710261. Minimize connections
Medium
Minimize connections
Summary
The problem is to minimize the number of connections needed between a set of houses and a school. The houses are located at different points on a line, and each house can be connected to the school in multiple ways. We need to find the minimum number of connections required such that every house is connected to the school.
Detailed Explanation
The problem can be solved using dynamic programming. Let's break down the solution step by step:
- First, we initialize a 2D array
dpof size(n+1) x (n+1)wherenis the number of houses. The celldp[i][j]will store the minimum number of connections required to connect houseito the school using the firstjpoints. - We iterate over all houses and for each house, we calculate the minimum number of connections required to connect it to the school. This is done by considering all possible connections from the current house to the school and choosing the one that results in the minimum number of connections.
- Finally, we return the value stored in
dp[n][n], which represents the minimum number of connections required to connect all houses to the school.
Here's an ASCII art diagram illustrating the concept:
+---------------+
| House 1 |
+---------------+
|
|
v
+---------------+
| School |
+---------------+
+---------------+
| House 2 |
+---------------+
|
|
v
+---------------+
| School |
+---------------+
...
Time complexity: O(n^2) Space complexity: O(n^2)
Optimized Solutions
Java
public int minimizeConnections(int[] houses, int n) {
int[][] dp = new int[n+1][n+1];
for (int i = 0; i <= n; i++) {
dp[i][i] = 1;
}
for (int i = 1; i <= n; i++) {
for (int j = 0; j < i; j++) {
dp[i][j] = Math.min(dp[i-1][j], dp[i-1][j+1]) + 1;
}
}
return dp[n][0];
}