Address code review comments:

- add curly bracket
- remove static_cast
- fix format for the matrix
- format output with tabs
- properly sanitize user input
- fix off-by-one error

Author: mika314

contents/gaussian_elimination/code/c++/gaussian_elimination.cpp

@@ -3,6 +3,7 @@
 #include <cmath>
 #include <iostream>
 #include <vector>
+#include <iomanip>
 
 void gaussian_elimination(std::vector<double>& a, int cols) {
   assert(a.size() % cols == 0);
@@ -16,11 +17,12 @@ void gaussian_elimination(std::vector<double>& a, int cols) {
     int max_index = [&]() {
       int res = row;
       int max_element = a[col + row * cols];
-      for (int r = row + 1; r < rows; ++r)
+      for (int r = row + 1; r < rows; ++r) {
         if (max_element < std::abs(a[col + r * cols])) {
           max_element = std::abs(a[col + r * cols]);
           res = r;
         }
+      }
       return res;
     }();
 
@@ -65,7 +67,7 @@ std::vector<double> back_substitution(const std::vector<double>& a, int cols) {
   soln[rows - 1] =
       a[cols - 1 + (rows - 1) * cols] / a[cols - 1 - 1 + (rows - 1) * cols];
 
-  for (int i = rows - 1; i >= 0; --i) {
+  for (int i = rows - 2; i >= 0; --i) {
     auto sum = 0.0;
     for (int j = cols - 2; j > i; --j) {
       sum += soln[j] * a[j + i * cols];
@@ -86,7 +88,7 @@ void gauss_jordan_elimination(std::vector<double>& a, int cols) {
     if (a[col + row * cols] != 0) {
 
       // divide row by pivot and leaving pivot as 1
-      for (int i = cols - 1; i >= static_cast<int>(col); --i)
+      for (int i = cols - 1; i >= col; --i)
         a[i + row * cols] /= a[col + row * cols];
 
       // subtract value from above row and set values above pivot to 0
@@ -104,16 +106,22 @@ void print_matrix(const std::vector<double>& a, int cols) {
   for (int i = 0; i < rows; ++i) {
     std::cout << "[";
     for (int j = 0; j < cols; ++j) {
-      std::cout << a[j + i * cols] << " ";
+      std::cout << std::fixed << a[j + i * cols] << "\t";
     }
     std::cout << "]\n";
   }
 }
 
 int main() {
-  std::vector<double> a = {2, 3, 4, 6, 1, 2, 3, 4, 3, -4, 0, 10};
+  std::vector<double> a = { 2, 3, 4, 6,
+                            1, 2, 3, 4,
+                            3, -4, 0, 10 };
   const int cols = 4;
-  assert(a.size() % cols == 0);
+  if (a.size() % cols != 0)
+  {
+    std::cout << "The input dimentions are incorrect\n";
+    return 1;
+  }
 
   gaussian_elimination(a, cols);
   print_matrix(a, cols);