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1. Order the following functions by growth rate: N , N , N 1.5 , N 2 , N log N , N log log
1. Order the following functions by growth rate: N, N, N1.5, N2, NlogN, N log log N, N log2 N, N log(N2), 2/N, 2N, 2N/2, 37, N2 log N, N3. Indicate which functions grow at the same rate.
2. For each of the following six program fragments, give an analysis of the running time (Big-Oh will do).
(1) sum = 0; for( i = 0; i < n; ++i )
++sum; (2) sum = 0;
for( i = 0; i < n; ++i ) for( j = 0; j < n; ++j )
++sum; (3) sum = 0;
for( i = 0; i < n; ++i ) for( j = 0; j < n * n; ++j )
++sum; (4) sum = 0;
for( i = 0; i < n; ++i ) for( j = 0; j < i; ++j )
++sum; (5) sum = 0;
for( i = 0; i < n; ++i ) for( j = 0; j < i * i; ++j )
for( k = 0; k < j; ++k ) ++sum;
(6) sum = 0; for( i = 1; i < n; ++i )
for( j = 1; j < i * i; ++j ) if( j % i == 0 )
for( k = 0; k < j; ++k ) ++sum;
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