Add the documentation about the detecting bugs in Codeforces solutions

docs/Codeforces.md

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+# Codeforces
+
+## Introduction
+
+Codeforces is a website that hosts competitive programming contests. The site presents several thousand programming and 
+algorithm tasks. The main feature of Codeforces is that if the solution sent to the testing system does not pass some 
+test from a set prepared by the authors of the problem, then this test will be not shown to the user. That is, you have 
+to try to come up with the input data yourself, on which the solution gives a wrong answer (verdict "Wrong answer") or 
+falls with an unhandled exception (verdict "Runtime error"). This is almost always very difficult, especially if the 
+mistake is not obvious.
+
+## Detecting the mistake with UnitTestBot
+
+To find the needed test on which the solution falls, we suggest using UnitTestBot. Consider two cases separately:
+
+- "Runtime error". In this case, you just need to run the test generation for a written solution, and, perhaps, 
+  UnitTestBot will find the test case on which the program will fail.
+- "Wrong answer". This case is more difficult. You can try to do one of the following (or all at once):
+  - The mistake can be that during the program's execution, some invariants cease to be true, but they are important to
+    your solution. Then it is worth writing `assert` instructions in those places where you can check these invariants. 
+    For example, if you are sure that the result of the calculation of some function is always greater than zero, then 
+    you can add the `assert result > 0;` before returning `result` as an answer. Then UnitTestBot will try to find a 
+    test on which `assert` fails.
+  - If the final answer can be easily verified for correctness, you can write the `assert` instructions again. For 
+    example, if you are sure that the answer is a non-empty sorted `array`, then you need to write something like:
+    ```java
+    for (int i = 0; i < array.length - 1; ++i) {
+        assert array[i] < array[i + 1];
+    }
+    ```
+    Now UnitTestBot will again try to find a test where these conditions are not met.
+  - If you have a slow, but the correct solution, then you can try to do something like:
+    ```java
+    var answer1 = fastButWrongSolve(input);
+    var answer2 = slowButCorrectSolve(input);
+    assert answer1 == answer2;
+    ```
+
+### Details of the UnitTestBot usage for this case
+
+There are two reasons why you can't just run UnitTestBot on a solution and expect it will find a bug (it's not possible
+now, maybe it is a future plan):
+
+- You need to read the input data from `stdin` and write the answer to `stdout` in Codeforces tasks. This is a problem
+  because UnitTestBot can generate tests for a specific function that has input parameters with specific types and a 
+  specific return value.
+- Quite strong restrictions are often imposed on the input data. For example, the number `n` that is in the input,
+  always is in the range from 1 to 100. Another example is the input string is not any but consists only of small
+  letters of the English alphabet.
+
+Therefore, it is proposed to transform the solution to a "good" form before starting the test generation:
+
+```java
+public class Main {
+
+    public static /* answer type */ solve(/* input parameters */) {
+        assume(/* constraints from the problem as the boolean predicate */);
+        // solve
+        return answer;
+    }
+
+    public static void main(String[] args) {
+        // read input
+        var answer = solve(/* input */);
+        // write output
+    }
+}
+```
+
+The `assume` method is located in the class `org.utbot.api.mock.UtMock`. 
+
+Now you can start the test generation for the `solve` function.
+
+### Example
+
+Let's look at an example of the described transformation on the 
+[solution](https://codeforces.com/contest/70/submission/25719914), which got the verdict "Runtime Error" in the 
+Codeforces testing system.
+
+It is said in the [problem](https://codeforces.com/contest/70/problem/A) that the input is an integer `n` in the range
+from 0 up to 1000. And that the answer should be printed modulo 1e6 + 3, so the answer should be less than 1e6 + 3.
+
+The transformed solution can look like:
+
+```java
+import java.util.Scanner;
+import static org.utbot.api.mock.UtMock.assume;
+
+public class Task_70A {
+
+    static final int mod = (int) 1e6 + 3;
+
+    public static int solve(int n) {
+        assume(0 <= n && n <= 1000);                 // assumption
+
+        int[] dp = new int[n];
+        dp[0] = 1;
+        for(int i = 1; i < n; ++i) {
+            dp[i] = (3 * dp[i - 1]) % mod;
+        }
+
+        assert 0 <= dp[n - 1] && dp[n - 1] < mod;    // assertion
+        return dp[n - 1];
+    }
+
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();                        // input
+        int answer = solve(n);                       // solve
+        System.out.println(answer);                  // output
+    }
+}
+```
+
+Now we can run the test generation for `solve` method.
+
+**The result**: UnitTestBot managed to generate the test `solve(0)` that leads to 
+`java.lang.ArrayIndexOutOfBoundsException` at the line `dp[0] = 1;`.
