sql reporting services qr code E.35 Testing the partial_sort_copy() Algorithm in Software

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EXAMPLE E.35 Testing the partial_sort_copy() Algorithm
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int main() { int a[] = {77,22,99,55,44,88,11,33,66}; print(a,9); int b[3]; partial_sort_copy(a,a+9,b,b+3); print(a,9); print(b,3); } n=9: {77,22,99,55,44,88,11,33,66} n=9: {77,22,99,55,44,88,11,33,66} n=3: {11,22,33}
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partial_sum(p,q,pp); // invariant: a[p,q[ is left unchanged; // postcondition b[i] == a[0]+...+a[i] for each b[i] in [pp,pp+q-p[;
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EXAMPLE E.36 Testing the partial_sum() Algorithm
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int main() { int a[] = {0,1,1,2,3,5,8,13,21,34}; int b[10]; partial_sum(a,a+10,b); print(a,10); print(b,10); } n=10: {0,1,1,2,3,5,8,13,21,34} n=10: {0,1,2,4,7,12,20,33,54,88} The partial_sum() algorithm is the inverse of the adjacent_difference() algorithm (Example E.2 on page 370).
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APP. E]
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STANDARD C++ GENERIC ALGORITHMS
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partition(p,q,P()); // partitions [p,q[ into [p,r[ and [r,q[ so that // x is in [p,r[ iff P(x) is true;
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EXAMPLE E.37 Testing the partition() Algorithm
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int main() { int a[] = {0,1,1,2,3,5,8,13,21,34}; print(a,10); partition(a,a+10,Odd()); print(a,10); } n=10: {0,1,1,2,3,5,8,13,21,34} n=10: {21,1,1,13,3,5,8,2,0,34}
pop_heap(p,q); // moves *p into temp, then shifts elements to the left so that the // remaining elements form a heap in [p,q-1[ into a heap, then copies // temp into *(q-1); // precondition: [p,q[ must be a heap; // postcondition: [p,q-1[ is a heap;
EXAMPLE E.38 Testing the pop_heap() Algorithm
int main() { int a[] = {44,88,33,77,11,99,66,22,55}; print(a,9); make_heap(a,a+9); print(a,9); pop_heap(a,a+9); print(a,9); print(a,8); } n=9: {44,88,33,77,11,99,66,22,55} n=9: {99,88,66,77,11,33,44,22,55} n=9: {88,77,66,55,11,33,44,22,99} n=8: {88,77,66,55,11,33,44,22} See Example E.25 on page 379 and Example E.38 on page 383.
88 77 55 22 99 11 33 66 44
prev_permutation(p,q); // permutes the elements of [p,q[; n! calls will cycle backward through // all n! permutations of the n elements, where n = q-p;
EXAMPLE E.39 Testing the prev_permutation() Algorithm
int main() { char* s="ABCD"; for (int i=0; i<24; i++) { prev_permutation(s,s+4); cout << (i%8 '\t':'\n') << s;
STANDARD C++ GENERIC ALGORITHMS
[APP. E
} } DCBA DCAB DBCA DBAC DACB DABC CDBA CDAB CBDA CBAD CADB CABD BDCA BDAC BCDA BCAD BADC BACD ADCB ADBC ACDB ACBD ABDC ABCD The prev_permutation() algorithm is the inverse of the next_permutation() algorithm (Example E.32 on page 381).
push_heap(p,q); // adds the element at *(q-1) to those in [p,q-1[ so that [p,q[ is a heap; // precondition: [p,q-1[ must be a heap; // postcondition: [p,q[ is a heap;
EXAMPLE E.40 Testing the push_heap() Algorithm
int main() { int a[] = {66,44,88,33,55,11,99,22,77}; print(a,8); make_heap(a,a+8); print(a,8); print(a,9); push_heap(a,a+9); print(a,9); } n=8: {66,44,88,33,55,11,99,22} n=8: {99,55,88,33,44,11,66,22} n=9: {99,55,88,33,44,11,66,22,77} n=9: {99,77,88,55,44,11,66,22,33} The push_heap() algorithm reverses the effect of pop_heap(). (See Example E.38.)
99 77 55 22 33 44 11 88 66
random_shuffle(p,q); // performs a random (but deterministic) shuffle on [pp,qq[
EXAMPLE E.41 Testing the random_shuffle() Algorithm
int main() { char* s="ABCDEFGHIJ"; cout << s << '\n'; for (int i=0; i<4; i++) { random_shuffle(s,s+10); cout << s << '\n'; } } ABCDEFGHIJ CIJDBEAHGF CFBDEIGAHJ IDJABEFGHC DBJIFEGACH
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APP. E]
STANDARD C++ GENERIC ALGORITHMS
remove(p,q,x); // removes all occurrences of x from [p,q[, shifting (copying) the // remaining elements to the left; // invariant: the length of the segment remains unchanged;
EXAMPLE E.42 Testing the remove() Algorithm
int main() { char* s="All is flux, nothing is stationary."; // Heraclitus int l = strlen(s); int n = count(s,s+l,' '); cout << "l=" << l << '\n'; cout << "n=" << n << '\n'; remove(s,s+l,' '); cout << s << '\n'; s[l-n] = 0; // truncate s cout << s << '\n'; } l=35 n=5 Allisflux,nothingisstationaryonary. Allisflux,nothingisstationary. Since 5 blanks were removed, the last 5 letters remain after their copies were shifted left.
remove_copy(p,q,pp,x); // copies all elements of [p,q[ that do not match x to [pp,pp+n[, // where n is the number of nonmatching elements; // returns pp+n; // invariant: [p,q[ remains unchanged;
EXAMPLE E.43 Testing the remove_copy() Algorithm
int main() { char* s="All is flux, nothing is stationary."; char buffer[80]; int l = strlen(s); int n = count(s,s+l,' '); cout << "l=" << l << '\n'; cout << "n=" << n << '\n'; char* ss = remove_copy(s,s+l,buffer,' '); *ss = 0; // truncate buffer cout << s << '\n'; cout << buffer << '\n'; cout << ss-buffer << '\n'; } l=35 n=5 All is flux, nothing is stationary. Allisflux,nothingisstationary. 30
// Heraclitus
STANDARD C++ GENERIC ALGORITHMS
[APP. E
remove_copy_if(p,q,pp,P()); // copies all elements x of [p,q[ for which !P(x) to [pp,pp+n[, // where n is the number of nonmatching elements; // returns pp+n; // invariant: [p,q[ remains unchanged;
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