General binary search approach

Author: Hieu Luong

src/binarysearch/ReadMe.java

@@ -2,53 +2,43 @@
 
 public class ReadMe {
 
-    /**
-     * summary of 2 most frequently used binary search templates.
-     * one is return index during the search:
-     *
-     * while lo <= hi:
-     *   mid = (lo+hi)/2
-     *   if nums[mid] == target:
-     *     return mid
-     *   if nums[mid] > target:
-     *     hi = mid-1
-     *   else:
-     *     lo = mid+1
-     * return -1
-     *
-     * Another more frequently used binary search template is for searching lowest element
-     * satisfy function(i) == True (the array should satisfy function(x) == False for 0 to i-1,
-     * and function(x) == True for i to n-1, and it is up to the question to define the function,
-     * like in the find peak element problem, function(x) can be nums[x] < nums[x+1] ),
-     * there are 2 ways to write it:
-     *
-     * while lo <= hi:
-     *   mid = (lo+hi)/2
-     *   if function(mid):
-     *     hi = mid-1
-     *   else:
-     *     lo = mid+1
-     * return lo
-     *
-     * or
-     *
-     * while lo <  hi:
-     *   mid = (lo+hi)/2
-     *   if function(mid):
-     *     hi = mid
-     *   else:
-     *     lo = mid+1
-     *
-     * return lo ---> lowest element that satifies function(x)
-     * return hi ---> highest element that not satifies function(x)
-     *
-     * No matter which one you use, just be careful about updating the hi and lo,
-     * which could easily lead to infinite loop.
-     * Some binary question is searching a floating number
-     * and normally the question will give you a precision,
-     * in which case you don't need to worry too much about the infinite loop
-     * but your while condition will become something like "while lo+1e-7<hi"
-     *
+    /*
+        |--x-----x------[v]vvvvvvvvvvvvvvvv|
+        while (lo <= hi) {
+            int mid = lo + (hi-lo)/2;
+            if function(mid)
+                hi = mid-1;
+            else
+                lo = mid+1;
+        }
+        return lo; ---> lowest element that satisfies function(x)
+
+        |vvvvvvvvvvvvv[v]-----x------x-------|
+        while (lo <= hi) {
+            int mid = lo + (hi-lo)/2;
+            if function(mid)
+                lo = mid+1;
+            else
+                hi = mid-1;
+        }
+        return hi; ---> highest element that satisfies function(x)
+
+        |----x----[v]----------x--------------|
+        while (lo <= hi) {
+            int mid = lo + (hi-lo)/2;
+            if function(mid) == target
+                return mid;
+            if function(mid) < target
+                lo = mid+1;
+            else
+                hi = mid-1;
+        }
+        return -1;
+
+        Note: function(x) is non-decreasing function
+     */
+
+     /*
      *
      * Collections.binarySearch
      * Array.binarySearch