From 2d4f09c315d7295256ab1e7bca17c80b5dfec5cd Mon Sep 17 00:00:00 2001
From: navid <mahdavinavid299@gmail.com>
Date: Fri, 24 Apr 2026 17:40:32 +0330
Subject: [PATCH] second exersises finished

---
 src/main/java/MainExercises.java | 177 +++++++++++++++++++++++++++++--
 1 file changed, 169 insertions(+), 8 deletions(-)

diff --git a/src/main/java/MainExercises.java b/src/main/java/MainExercises.java
index 21581ea..43e0467 100644
--- a/src/main/java/MainExercises.java
+++ b/src/main/java/MainExercises.java
@@ -1,3 +1,7 @@
+import java.util.ArrayList;
+import java.util.Collections;
+import java.util.stream.IntStream;
+
 public class MainExercises
 {
     /*
@@ -19,9 +23,29 @@ public class MainExercises
     the output has to be a two-dimensional array of characters, so don't just print the triangle!
  */
     public char[][] generateTriangle(int n) {
-
-        // todo
-        return null;
+        char[][] gt = new char[n][];
+        for(int i = 0 ; i<n ; i ++){
+            gt[i] = new char[i+1];
+            if (i == n-1){
+                for ( int k= 0 ; k< n ; k++ ){
+                    gt[i][k] ='*';
+                }
+                break;
+            }
+            for(int j= 0 ; j<= i; j++){
+                if (j == 0 ){
+                    gt[i][j]= '*';
+                }else if (i>=1 ){
+                    if(j == (i)){
+                        gt[i][j]= '*';
+                    }
+                }
+                if(j!= 0 && j <i){
+                    gt[i][j] = ' ';
+                }
+            }
+        }
+        return gt;
 
     }
 
@@ -58,9 +82,72 @@ public class MainExercises
            - Number of columns: matrix[0].length (if rectangular)
    */
     public int[] spiralTraversal(int[][] matrix) {
-        // todo
-        return null;
-    }
+        int n1 = matrix.length;
+        int n2 = matrix[0].length;
+        int[] n3;
+        if (n2 != 1 && n1 != 1) {
+            n3 = new int[(2 * n1) + (2 * n2) - 4];
+        } else if (n1 == 1) {
+            n3 = new int[n2];
+        } else {
+            n3 = new int[n1];
+        }
+            int o = 0;
+            if (n2 == 1) {
+                for (int i = 0; i < n1; i++) {
+                    n3[o] = matrix[i][0];
+                    o += 1;
+                }
+                return (n3);
+            } else if (n1 == 1) {
+                for (int i = 0; i < n2; i++) {
+                    n3[o] = matrix[0][i];
+                    o += 1;
+                }
+                return (n3);
+
+            }
+
+            for (int i = 0; i < n2; i++) {
+                n3[o] = matrix[0][i];
+                o += 1;
+            }
+            for (int j = 1; j < n1; j++) {
+
+                n3[o] = matrix[j][n2 - 1];
+                o += 1;
+            }
+            for (int k = n2 - 2; k >= 0; k--) {
+                n3[o] = matrix[n1 - 1][k];
+                o += 1;
+            }
+            for (int h = n1 - 2; h >= 1; h--) {
+
+                n3[o] = matrix[h][0];
+                o += 1;
+            }
+            if (n1== 2) {
+                return (n3);
+            } else {
+                int x1 = 0;
+                int x2 = 0;
+                int[][] n4 = new int[n1 - 2][n2 - 2];
+                for (int i = 1; i < n1 - 1; i++) {
+                    for (int j = 1; j < n2 - 1; j++) {
+                        n4[x1][x2] = matrix[i][j];
+                        x2 += 1;
+
+                    }
+                    x1 += 1;
+                    x2 = 0;
+                }
+                int[] n5 = spiralTraversal(n4);
+                int[] c = IntStream.concat(IntStream.of(n3), IntStream.of(n5)).toArray();
+                return (c);
+            }
+
+        }
+
 
     /*
         integer partitioning is a combinatorics problem in discreet maths
@@ -91,8 +178,82 @@ public class MainExercises
     */
 
     public int[][] intPartitions(int n) {
-        // todo
-        return null;
+        ArrayList<Integer> a = new ArrayList<>();
+        ArrayList<int[]> a1 = new ArrayList<>();
+        ArrayList<int[]> a2 = new ArrayList<>();
+        ArrayList<int[]> a3 = new ArrayList<>();
+        ArrayList<Integer> a4 = new ArrayList<>();
+        int[][] n1;
+
+        if (n == 1) {
+            n1 = new int[1][1];
+            n1[0][0] = 1;
+            return n1;
+        }
+
+        if (n == 2) {
+            n1 = new int[2][];
+            n1[0] = new int[]{2};
+            n1[1] = new int[]{1, 1};
+            return n1;
+        }
+
+        int[] y = new int[1];
+        y[0] = n;
+        a1.add(y);
+
+        for (int i = n - 1; i >= 1; i--) {
+            int b = n - i;
+            int[][] n22 = intPartitions(b);
+
+            for (int[] n3 : n22) {
+                if (n3[0] <= i) {
+                    a.clear();
+                    a.add(i);
+                    for (int f : n3) {
+                        a.add(f);
+                    }
+                    Collections.sort(a, Collections.reverseOrder());
+
+                    int[] n5 = new int[a.size()];
+                    for (int k = 0; k < a.size(); k++) {
+                        n5[k] = a.get(k);
+                    }
+                    a1.add(n5);
+                }
+            }
+        }
+
+        for (int i = n; i >= 0; i--) {
+            a3.clear();
+            for (int[] j : a1) {
+                if (j[0] == i) {
+                    a3.add(j);
+                }
+            }
+
+            if (a3.size() > 0) {
+                a4.clear();
+                for (int[] k : a3) {
+                    a4.add(k.length);
+                }
+                Collections.sort(a4);
+
+                for (int k = 0; k < a4.size(); k++) {
+                    for (int[] w : a3) {
+                        if (w.length == a4.get(k)) {
+                            a2.add(w);
+                        }
+                    }
+                }
+            }
+        }
+
+        n1 = new int[a2.size()][];
+        for (int i = 0; i < a2.size(); i++) {
+            n1[i] = a2.get(i);
+        }
+        return n1;
     }