Initial commit -Alpha Edition-

Author: Muhammad-Magdi

BinarySearch.cpp

@@ -0,0 +1,73 @@
+What else?
+  -BinarySearch in Integer Domain.
+  -BinarySearch in Real Domain.
+
+Terminology:
+  Search Space
+  low
+  high
+  median
+  Check function
+
+You can solve the problem using BinarySearch if and only if:
+- You can design a check function whose domain is the problem's search space
+  and its range is separated into at most one "False" segment and one "True" segment.
+
+
+Can you design the upper_bound function?
+
+bool isGreater(int a, int b){
+  return a > b;
+}
+
+int upperBound(int *A, int val){
+  int lo = 0, med, hi = n-1;
+  while(lo<hi){
+    mid = (lo+hi)>>1;
+    if(isGreater(A[med], val))  hi = mid;
+    else  lo = med+1;
+  }
+  return lo;
+}
+
+
+We have two cases:
+1- Minimization Problems:
+  -FFFFFFFFFFFFFFFFFFFTTTTTTTTTTTTTTTT
+  -the range is separated into False-True range.
+  -the target is the first True
+  -We ceil the low and floor the median.
+
+bool ok(int val){
+  //Some Checking Statements
+}
+
+int binarySearch(){
+  int lo = 0, med, hi = 1000000000;
+  while(lo<hi){
+    mid = (lo+hi)>>1;
+    if(ok(A[med]))  hi = med;
+    else  lo = med+1;
+  }
+  return hi;
+}
+
+2- Maximization Problems:
+  -TTTTTTTTTTTTTTTFFFFFFFFFFFFFFF
+  -the range is separated into True-False range.
+  -the target is the last True.
+  -We ceil the median and floor the high.
+
+bool ok(int val){
+  //Some Checking Statements
+}
+
+int binarySearch(){
+  int lo = 0, med, hi = 1000000000;
+  while(lo<hi){
+    mid = (lo+hi+1)>>1;
+    if(ok(A[med]))  lo = med;
+    else  hi = med-1;
+  }
+  return lo;
+}