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Binary Search

Binary Search. 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. 6. 13. 14. 25. 33. 43. 51. 53. 64. 72. 84. 93. 95.

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Binary Search

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

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

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

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

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

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

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

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

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

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