50, 20]
+Output: 30
+Explanation: Geek will follow the path 1->2->5, the total cost would be | 10-30| + |30-20| = 30, which is minimum
+Input: k = 1, arr[]= [10, 20, 10]
+Output: 20
+Explanation: Geek will follow the path 1->2->3, the total cost would be |10 - 20| + |20 - 10| = 20.
+Expected Time Complexity: O(n*k)
+Expected Auxilary Space: O(n)
+
+Constraint:
+1<= arr.size() <=104
+1 <= k <= 100
+1 <= arr[i] <= 104
+
+//I have written this solution acc to given contraintand tried to make it as short as possible for easy to understand
+CODE:
+public int minimizeCost(int k, int arr[]) {
+        // code here
+        int[] dp = new int[arr.length];
+        Arrays.fill(dp,Integer.MAX_VALUE);
+        dp[0] = 0;
+        
+        for(int i=0; i<arr.length; i++) {
+            for(int j=1;j<=k && i+j<arr.length; j++) {
+                
+                dp[i+j] = Math.min(dp[i+j], dp[i] + Math.abs(arr[i]-arr[i+j]));
+            }
+        }
+        
+        return dp[arr.length-1];
+    }