第四章 编写正确的程序

编写正确的程序原理:

     

      编写正确的二分查找程序:

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define MAXN 1000000

typedef int DataType;

DataType x[MAXN];
int n;

/* Scaffolding */

int i = -999999;
#define assert(v) { if ((v) == 0) printf("  binarysearch bug %d %d\n", i, n); }

/* Alg 1: From Programming Pearls, Column 4: raw transliteration */

int binarysearch1(DataType t)
{int l, u, m;
l = 0;
u = n-1;
for (;;) {
if (l > u)
return -1;
m = (l + u) / 2;
if (x[m] < t)
l = m+1;
else if (x[m] == t)
return m;
else /* x[m] > t */
u = m-1;
}
}

/* Alg 2: Make binarysearch1 more c-ish */

int binarysearch2(DataType t)
{int l, u, m;
l = 0;
u = n-1;
while (l <= u) {
m = (l + u) / 2;
if (x[m] < t)
l = m+1;
else if (x[m] == t)
return m;
else /* x[m] > t */
u = m-1;
}
return -1;
}

/* Alg 3: From PP, Col 8 */

int binarysearch3(DataType t)
{int l, u, m;
l = -1;
u = n;
while (l+1 != u) {
m = (l + u) / 2;
if (x[m] < t)
l = m;
else
u = m;
}
if (u >= n || x[u] != t)
return -1;
return u;
}

/* Alg 4: From PP, Col 9 */

int binarysearch4(DataType t)
{int l, p;
if (n != 1000)
return binarysearch3(t);
l = -1;
if (x[511]   < t) l = 1000 - 512;
if (x[l+256] < t) l += 256;
if (x[l+128] < t) l += 128;
if (x[l+64 ] < t) l += 64;
if (x[l+32 ] < t) l += 32;
if (x[l+16 ] < t) l += 16;
if (x[l+8  ] < t) l += 8;
if (x[l+4  ] < t) l += 4;
if (x[l+2  ] < t) l += 2;
if (x[l+1  ] < t) l += 1;
p = l+1;
if (p >= n || x[p] != t)
return -1;
return p;
}

/* Alg 9: Buggy, from Programming Pearls, Column 5 */

int sorted()
{   int i;
    for (i = 0; i < n-1; i++)
        if (x[i] > x[i+1])
            return 0;
    return 1;
}

int binarysearch9(DataType t)
{int l, u, m;
/* int oldsize, size = n+1; */
l = 0;
u = n-1;
while (l <= u) {
/* oldsize = size;
size = u - l +1;
assert(size < oldsize); */
m = (l + u) / 2;
/* printf("  %d %d %d\n", l, m, u); */
if (x[m] < t)
l = m;
else if (x[m] > t)
u = m;
else {
/* assert(x[m] == t); */
return m;
}
}
/* assert(x[l] > t && x[u] < t); */
return -1;
}

/* Alg 21: Simple sequential search */

int seqsearch1(DataType t)
{int i;
for (i = 0; i < n; i++)
if (x[i] == t)
return i;
return -1;
}

/* Alg 22: Faster sequential search: Sentinel */

int seqsearch2(DataType t)
{int i;
DataType hold = x[n];
x[n] = t;
for (i = 0; ; i++)
if (x[i] == t)
break;
x[n] = hold;
if (i == n)
return -1;
else
return i;
}

/* Alg 23: Faster sequential search: loop unrolling */

int seqsearch3(DataType t)
{int i;
DataType hold = x[n];
x[n] = t;
for (i = 0; ; i+=8) {
if (x[i] == t)   {          break; }
if (x[i+1] == t) { i += 1; break; }
if (x[i+2] == t) { i += 2; break; }
if (x[i+3] == t) { i += 3; break; }
if (x[i+4] == t) { i += 4; break; }
if (x[i+5] == t) { i += 5; break; }
if (x[i+6] == t) { i += 6; break; }
if (x[i+7] == t) { i += 7; break; }
}
x[n] = hold;
if (i == n)
return -1;
else
return i;
}


/* Scaffolding to probe one algorithm */

void probe1()
{int i;
DataType t;
while (scanf("%d %d", &n, &t) != EOF) {
for (i = 0; i < n; i++)
x[i] = 10*i;
printf(" %d\n", binarysearch9(t));
}
}


/* Torture test one algorithm */

#define s seqsearch3
void test(int maxn)
{int i;
for (n = 0; n <= maxn; n++) {
printf("n=%d\n", n);
/* distinct elements (plus one at top) */
for (i = 0; i <= n; i++)
x[i] = 10*i;
for (i = 0; i < n; i++) {
assert(s(10*i)     ==  i);
assert(s(10*i - 5) == -1);
}
assert(s(10*n - 5) == -1);
assert(s(10*n)     == -1);
/* equal elements */
for (i = 0; i < n; i++)
x[i] = 10;
if (n == 0) {
assert(s(10) == -1);
} else {
assert(0 <= s(10) && s(10) < n);
}
assert(s(5) == -1);
assert(s(15) == -1);
}
}

/* Timing */

int p[MAXN];

void scramble(int n)
{int i, j;
DataType t;
for (i = n-1; i > 0; i--) {
j = (RAND_MAX*rand() + rand()) % (i + 1);
t = p[i]; p[i] = p[j]; p[j] = t;
}
}

void timedriver()
{int i, algnum, numtests, test, start, clicks;
while (scanf("%d %d %d", &algnum, &n, &numtests) != EOF) {
for (i = 0; i < n; i++)
x[i] = i;
for (i = 0; i < n; i++)
p[i] = i;
scramble(n);
start = clock();
for (test = 0; test < numtests; test++) {
for (i = 0; i < n; i++) {
switch (algnum) {
case 1:  assert(binarysearch1(p[i]) == p[i]); break;
case 2:  assert(binarysearch2(p[i]) == p[i]); break;
case 3:  assert(binarysearch3(p[i]) == p[i]); break;
case 4:  assert(binarysearch4(p[i]) == p[i]); break;
case 9:  assert(binarysearch9(p[i]) == p[i]); break;
case 21: assert(seqsearch1(p[i]) == p[i]); break;
case 22: assert(seqsearch2(p[i]) == p[i]); break;
case 23: assert(seqsearch3(p[i]) == p[i]); break;
}
}
}
clicks = clock() - start;
printf("%d\t%d\t%d\t%d\t%g\n",
algnum, n, numtests, clicks,
1e9*clicks/((float) CLOCKS_PER_SEC*n*numtests));
}
}

/* Main */

int main()
{/* probe1(); */
/* test(25); */
timedriver();
return 0;
}