add gas station

Author: tg123

gas-station/README.md

@@ -1,4 +1,14 @@
+## Guessing
 
-## TODO 
-  * write down thinking
+This problem is to find a UNIQUE station `i`, such that
 
+ * SUM(gas[0 .. i-1]) - SUM(cost[0 .. i-1]) + SUM(gas[i .. end]) - SUM(cost[i .. end]) >= 0
+ * SUM(gas[0 .. i-1]) - SUM(cost[0 .. i-1]) < 0
+
+`SUM(gas[0 .. i-1]) - SUM(cost[0 .. i-1]) < 0` is to guarantee that the `i` is unique.
+
+If `SUM(gas[0 .. i-1]) - SUM(cost[0 .. i-1]) < 0` and `SUM(gas[0 .. i-1]) - SUM(cost[0 .. i-1]) + SUM(gas[i .. end]) - SUM(cost[i .. end]) >= 0`, that is, `0 .. i-1` are all valid stations.
+
+## Brute force
+
+Just search through from `0` to `end`, find the valid `i`.