Longest Increasing Subsequence

Author: AmanPandey0198

Java/Longest Increasing Subsequence.java

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+/* A Naive Java Program for LIS Implementation */
+class LIS {
+	static int max_ref; // stores the LIS
+
+	/* To make use of recursive calls, this function must
+	return two things: 1) Length of LIS ending with element
+	arr[n-1]. We use max_ending_here for this purpose 2)
+	Overall maximum as the LIS may end with an element
+	before arr[n-1] max_ref is used this purpose.
+	The value of LIS of full array of size n is stored in
+	*max_ref which is our final result */
+	static int _lis(int arr[], int n)
+	{
+		// base case
+		if (n == 1)
+			return 1;
+
+		// 'max_ending_here' is length of LIS ending with
+		// arr[n-1]
+		int res, max_ending_here = 1;
+
+		/* Recursively get all LIS ending with arr[0],
+		arr[1] ... arr[n-2]. If arr[i-1] is smaller
+		than arr[n-1], and max ending with arr[n-1] needs
+		to be updated, then update it */
+		for (int i = 1; i < n; i++) {
+			res = _lis(arr, i);
+			if (arr[i - 1] < arr[n - 1]
+				&& res + 1 > max_ending_here)
+				max_ending_here = res + 1;
+		}
+
+		// Compare max_ending_here with the overall max. And
+		// update the overall max if needed
+		if (max_ref < max_ending_here)
+			max_ref = max_ending_here;
+
+		// Return length of LIS ending with arr[n-1]
+		return max_ending_here;
+	}
+
+	// The wrapper function for _lis()
+	static int lis(int arr[], int n)
+	{
+		// The max variable holds the result
+		max_ref = 1;
+
+		// The function _lis() stores its result in max
+		_lis(arr, n);
+
+		// returns max
+		return max_ref;
+	}
+
+	// driver program to test above functions
+	public static void main(String args[])
+	{
+		int arr[] = { 10, 22, 9, 33, 21, 50, 41, 60 };
+		int n = arr.length;
+		System.out.println("Length of lis is " + lis(arr, n)
+						+ "\n");
+	}
+}