From d91fc4b93390557f0038385f59e7c0f7f956f8fd Mon Sep 17 00:00:00 2001
From: Amir mohammad <amir.talaee1386@gmail.com>
Date: Sat, 16 May 2026 11:32:59 +0330
Subject: [PATCH]  implement

---
 src/main/java/MainExercises.java | 94 ++++++++++++++++++++++++++++++--
 1 file changed, 88 insertions(+), 6 deletions(-)

diff --git a/src/main/java/MainExercises.java b/src/main/java/MainExercises.java
index 21581ea..08a4e08 100644
--- a/src/main/java/MainExercises.java
+++ b/src/main/java/MainExercises.java
@@ -1,3 +1,5 @@
+import java.util.ArrayList;
+
 public class MainExercises
 {
     /*
@@ -20,8 +22,24 @@ public class MainExercises
  */
     public char[][] generateTriangle(int n) {
 
-        // todo
-        return null;
+        char[][] triangle = new char [n][];
+        for ( int i = 0; i < n; i++)
+        {
+            triangle [i] = new char [i + 1];
+
+            for ( int j = 0; j <= i; j++)
+            {
+                if( i == 0 || j == 0 || i == j || i == n -1)
+                {
+                    triangle [i][j] = '*';
+                }
+                else
+                {
+                    triangle [i][j] = ' ';
+                }
+            }
+        }
+        return triangle;
 
     }
 
@@ -58,10 +76,48 @@ public class MainExercises
            - Number of columns: matrix[0].length (if rectangular)
    */
     public int[] spiralTraversal(int[][] matrix) {
-        // todo
-        return null;
+
+        int rows = matrix.length;
+        int cols = matrix[0].length;
+        int[] finalmatrix = new int[rows * cols];
+        int index = 0;
+
+        int top = 0;
+        int bottom = rows - 1;
+        int left = 0;
+        int right = cols - 1;
+
+        while (top <= bottom && left <= right) {
+            
+            for (int i = left; i <= right; i++) {
+                finalmatrix[index++] = matrix[top][i];
+            }
+            top++;
+
+            for (int i = top; i <= bottom; i++) {
+                finalmatrix[index++] = matrix[i][right];
+            }
+            right--;
+
+            if (top <= bottom) {
+                for (int i = right; i >= left; i--) {
+                    finalmatrix[index++] = matrix[bottom][i];
+                }
+                bottom--;
+            }
+
+            if (left <= right) {
+                for (int i = bottom; i >= top; i--) {
+                    finalmatrix[index++] = matrix[i][left];
+                }
+                left++;
+            }
+        }
+
+        return finalmatrix;
     }
 
+
     /*
         integer partitioning is a combinatorics problem in discreet maths
         the problem is to generate sum numbers which their summation is the input number
@@ -91,10 +147,36 @@ public class MainExercises
     */
 
     public int[][] intPartitions(int n) {
-        // todo
-        return null;
+
+        ArrayList<int[]> result = new ArrayList<>();
+        int[] current = new int[n];
+
+
+        partition(n, n, 0, current, result);
+
+        int[][] output = new int[result.size()][];
+        for (int i = 0; i < result.size(); i++) {
+            output[i] = result.get(i);
+        }
+        return output;
     }
 
+    private void partition(int remain, int max, int index, int[] current, ArrayList<int[]> result) {
+        if (remain == 0) {
+
+            int[] a = new int[index];
+            for (int i = 0; i < index; i++) {
+                a[i] = current[i];
+            }
+            result.add(a);
+            return;
+        }
+
+        for (int next = Math.min(max, remain); next >= 1; next--) {
+            current[index] = next;
+            partition(remain - next, next, index + 1, current, result);
+        }
+    }
 
     public static void main()
     {