From 44f07de53c79ef8a54f44194c38ed5679f35a205 Mon Sep 17 00:00:00 2001
From: SYury <yusemru@gmail.com>
Date: Mon, 14 Oct 2019 18:23:56 +0300
Subject: [PATCH] Added some tests for linear algebra

---
 src/linear_algebra/linear-system-gauss.md |  8 +++-
 src/linear_algebra/rank-matrix.md         |  2 +-
 test/test_gauss.cpp                       | 49 ++++++++++++++++++++
 test/test_rank_matrix.cpp                 | 55 +++++++++++++++++++++++
 4 files changed, 112 insertions(+), 2 deletions(-)
 create mode 100644 test/test_gauss.cpp
 create mode 100644 test/test_rank_matrix.cpp

diff --git a/src/linear_algebra/linear-system-gauss.md b/src/linear_algebra/linear-system-gauss.md
index a0233f2b5..9640d84bd 100644
--- a/src/linear_algebra/linear-system-gauss.md
+++ b/src/linear_algebra/linear-system-gauss.md
@@ -70,7 +70,10 @@ The input to the function `gauss` is the system matrix $a$. The last column of t
 
 The function returns the number of solutions of the system $(0, 1,\textrm{or } \infty)$. If at least one solution exists, then it is returned in the vector $ans$.
 
-```cpp
+```cpp gauss
+const double EPS = 1e-9;
+const int INF = 2; // it doesn't actually have to be infinity or a big number
+
 int gauss (vector < vector<double> > a, vector<double> & ans) {
 	int n = (int) a.size();
 	int m = (int) a[0].size() - 1;
@@ -194,3 +197,6 @@ Thus, the solution turns into two-step: First, Gauss-Jordan algorithm is applied
 * [Codechef - Knight Moving](https://www.codechef.com/SEP12/problems/KNGHTMOV)
 * [Lightoj - Graph Coloring](http://lightoj.com/volume_showproblem.php?problem=1279)
 * [UVA 12910 - Snakes and Ladders](https://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&problem=4775)
+* [TIMUS1042 Central Heating](http://acm.timus.ru/problem.aspx?space=1&num=1042)
+* [TIMUS1766 Humpty Dumpty](http://acm.timus.ru/problem.aspx?space=1&num=1766)
+* [TIMUS1266 Kirchhoff's Law](http://acm.timus.ru/problem.aspx?space=1&num=1266)
diff --git a/src/linear_algebra/rank-matrix.md b/src/linear_algebra/rank-matrix.md
index 48c213d79..23e56eb95 100644
--- a/src/linear_algebra/rank-matrix.md
+++ b/src/linear_algebra/rank-matrix.md
@@ -20,7 +20,7 @@ This algorithm runs in $\mathcal{O}(n^3)$.
 
 ## Implementation
 
-```cpp
+```cpp matrix-rank
 const double EPS = 1E-9;
 
 int compute_rank(vector<vector<double>> A) {
diff --git a/test/test_gauss.cpp b/test/test_gauss.cpp
new file mode 100644
index 000000000..c2d263343
--- /dev/null
+++ b/test/test_gauss.cpp
@@ -0,0 +1,49 @@
+#include<bits/stdc++.h>
+
+using namespace std;
+
+#include "gauss.h"
+
+typedef double dbl;
+typedef vector<vector<dbl> > matrix;
+typedef vector<dbl> vec;
+
+void test1(){
+    //x + y = 0
+    matrix A = {{1, 1}};
+    vec b = {0};
+    vec ans(2);
+    A[0].push_back(b[0]);
+    assert(gauss(A, ans) == INF);
+}
+
+void test2(){
+    //x + y = 0
+    //2x + 3y = 1
+    matrix A = {{1, 1}, {2, 3}};
+    vec b = {0, 1};
+    vec ans(2);
+    A[0].push_back(b[0]);
+    A[1].push_back(b[1]);
+    assert(gauss(A, ans) == 1);
+    assert(abs(ans[0] + 1) < EPS && abs(ans[1] - 1) < EPS);
+}
+
+void test3(){
+    //x = 0
+    //y = 1
+    //x + y = 2
+    matrix A = {{1, 0}, {0, 1}, {1, 1}};
+    vec b = {0, 1, 2};
+    vec ans(2);
+    A[0].push_back(b[0]);
+    A[1].push_back(b[1]);
+    A[2].push_back(b[2]);
+    assert(gauss(A, ans) == 0);
+}
+
+int main(){
+    test1();
+    test2();
+    test3();
+}
diff --git a/test/test_rank_matrix.cpp b/test/test_rank_matrix.cpp
new file mode 100644
index 000000000..e494f024f
--- /dev/null
+++ b/test/test_rank_matrix.cpp
@@ -0,0 +1,55 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+#include "matrix-rank.h"
+
+typedef double dbl;
+typedef vector<vector<dbl> > matrix;
+
+void test1(){
+    matrix A(3);
+    A[0] = {1, 1, 0};
+    A[1] = {0, 1, 0};
+    A[2] = {1, 0, 0};
+    assert(compute_rank(A) == 2);
+}
+
+void test2(){
+    matrix A(3);
+    A[0] = {1, 1, 1};
+    A[1] = {0, 1, 1};
+    A[2] = {0, 0, 1};
+    assert(compute_rank(A) == 3);
+}
+
+void test3(){
+    matrix A(3);
+    A[0] = {0, 0, 0};
+    A[1] = {0, 0, 0};
+    A[2] = {0, 0, 0};
+    assert(compute_rank(A) == 0);
+}
+
+void test4(){
+    matrix A(3);
+    A[0] = {1, 1, 1};
+    A[1] = {1, 1, 1};
+    A[2] = {1, 1, 1};
+    assert(compute_rank(A) == 1);
+}
+
+void test5(){
+    matrix A(2);
+    A[0] = {1, 0, 1, 0};
+    A[1] = {0, 1, 0, 1};
+    assert(compute_rank(A) == 2);
+}
+
+int main(){
+    test1();
+    test2();
+    test3();
+    test4();
+    test5();
+}

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