Binary%20Search

1
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lo
hi
2
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lo
mid
hi
3
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lo
hi
4
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lo
mid
hi
5
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lo
hi
6
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lo
hi
mid
7
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lohi
8
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lohimid
9
Binary Search

• Binary search. Given value and sorted array
  a, find index isuch that ai value, or
  report that no such index exists.
• Invariant. Algorithm maintains alo ? value ?
  ahi.
• Ex. Binary search for 33.

64
14
13
25
33
51
43
53
84
72
93
95
97
96
6
8
2
1
3
4
6
5
7
10
9
11
12
14
13
0
lohimid