
    Design a ride-matching algorithm for a dynamic ride-sharing platform that maximizes total revenue by selecting a sequence of passenger pickups up to the current time period while ensuring a specific future VIP booking is accommodated. The algorithm must maintain chronological order of pickups (earlier selected rides must have lower revenue values than later ones) to ensure operational feasibility. Given a list of ride requests where each value represents potential revenue, find the optimal combination of rides that gives maximum revenue while adhering to the sequential constraint and mandatory inclusion of the future VIP booking. The sequence must be strictly increasing to prevent driver schedule conflicts, and the solution must consider all possible combinations up to the current dispatch window while guaranteeing the inclusion of the pre-booked VIP ride.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a ride-matching algorithm for a dynamic ride-sharing platform that maximizes total revenue by selecting a sequence of passenger pickups up to the current time period while ensuring a specific future VIP booking is accommodated. The algorithm must maintain chronological order of pickups (earlier selected rides must have lower revenue values than later ones) to ensure operational feasibility. Given a list of ride requests where each value represents potential revenue, find the optimal combination of rides that gives maximum revenue while adhering to the sequential constraint and mandatory inclusion of the future VIP booking. The sequence must be strictly increasing to prevent driver schedule conflicts, and the solution must consider all possible combinations up to the current dispatch window while guaranteeing the inclusion of the pre-booked VIP ride.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a ride-matching algorithm for a dynamic ride-sharing platform that maximizes total revenue by selecting a sequence of passenger pickups up to the current time period while ensuring a specific future VIP booking is accommodated. The algorithm must maintain chronological order of pickups (earlier selected rides must have lower revenue values than later ones) to ensure operational feasibility. Given a list of ride requests where each value represents potential revenue, find the optimal combination of rides that gives maximum revenue while adhering to the sequential constraint and mandatory inclusion of the future VIP booking. The sequence must be strictly increasing to prevent driver schedule conflicts, and the solution must consider all possible combinations up to the current dispatch window while guaranteeing the inclusion of the pre-booked VIP ride.
    

    """
    dp = [[0 for i in range(n)] for i in range(n)]
    for i in range(n):
        if a[i] > a[0]:
            dp[0][i] = a[i] + a[0]
        else:
            dp[0][i] = a[i]
    for i in range(1, n):
        for j in range(n):
            if a[j] > a[i] and j > i:
                if dp[i - 1][i] + a[j] > dp[i - 1][j]:
                    dp[i][j] = dp[i - 1][i] + a[j]
                else:
                    dp[i][j] = dp[i - 1][j]
            else:
                dp[i][j] = dp[i - 1][j]
    return dp[index][k]