feat: readme

Assignment1/B/nqueens.lp

@@ -1,5 +1,4 @@
-#const n = 20.
-#const k = 5.
+#const n = 500.
 
 % n-Queens encoding
 

Assignment1/B/reach.lp

@@ -0,0 +1,16 @@
+#include "reachin1000".
+
+source(3).
+
+% Way 1
+reach(X) :- source(X).
+reach(Y) :- edge(X,Y), reach(X).
+% Way 2
+%reach(Y) :- edge(X,Y), reach(X).
+%reach(X) :- source(X).
+% Way 3
+%reach(X) :- source(X).
+%reach(Y) :- reach(X), edge(X,Y).
+% Way 4
+%reach(Y) :- reach(X), edge(X,Y).
+%reach(X) :- source(X).

Assignment1/README.md

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+# Assignment 1  
+
+## Part A  
+
+### Append  
+```shell
+xsb
+```  
+```prolog
+['A/append.P'].
+suffix([1,2], [1,2,3,4]).
+cut([1,2,3]).
+```  
+### Reach  
+generate input set  
+```shell
+python randomgen.py [number of nodes]
+```  
+### Transitive closure and cycle  
+```shell
+xsb
+```  
+```prolog
+['A/cycle.P'].
+path(1,2) .
+cycle(1).
+```  
+### N-queens  
+```shell
+xsb
+```  
+```prolog
+['A/queens.P'].
+timeNQueen(8).
+timeOneQueen(8).
+```  
+
+## Part B
+### Reach  
+generate input set  
+```shell
+python randomgen.py [number of nodes]
+```  
+```shell
+clingo --models 0 B/reach.lp
+```
+| Input size | Way 1   | Way 2  | Way 3  | Way 4  |
+| ---------- | ------- | ------ | ------ | ------ |
+| 10000      | 0.655s  | 0.703s | 0.664s | 0.665s |
+| 20000      | 1.376s  | 1.446s | 1.290s | 1.292s |
+| 50000      | 3.355s  | 3.501s | 2.750s | 1.645s |
+| 100000     | 6.778s  | 5.002s | 3.375s | 3.438s |
+| 200000     | 12.119s | 7.514s | 7.267s | 7.021s |  
+
+Though it looks like the Way4 is way better tha Way 1(Almost twice as fast), but if we let the computer to rest for a while and rerun them the other way(start from 4, then 3, follow by 2 and 1), we got  
+| Input size | Way 1  | Way 2  | Way 3  | Way 4   |
+| ---------- | ------ | ------ | ------ | ------- |
+| 200000     | 7.146s | 7.610s | 7.120s | 12.103s |  
+
+It is exactly the other way around! I belive it is because the input file becomes too large
+(42 MByte), so it waste a lot of time to load it to memory then cache, and the following ones has much higher cache hits rate, so the first one takes way longer than the others.
+### N-queens
+```shell
+clingo --models 0 B/nqueens.lp
+```  
+```shell
+clingo --models 1 B/nqueens.lp
+```  
+| Number of queens | Time for 1 queen | Time for all queens |
+| ---------------- | ---------------- | ------------------- |
+| 8                | 0.004s           | 0.006s              |
+| 10               | 0.003s           | 0.086s              |
+| 12               | 0.004s           | 4.909s              |
+| 14               | 0.006s           | Too long to run     |
+| 20               | 0.011s           |                     |
+| 50               | 0.073s           |                     |
+| 100              | 0.463s           |                     |
+| 200              | 3.233s           |                     |
+| 500              | 35.073s          |                     |  
+
+
+## Part C  
+### N-queens

Assignment1/randomgen.py

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+import random
+import sys
+if len(sys.argv) == 2: x = int(sys.argv[1])
+else: x = 1000
+file = open("reachin1000", "w") 
+for i in range(10 * x):
+    j = random.randint(1,x)
+    k = random.randint(1,x)
+    file.write("edge({}, {}).\n".format(i, j))
+file.close()

B/reach.lp

@@ -1,5 +0,0 @@
-#include "reachin1000".
-
-source(3).
-reach(Y) :- edge(X,Y), reach(X).
-reach(X) :- source(X).

randomgen.py

@@ -1,6 +0,0 @@
-import random
-x = int(input())
-for i in range(10 * x):
-    j = random.randint(1,x)
-    k = random.randint(1,x)
-    print("edge(", j, ",", k, ").")