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Add the answer of Exercise 1.5.3 #18

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3b94b15
first commit
dilika Apr 11, 2025
c0ce89c
Finish Reading section 1.5, Exercices in progress...
dilika Apr 14, 2025
15868e0
exercice1.5.2 ok
dilika May 16, 2025
4826605
exercice1.5.3 ok
dilika May 24, 2025
a6f4260
exercice1.5.3 ok
dilika May 24, 2025
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5 changes: 4 additions & 1 deletion 1-Fundamentals/1-5-UnionFind/UF.java
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****************************************************************************/


import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

/**
* The <tt>UF</tt> class represents a union-find data data structure.
* The <tt>UF</tt> class represents a union-find data structure.
* It supports the <em>union</em> and <em>find</em>
* operations, along with a method for determining the number of
* disjoint sets.
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3 changes: 3 additions & 0 deletions 1-Fundamentals/1-5-UnionFind/WeightedQuickUnionUF.java
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import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

/****************************************************************************
* Compilation: javac WeightedQuickUnionUF.java
* Execution: java WeightedQuickUnionUF < input.txt
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76 changes: 76 additions & 0 deletions 1-Fundamentals/1-5-UnionFind/exercices/Ex_1_5_1.java
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import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;



/*
*Exercie:
* 1.5.1 Show the contents of the id[] array and the number of times the array
* is accessed for each input pair when you use quick-find for the sequence
@input = 9-0 3-4 5-8 7-2 2-1 5-7 0-3 4-2.
* */

public class Ex_1_5_1 {
private int id[];
private int count;

public Ex_1_5_1(int N) {
id = new int[N];
for (int i = 0; i < N; i++) {
id[i] = i;
}
}

public static void main(String[] args) {
int N = StdIn.readInt();
Ex_1_5_1 ex = new Ex_1_5_1(N);

while (!StdIn.isEmpty()) {
int pid = StdIn.readInt();
int qid = StdIn.readInt();
if (ex.connected(pid, qid)) return;
ex.union(pid, qid);
StdOut.println(pid + " " + qid);
}
StdOut.println("# components: " + ex.count());
}

public boolean connected(int p, int q) {
return find(p) == find(q);
}

public int find(int p) {
return id[p];
}

public void union(int p, int q) {
int pid = find(p);
int qid = find(q);
if (pid == qid) return;

for (int i = 0; i < id.length; i++)
if (id[i] == pid) id[i] = qid;
count--;
}

public int count() {
return count;
}
}

// Solution
/*
------------------------------------------------------------------
| Operation | id\[] after operation | Array Accesses |
| --------- | ------------------------------- | -------------- |
| 9-0 | [0, 1, 2, 3, 4, 5, 6, 7, 8, 0] | 13 |
| 3-4 | [0, 1, 2, 4, 4, 5, 6, 7, 8, 0] | 13 |
| 5-8 | [0, 1, 2, 4, 4, 8, 6, 7, 8, 0] | 13 |
| 7-2 | [0, 1, 2, 4, 4, 8, 6, 2, 8, 0] | 13 |
| 2-1 | [0, 1, 1, 4, 4, 8, 6, 1, 8, 0] | 14 |
| 5-7 | [0, 1, 1, 4, 4, 1, 6, 1, 1, 0] | 14 |
| 0-3 | [4, 1, 1, 4, 4, 1, 6, 1, 1, 4] | 14 |
| 4-2 | [1, 1, 1, 1, 1, 1, 6, 1, 1, 1] | 16 |
------------------------------------------------------------------
*
* */
101 changes: 101 additions & 0 deletions 1-Fundamentals/1-5-UnionFind/exercices/Ex_1_5_2.java
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import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;



/*
1.5.2 Do Exercise 1.5.1, but use quick-union (page 224). In addition, draw the forest of
trees represented by the id[] array after each input pair is processed.
* */

public class Ex_1_5_2 {
private int id[];
private int count;

public Ex_1_5_2(int N) {
id = new int[N];
for (int i = 0; i < N; i++) {
id[i] = i;
}
}

public boolean connected(int p, int q) {
return find(p) == find(q);
}

public int find(int p) {
while (p != id[p]) p = id[p];
return p;
}

public void union(int p, int q) {
int i = find(p);
int j = find(q);
if (i == j) return;

id[i] = j;
count--;
}

public int count() {
return count;
}

public static void main(String[] args) {
int N = StdIn.readInt();
Ex_1_5_2 ex = new Ex_1_5_2(N);

while (!StdIn.isEmpty()) {
int pid = StdIn.readInt();
int qid = StdIn.readInt();
if (ex.connected(pid, qid)) return;
ex.union(pid, qid);
StdOut.println(pid + " " + qid);
}
StdOut.println("# components: " + ex.count());
}
}

