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8 2 1 3 4 6 5 7 10 9 11 12 14 13 0 64 14 13 25 33 51 43 53 84 72 93 95 97 96 6 Binary Search lo Binary search. Given a key and sorted array a[], find index i such that a[i] = key, or report that no such index exists. Invariant. Algorithm maintains a[lo] key a[hi]. Ex. Binary search for 33. hi

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821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lo himid

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lo hi

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lo mid hi

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lo hi

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lo himid

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lohi

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lohimid

Binary Search

Binary search. Given a key and sorted array a[], find index isuch that a[i] = key, or report that no such index exists.

Invariant. Algorithm maintains a[lo] key a[hi].

Ex. Binary search for 33.

821 3 4 65 7 109 11 12 14130

641413 25 33 5143 53 8472 93 95 97966

lohimid

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