Minimum Cost to Connect Two Groups of Points

arraydynamic programmingbit manipulation

Problem Statement

You are given two groups of points where the first group has size _1 points, the second group has size _2 points, and size _1 >= size _2 .

The cost of the connection between any two points are given in an size _1 x size _2 matrix where cost[i][j] is the cost of connecting point i of the first group and point j of the second group. The groups are connected if each point in both groups is connected to one or more points in the opposite group . In other words, each point in the first group must be connected to at least one point in the second group, and each point in the second group must be connected to at least one point in the first group.

Return the minimum cost it takes to connect the two groups .

Examples

Example 1

Input: cost = [[15, 96], [36, 2]]
Output: 17
 Explanation : The optimal way of connecting the groups is:
1--A
2--B
This results in a total cost of 17.

Example 2

Input: cost = [[1, 3, 5], [4, 1, 1], [1, 5, 3]]
Output: 4
 Explanation : The optimal way of connecting the groups is:
1--A
2--B
2--C
3--A
This results in a total cost of 4.
Note that there are multiple points connected to point 2 in the first group and point A in the second group. This does not matter as there is no limit to the number of points that can be connected. We only care about the minimum total cost.

Example 3

Input: cost = [[2, 5, 1], [3, 4, 7], [8, 1, 2], [6, 2, 4], [3, 8, 8]]
Output: 10

Constraints

size _1 == cost.length

size _2 == cost[i].length

1 <= size _1 , size _2 <= 12

size _1 >= size _2

0 <= cost[i][j] <= 100

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming