Data Structures and Programming Methodology CS61

1 Asymptotics
(a) We have a function findMax that iterates through an unsorted int array once and returns the
maximum element found in that array. Give the tightest lower (Ω( · )) and upper bounds ( O ( · )) of
findMax in terms of N , the length of the array. Is it possible to define a Θ( · ) bound for findMax ?
(b) Give the worst case and best case runtime in terms of M and N . Assume ping is in Θ(1) and returns
an int .
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for ( int i = N; i > 0; i--) {
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for ( int j = 0; j <= M; j++) {
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if (ping(i, j) > 64) break ;
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}
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}
(c) Below we have a function that returns true if every int has a duplicate in the array, and false if there
is any unique int in the array. Assume sort(array) is in Θ( N log N ) and returns array sorted.
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public static boolean noUniques( int [] array) {
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array = sort(array);
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int N = array.length;
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for ( int i = 0; i < N; i += 1) {
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boolean hasDuplicate = false ;
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for ( int j = 0; j < N; j += 1) {
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if (i != j && array[i] == array[j]) {
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hasDuplicate = true ;
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}
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}
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if (!hasDuplicate) return false ;
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}
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return true ;
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}
Give the worst case and best case runtime in Θ( · ) notation, where N = array.length .