Sparse

Author: Pragati Gupta

CPP/algorithms/mathematical/sparse_matrix.cpp

@@ -1,129 +1,182 @@
 #include <bits/stdc++.h>
 using namespace std;
 
+/*
+==========================================
+   Sparse Matrix - Basic Operations
+   Operations: Addition, Subtraction, Multiplication
+   Representation: Triplet (row, col, value)
+==========================================
+*/
+
 // Structure to store a non-zero element of a sparse matrix
 struct Element {
     int row;
     int col;
     int value;
 };
 
-// Class to represent a sparse matrix
+// Class to represent a Sparse Matrix
 class SparseMatrix {
 private:
-    int rows, cols, nonZeroCount;
-    vector<Element> elements;
+    int rows, cols;                  // Matrix dimensions
+    vector<Element> elements;        // Store only non-zero elements
 
 public:
+    // Constructor to initialize the matrix with given rows and columns
     SparseMatrix(int r, int c) {
         rows = r;
         cols = c;
-        nonZeroCount = 0;
     }
 
-    // Add a non-zero element
+    // Add a non-zero element to the sparse matrix
     void addElement(int r, int c, int val) {
-        if(val != 0) {
+        if (val != 0) {
             elements.push_back({r, c, val});
-            nonZeroCount++;
         }
     }
 
-    // Print sparse matrix
-    void print() {
+    // Print the full matrix (converts sparse → dense for display)
+    void print() const {
         vector<vector<int>> full(rows, vector<int>(cols, 0));
-        for(auto &e : elements) {
+        for (const auto &e : elements) {
             full[e.row][e.col] = e.value;
         }
-        for(int i = 0; i < rows; i++) {
-            for(int j = 0; j < cols; j++) {
+        for (int i = 0; i < rows; i++) {
+            for (int j = 0; j < cols; j++) {
                 cout << full[i][j] << " ";
             }
             cout << endl;
         }
     }
 
-    // Addition of two sparse matrices
-    SparseMatrix add(SparseMatrix &other) {
-        if(rows != other.rows || cols != other.cols) {
+    // ------------------------
+    // Matrix Addition
+    // ------------------------
+    SparseMatrix add(const SparseMatrix &other) const {
+        if (rows != other.rows || cols != other.cols) {
             throw invalid_argument("Matrix dimensions must match for addition.");
         }
+
         SparseMatrix result(rows, cols);
         int i = 0, j = 0;
-        while(i < elements.size() && j < other.elements.size()) {
+
+        while (i < elements.size() && j < other.elements.size()) {
             int pos1 = elements[i].row * cols + elements[i].col;
             int pos2 = other.elements[j].row * cols + other.elements[j].col;
-            if(pos1 < pos2) {
+
+            if (pos1 < pos2) {
                 result.addElement(elements[i].row, elements[i].col, elements[i].value);
                 i++;
-            } else if(pos1 > pos2) {
+            } else if (pos1 > pos2) {
                 result.addElement(other.elements[j].row, other.elements[j].col, other.elements[j].value);
                 j++;
             } else {
                 int sum = elements[i].value + other.elements[j].value;
-                result.addElement(elements[i].row, elements[i].col, sum);
+                if (sum != 0) {
+                    result.addElement(elements[i].row, elements[i].col, sum);
+                }
                 i++; j++;
             }
         }
-        while(i < elements.size()) result.addElement(elements[i].row, elements[i].col, elements[i].value), i++;
-        while(j < other.elements.size()) result.addElement(other.elements[j].row, other.elements[j].col, other.elements[j].value), j++;
+
+        while (i < elements.size()) {
+            result.addElement(elements[i].row, elements[i].col, elements[i].value);
+            i++;
+        }
+        while (j < other.elements.size()) {
+            result.addElement(other.elements[j].row, other.elements[j].col, other.elements[j].value);
+            j++;
+        }
+
         return result;
     }
 
-    // Subtraction of two sparse matrices
-    SparseMatrix subtract(SparseMatrix &other) {
+    // ------------------------
+    // Matrix Subtraction
+    // ------------------------
+    SparseMatrix subtract(const SparseMatrix &other) const {
         SparseMatrix negOther = other;
-        for(auto &e : negOther.elements) e.value = -e.value;
+        // Negate all values in the second matrix
+        for (auto &e : negOther.elements) {
+            e.value = -e.value;
+        }
         return add(negOther);
     }
 
-    // Multiplication of two sparse matrices (naive)
-    SparseMatrix multiply(SparseMatrix &other) {
-        if(cols != other.rows) {
-            throw invalid_argument("Matrix dimensions incompatible for multiplication.");
+    // ------------------------
+    // Matrix Multiplication (Naive)
+    // ------------------------
+    SparseMatrix multiply(const SparseMatrix &other) const {
+        if (cols != other.rows) {
+            throw invalid_argument("Matrix dimensions are incompatible for multiplication.");
         }
+
         SparseMatrix result(rows, other.cols);
-        vector<vector<int>> full1(rows, vector<int>(cols,0));
-        vector<vector<int>> full2(other.rows, vector<int>(other.cols,0));
-        for(auto &e : elements) full1[e.row][e.col] = e.value;
-        for(auto &e : other.elements) full2[e.row][e.col] = e.value;
 
-        for(int i = 0; i < rows; i++) {
-            for(int j = 0; j < other.cols; j++) {
+        // Convert both matrices to full form for easier multiplication
+        vector<vector<int>> full1(rows, vector<int>(cols, 0));
+        vector<vector<int>> full2(other.rows, vector<int>(other.cols, 0));
+
+        for (const auto &e : elements)
+            full1[e.row][e.col] = e.value;
+
+        for (const auto &e : other.elements)
+            full2[e.row][e.col] = e.value;
+
+        // Multiply
+        for (int i = 0; i < rows; i++) {
+            for (int j = 0; j < other.cols; j++) {
                 int sum = 0;
-                for(int k = 0; k < cols; k++) {
+                for (int k = 0; k < cols; k++) {
                     sum += full1[i][k] * full2[k][j];
                 }
-                if(sum != 0) result.addElement(i,j,sum);
+                if (sum != 0) {
+                    result.addElement(i, j, sum);
+                }
             }
         }
+
         return result;
     }
 };
 
-// Example usage
+// ------------------------
+// Main Function - Example Usage
+// ------------------------
 int main() {
+    // Define Matrix A
     SparseMatrix A(3, 3);
     A.addElement(0, 0, 1);
     A.addElement(0, 2, 2);
     A.addElement(1, 1, 3);
 
+    // Define Matrix B
     SparseMatrix B(3, 3);
     B.addElement(0, 0, 4);
     B.addElement(0, 2, 5);
     B.addElement(2, 2, 6);
 
-    cout << "Matrix A:\n"; A.print();
-    cout << "\nMatrix B:\n"; B.print();
+    cout << "Matrix A:\n";
+    A.print();
+
+    cout << "\nMatrix B:\n";
+    B.print();
 
+    // Addition
+    cout << "\nA + B:\n";
     SparseMatrix C = A.add(B);
-    cout << "\nA + B:\n"; C.print();
+    C.print();
 
+    // Subtraction
+    cout << "\nA - B:\n";
     SparseMatrix D = A.subtract(B);
-    cout << "\nA - B:\n"; D.print();
+    D.print();
 
+    // Multiplication
+    cout << "\nA * B:\n";
     SparseMatrix E = A.multiply(B);
-    cout << "\nA * B:\n"; E.print();
+    E.print();
 
     return 0;
 }