+
+### Experiments
+
+Experiments were conducted to understand whether the described approach can be used in practice. During the analysis,
+several dozen incorrect solutions from Codeforces were selected (manually or automatically, using the 
+[Codeforces API](https://codeforces.com/apiHelp )). The solutions were transformed to the "good" form manually, and 
+after that, the test generation was run for them.
+
+Consider the results for verdicts "Runtime error" and "Wrong answer" separately.
+
+#### Testing solutions with Runtime error
+
+We managed to find several examples when UnitTestBot can find an error in the solution. The full list of such solutions
+located at the `./utbot-junit-contest/src/main/resources/projects/codeforces`. Now let's look at one interesting 
+example in more detail.
+
+[Original sumbit](https://codeforces.com/contest/1702/submission/167461682)
+
+Transformed solution:
+
+```java
+import static org.utbot.api.mock.UtMock.assume;
+
+import java.util.Scanner;
+
+public class Expected_SIOBE {
+
+    public static int solve(String s) {
+        // ======== assumptions =========
+        for (int i = 0; i < s.length(); ++i) {
+            assume('a' <= s.charAt(i) && s.charAt(i) <= 'z');
+        }
+
+        // ========== solution ==========
+        int counter = 0;
+        int count = 0;
+        while (count < s.length()) {
+            counter++;
+            char mem1 = s.charAt(count++);
+            while (count < s.length() && s.charAt(count) == mem1) {
+                count++;
+            }
+            if (count >= s.length()) {
+                break;
+            }
+            char mem2 = s.charAt(count++);
+            while (count < s.length() && (s.charAt(count) == mem1 || s.charAt(count) == mem2)) {
+                count++;
+            }
+            char mem3 = s.charAt(count++);
+            while (count < s.length() && (s.charAt(count) == mem1 || s.charAt(count) == mem2 || s.charAt(count) == mem3)) {
+                count++;
+            }
+        }
+        return counter;
+    }
+
+    public static void main(String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int t = sc.nextInt();              // multiple tests
+        while (t-- > 0) {
+            String s = sc.next();          // read input
+            System.out.println(solve(s));  // write output
+        }
+    }
+}
+```
+
+**The result**: UniTestBot can detect an unexpected exception `java.lang.StringIndexOutOfBoundsException` 
+at the line `char mem3 = s.charAt(count++);`. The mistake is not obvious, so UnitTestBot really helps.
+
+#### Testing solutions with Wrong answer
+
+For all solutions that were compared with the principle "slow, but correct" vs "fast, but wrong", UnitTestBot 
+could not find the bug. Most likely, it is because the tool has poor performance. In other words, it is not
+applicable in this case yet.
+
+Anyway, let's look at the example of correct and wrong solutions. The example is quite simple, but UnitTestBot is 
+failed to find a bug.
+
+- [Original submit WA](https://codeforces.com/contest/1718/submission/168870501)
+- [Original submit AC](https://codeforces.com/contest/1718/submission/168871045)
+
+Transformed code:
+
+```java
+import static org.utbot.api.mock.UtMock.assume;
+
+import java.util.*;
+
+class Compare {
+
+    public static void check(int n, int[] a) {
+        assume(1 <= n && n <= 1e5);
+        assume(a.length == n);
+        for (int e : a) {
+            assume(e >= 0);
+        }
+        assert wrongSolve(n, a) == correctSolve(n, a);
+    }
+
+    public static int wrongSolve(int n, int[] a) {
+        int ans = 0, len = 0, xor = 0;
+        for (int i = 0; i < n; i++) {
+            xor ^= a[i];
+            if (xor == 0 || a[i] == 0) {
+                ans += len;
+                len = xor = 0;
+            } else {
+                len++;
+            }
+        }
+        ans += len;
+        return ans;
+    }
+
+    public static int correctSolve(int n, int[] a) {
+        int xor = 0, ans = 0;
+        Set<Integer> set = new HashSet<>();
+        set.add(0);
+        for (int i = 0; i < n; i++) {
+            xor ^= a[i];
+            if (set.contains(xor)) {
+                set.clear();
+                ans++;
+                xor = 0;
+                set.add(0);
+            } else {
+                set.add(xor);
+            }
+        }
+        ans = n - ans;
+        return ans;
+    }
+
+    public static void main(String[] args) throws Exception {
+        Scanner sc = new Scanner(System.in);
+        int t = sc.nextInt();
+        while (t-- > 0) {
+            int n = sc.nextInt();
+            int[] a = new int[n];
+            for (int i = 0; i < n; i++) {
+                a[i] = sc.nextInt();
+            }
+            System.out.println(wrongSolve(n, a));
+        }
+    }
+}
+```
+
+**The result**: After the test generation for the method `check` we want to get a test case that would show 
+the difference between the two solutions, but UnitTestBot can't generate it (even with a large time budget ~ 10 min).