Building Bridges

Explore how to solve the problem of building the maximum number of non-overlapping bridges between two cities by applying dynamic programming techniques. Understand the naive recursive approach, then learn optimized top-down and bottom-up DP methods to efficiently compute the longest increasing subsequence for bridge coordination, improving time complexity and scalability in complex scenarios.

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Statement

Two cities are to be connected via $n$ number of bridges over a river. The north bank of the river belongs to city $A$ , while the south bank to city $B$ . Considering this scenario, suppose we have two arrays, north and south, consisting of positive integers.

Note: north represents the coordinates of bridges on the northern bank of the river, whereas south represents the coordinates of bridges on the southern bank.

What is the maximum number of bridges if the ${i^{th}}$ point of city $A$ is connected to the ${i^{th}}$ point of city $B$ , keeping in view that no two bridges overlap each other? While building bridges, you can only connect the $A[i^{th}]$ bridge on the north bank with the $B[i^{th}]$ point on the south bank.

For example, we have two arrays:

$north = [6, 4, 2, 1]$
$s o u t h = [2$ ...

1.Getting Started

2.0/1 Knapsack

3.Unbounded Knapsack

4.Recursive Numbers

5.Longest Common Substring

6.Palindromic Subsequence

7.Conclusion

Building Bridges

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