/*
* EX1.5.2: Solution
* ------------------------------------------------------------------
* | Operation | id\[] after operation | Array Accesses |
* | --------- | ------------------------------- | -------------- |
* | 9-0 | [0, 1, 2, 3, 4, 5, 6, 7, 8, 0] | 2r+1w=3 | 1) 0 1 2 3 4 5 6 7 8
* | 3-4 | [9, 1, 2, 4, 4, 5, 6, 7, 8, 0] | 2r+1w=3 | |
* | 5-8 | [0, 1, 2, 4, 4, 8, 6, 7, 8, 0] | 2r+1w=3 | 9
* | 7-2 | [0, 1, 2, 4, 4, 8, 6, 2, 8, 0] | 2r+1w=3 | 2) 0 1 2 4 5 6 7 8
* | 2-1 | [0, 1, 1, 4, 4, 8, 6, 2, 8, 0] | 2r+1w=3 | | |
* | 5-7 | [0, 1, 1, 4, 4, 8, 6, 2, 1, 0] | 6r+4w=10 | 9 3
* | 0-3 | [4, 1, 1, 4, 4, 1, 6, 1, 1, 4] | 3r+2w=5 | 3) 0 1 2 4 6 7 8
* | 4-2 | [1, 1, 1, 1, 1, 1, 6, 1, 1, 1] | 3r+2w=5 | | | |
* ------------------------------------------------------------------ 9 3 5
* 4) 0 1 2 4 6 8
* | | | |
* 9 7 3 5
* 5) 0 1 4 6
| | |
9 2 3
* / \
* 8 7
* |
* 5
* 7) 4 1 6
* / \ |
* 0 3 2
* | / \
* 9 8 7
* |
* 5
*
* 4 -------1 6
* / \ \
* 0 3 2
* | / \
* 9 8 7
* |
* 5
*
*
*
* */
77 changes: 77 additions & 0 deletions 1-Fundamentals/1-5-UnionFind/exercices/Ex_1_5_3.java
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import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;
/*
Do Exercise 1.5.1, but use weighted quick-union (page 228).
* */

public class Ex_1_5_3 {
private int id[];
private int sz[];
private int count;

public Ex_1_5_3(int N) {
id = new int[N];
sz = new int[N];
for (int i = 0; i < N; i++) {
id[i] = i;
sz[i] = 1;
}
}

public boolean connected(int p, int q) {
return find(p) == find(q);
}

public int find(int p) {
while (p != id[p]) p = id[p];
return p;
}

public void union(int p, int q) {
int i = find(p);
int j = find(q);
if (i == j) return;

if(sz[i] < sz[j]) {id[i] = j; sz[j] += sz[i]}
else {id[j] = i; sz[i] += sz[j]}
count--;
}

public int count() {
return count;
}

public static void main(String[] args) {
int N = StdIn.readInt();
Ex_1_5_3 ex = new Ex_1_5_3(N);

while (!StdIn.isEmpty()) {
int pid = StdIn.readInt();
int qid = StdIn.readInt();
if (ex.connected(pid, qid)) return;
ex.union(pid, qid);
StdOut.println(pid + " " + qid);
}
StdOut.println("# components: " + ex.count());
}
}
/*
* EX1.5.3: Solution
* --------------------------------------------------------------------------------------------
* | Operation | id\[] after operation | Array Accesses | Size Accesses |
* | --------- | ------------------------------- | -------------- | ------------------------|
* | 9-0 | [9, 1, 2, 3, 4, 5, 6, 7, 8, 9] | 2r+1w=3 | 3r+1w=4 sz[9] = 2 |
* | 3-4 | [9, 1, 2, 3, 3, 5, 6, 7, 8, 9] | 2r+1w=3 | 3r+1w=4 sz[3] = 2 |
* | 5-8 | [9, 1, 2, 3, 3, 5, 6, 7, 5, 9] | 2r+1w=3 | 3r+1w=4 sz[9] = 2 |
* | 7-2 | [9, 1, 7, 3, 3, 5, 6, 7, 5, 9] | 2r+1w=3 | 3r+1w=4 sz[7] = 2 |
* | 2-1 | [9, 7, 7, 3, 3, 5, 6, 7, 5, 9] | 4r+1w=5 | 3r+1w=4 sz[7] = 3 |
* | 5-7 | [9, 7, 7, 3, 3, 7, 6, 7, 5, 9] | 2r+1w=3 | 3r+1w=4 sz[7] = 4 |
* | 0-3 | [9, 7, 7, 9, 3, 7, 6, 7, 5, 9] | 3r+1w=4 | 3r+1w=4 sz[9] = 4 |
* | 4-2 | [9, 7, 7, 9, 3, 7, 6, 7, 5, 7] | 8r+2w=5 | 3r+1w=4 sz[9] = 8 |
* --------------------------------------------------------------------------------------------
*
*
* my solution
* [9, 7, 7, 9, 3, 7, 6, 7, 5, 7]
*
* */
3 changes: 3 additions & 0 deletions 2-Sorting/2-1-ElementarySorts/Insertion.java
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*
*************************************************************************/

import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

import java.util.Comparator;

public class Insertion {
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