2. Binary search algorithm
• Binary searching for a key in an array is similar to
looking for a word in dictionary
• Take the midpoint of the dictionary and see if the
key is in the lower half or upper half
• Pick the half the contains the key and take the
midpoint of the half and see which quarter the
key is in
• Repeat the above step until the key is matched or
the dictionary cannot be halved any more
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3. Use helper method
• Given int[] list and int key
• You are asked to return
– the position of key in the array if matched or
– -1 if not matched
• What additional information do you need to
apply the algorithm above?
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4. /** Use binary search to find the key in the list */
public static int recursiveBinarySearch(int[] list, int key) {
int low = 0;
int high = list.length - 1;
return recursiveBinarySearch(list, key, low, high); // use helper method
}// recursiveBinarySearch method
/** Use binary search to find the key in the list between list[low] and list[high] */
public static int recursiveBinarySearch(int[] list, int key, int low, int high)
{
if (low > high) // The list has been exhausted without a match
return -1;
int mid = (low + high) / 2;
if (key < list[mid])
return recursiveBinarySearch(list, key, low, mid - 1);
else if (key == list[mid])
return mid;
else
return recursiveBinarySearch(list, key, mid + 1, high);
}// recursiveBinarySearch method
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5. What is the difference between:
public static int recursiveBinarySearch(
int[] list, int key){ . . . }
and
public static int recursiveBinarySearch(
int[] list, int key, int low, int high) { . . . }
The first method calls the second method.
Is it recursive call?
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6. Recursion versus iteration
Iteration Recursion
• Uses for or while loop for • Recursion achieves
repetition but no recursion repetition without a loop
• Price paid: memory
overhead and run time
(Every time a method is
called, some space in
memory must be reserved
or allocated to
store the method’s local
• Why use recursion? variables and formal
parameters, if any)
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7. public class NestedCalls {
public static void m1() {
int m1_x = 1;
int m1_y = 2;
m2(); // m1 calls m2
} // m1 method
public static void m2() {
int m2_ = 3;
int z = 4;
z = m3(); //m2 calls m3
}// m2 method
public static int m3() {
int m3_x =5;
int m3_y = 6;
return 1;
}//m3 method
}//NestedCalls class
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9. View of stack at various points of execution of
NestedCalls.java
Stack frame for m3:
m3_x: 5
m3_y: 6
Stack frame for m2: Stack frame for m2:
m2_x: 3 m2_x: 3
m2_z: 4 m2_z: 4
Stack frame for m1: Stack frame for m1: Stack frame for m1:
m1_x: 1 m1_x: 1 m1_x: 1
m1_y: 2 m1_y: 2 m1_y: 2
Just before Just before Just before m3
calling m2 calling m3 returns
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10. Stack of Binary Search just before returning from the
last recursive call
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11. Why use recursion?
In some problems, iterative solutions are hard to
find.
But recursion is easy - See the Towers of Hanoi
problem in textbook. Animation by Michael Iverson
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12. Other problems that are neatly solved by recursion:
Fractals:
• The Koch snowflake (demo)
• Sierpinski triangle (demo)
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