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lecture4 - Lecture 4 Divide and Conquer for Nearest...

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Unformatted text preview: Lecture 4 Divide and Conquer for Nearest Neighbor Problem Shang-Hua Teng Merge-Sort( A,p,r ) A procedure sorts the elements in the sub-array A [ p..r ] using divide and conquer Merge-Sort( A,p,r ) if p >= r , do nothing if p< r then Merge-Sort( A,p,q ) Merge-Sort( A,q+1,r ) Merge( A,p,q,r ) Starting by calling Merge-Sort( A,1,n ) 2 / ) ( r p q + A = MergeArray( L,R ) Assume L [ 1:s ] and R[ 1:t ] are two sorted arrays of elements: Merge-Array( L,R ) forms a single sorted array A [ 1:s+t ] of all elements in L and R . A = MergeArray( L,R ) for k 1 to s + t do if then else 1 ]; [ ] [ + i i i L k A 1 ]; [ ] [ + j j j R k A + + ] 1 [ ; ] 1 [ t R s L ] [ ] [ j R i L 1 ; 1 j i Complexity of MergeArray At each iteration, we perform 1 comparison, 1 assignment (copy one element to A ) and 2 increments (to k and i or j ) So number of operations per iteration is 4. Thus, Merge-Array takes at most 4(s+t) time. Linear in the size of the input . Merge ( A,p,q,r ) Assume A [ p..q ] and A[ q+1..r ] are two sorted Merge( A,p,q,r ) forms a single sorted array A [ p..r ]. Merge (A,p,q,r) + + ] 1 [ ; ] 1 [ t R s L ; ; 1 q r t p q s- +- ] , 1 [ ]; .. [ r q A R q p A L + ) , ( ] .. [ R L MergeArray r p A Merge-Sort( A,p,r ) A procedure sorts the elements in the sub-array A [ p..r ] using divide and conquer...
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lecture4 - Lecture 4 Divide and Conquer for Nearest...

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