LCS_dp.cpp

#include <iostream>
using namespace std;
 
/* 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
*/
int _lis(int arr[], int n, int* max_ref)
{
    /* 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, max_ref);
        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()
int lis(int arr[], int n)
{
    // The max variable holds the result
    int max = 1;
 
    // The function _lis() stores its result in max
    _lis(arr, n, &max);
 
    // returns max
    return max;
}
 
/* Driver program to test above function */
int main()
{
    int arr[] = { 10, 22, 9, 33, 21, 50, 41, 60 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout <<"Length of lis is "<< lis(arr, n);
    return 0;
}