sparse metrix

Author: JitinSaxenaa

CPP/algorithms/mathematical/sparse_matrix.cpp

@@ -0,0 +1,129 @@
+#include <bits/stdc++.h>
+using namespace std;
+
+// 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 SparseMatrix {
+private:
+    int rows, cols, nonZeroCount;
+    vector<Element> elements;
+
+public:
+    SparseMatrix(int r, int c) {
+        rows = r;
+        cols = c;
+        nonZeroCount = 0;
+    }
+
+    // Add a non-zero element
+    void addElement(int r, int c, int val) {
+        if(val != 0) {
+            elements.push_back({r, c, val});
+            nonZeroCount++;
+        }
+    }
+
+    // Print sparse matrix
+    void print() {
+        vector<vector<int>> full(rows, vector<int>(cols, 0));
+        for(auto &e : elements) {
+            full[e.row][e.col] = e.value;
+        }
+        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) {
+            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()) {
+            int pos1 = elements[i].row * cols + elements[i].col;
+            int pos2 = other.elements[j].row * cols + other.elements[j].col;
+            if(pos1 < pos2) {
+                result.addElement(elements[i].row, elements[i].col, elements[i].value);
+                i++;
+            } 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);
+                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++;
+        return result;
+    }
+
+    // Subtraction of two sparse matrices
+    SparseMatrix subtract(SparseMatrix &other) {
+        SparseMatrix negOther = other;
+        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.");
+        }
+        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++) {
+                int sum = 0;
+                for(int k = 0; k < cols; k++) {
+                    sum += full1[i][k] * full2[k][j];
+                }
+                if(sum != 0) result.addElement(i,j,sum);
+            }
+        }
+        return result;
+    }
+};
+
+// Example usage
+int main() {
+    SparseMatrix A(3, 3);
+    A.addElement(0, 0, 1);
+    A.addElement(0, 2, 2);
+    A.addElement(1, 1, 3);
+
+    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();
+
+    SparseMatrix C = A.add(B);
+    cout << "\nA + B:\n"; C.print();
+
+    SparseMatrix D = A.subtract(B);
+    cout << "\nA - B:\n"; D.print();
+
+    SparseMatrix E = A.multiply(B);
+    cout << "\nA * B:\n"; E.print();
+
+    return 0;
+}