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/* how many time are the if conditions executed? */ public static void fw (int[] [] G) { int n G.length; // G is a square array for(int i=0; i G[j] [i] + G[i] [k]) { G[j] [k] = G[j] [i] + G[i] [k]; } /* how would you describe the runtime of the above code? */

/* how many time are the if conditions executed? */ public static void fw (int[] [] G) { int n G.length; // G is a square array for(int i=0; i G[j] [i] + G[i] [k]) { G[j] [k] = G[j] [i] + G[i] [k]; } /* how would you describe the runtime of the above code? */

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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I need help finding out the run time of the following algorithm (warshalls)  And the number of times that the if conditions would execute.

```java /* how many time are the if conditions executed? */ public static void fw(int[][] G) { int n = G.length; // G is a square array for (int i=0; i<G.length; i++ ) { for (int j=0; j<n; j++ ) { if( i==j ) { continue; } else { G[i][j] = (int) (Math.random()*n); } } } for (int i=0; i<n; i++ ) { for (int j=0; j<n; j++ ) { for (int k=0; k<n; k++ ) { if( G[j][k] > G[j][i] + G[i][k] ) { G[j][k] = G[j][i] + G[i][k]; } } } } } /* how would you describe the runtime of the above code? */ ``` ### Explanation: This code defines a method `fw` that operates on a square 2D integer array `G`. 1. **First Nested Loops:** - The first set of nested loops iterates through all elements of the array `G` except for diagonal elements (where `i == j`). - If `i != j`, it assigns a random integer to `G[i][j]`. 2. **Second Nested Loops:** - The second set of nested loops performs an operation similar to the Floyd-Warshall algorithm for finding shortest paths between all pairs of nodes in a weighted graph. - It checks if the direct path from `j` to `k` is more than the path going through `i` (`G[j][i] + G[i][k]`). If so, it updates `G[j][k]` to be the smaller path sum. ### Runtime: The runtime complexity for this code is O(n³), where `n` is the length of one side of the square array `G`. This is because of the three nested loops iterating over `n` elements. The questions raised are: - How many times are the if conditions executed? - How would you describe the runtime of the provided code?
Transcribed Image Text:```java /* how many time are the if conditions executed? */ public static void fw(int[][] G) { int n = G.length; // G is a square array for (int i=0; i<G.length; i++ ) { for (int j=0; j<n; j++ ) { if( i==j ) { continue; } else { G[i][j] = (int) (Math.random()*n); } } } for (int i=0; i<n; i++ ) { for (int j=0; j<n; j++ ) { for (int k=0; k<n; k++ ) { if( G[j][k] > G[j][i] + G[i][k] ) { G[j][k] = G[j][i] + G[i][k]; } } } } } /* how would you describe the runtime of the above code? */ ``` ### Explanation: This code defines a method `fw` that operates on a square 2D integer array `G`. 1. **First Nested Loops:** - The first set of nested loops iterates through all elements of the array `G` except for diagonal elements (where `i == j`). - If `i != j`, it assigns a random integer to `G[i][j]`. 2. **Second Nested Loops:** - The second set of nested loops performs an operation similar to the Floyd-Warshall algorithm for finding shortest paths between all pairs of nodes in a weighted graph. - It checks if the direct path from `j` to `k` is more than the path going through `i` (`G[j][i] + G[i][k]`). If so, it updates `G[j][k]` to be the smaller path sum. ### Runtime: The runtime complexity for this code is O(n³), where `n` is the length of one side of the square array `G`. This is because of the three nested loops iterating over `n` elements. The questions raised are: - How many times are the if conditions executed? - How would you describe the runtime of the provided code?
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