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Optimize palindrome.cal

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In cal/palindrome.cal:

Improved the performace of nextpal() and nextprimepal()
by adding and using palnextpal().

Improved the performace of prevpal() and prevprimepal()
by adding and using palprevpal().

Test showed that runs that took 0.0530 cpu seconds can
now be done in as little as 0.0327 cpu seconds.
This commit is contained in:
Landon Curt Noll
2021-11-07 14:15:19 -08:00
parent 3d1e938cb6
commit b7a42a9d3d
1 changed files with 133 additions and 42 deletions
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175
cal/palindrome.cal
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@@ -202,6 +202,70 @@ define ispal(val)
}
/*
* palnextpal - return next palindrome from a known palindrome
*
* NOTE: We assume base 10 digits and place 1 is the units digit.
*
* given:
* pal a palindrome
*
* returns:
* next palindrome > pal
*/
define palnextpal(pal)
{
local paldigits; /* digits in pal */
local half; /* upper half of newval */
local newhalf; /* half+1 */
local newpal; /* new palindrome */
/* case: negative palindrome */
if (pal < 0) {
return -(palprevpal(-pal));
}
/*
* start with upper half
*/
half = upperhalf(pal);
/*
* prep to find a larger palindrome
*/
newhalf = half+1;
/*
* form palindrome from new upper half
*
* We need to watch for the corner case where changing the
* half changes the number of digits as this will impact
* or even/odd number of digits processing.
*/
paldigits = digits(pal);
if (digits(newhalf) == digits(half)) {
/* no change in half digits: process as normal */
if (iseven(paldigits)) {
newpal = mkpal(newhalf);
} else {
newpal = mkpalmiddigit(newhalf // 10, newhalf % 10);
}
} else {
/* change in half digits: process as opposite */
if (iseven(paldigits)) {
newpal = mkpalmiddigit(newhalf // 10, newhalf % 10);
} else {
newpal = mkpal(newhalf);
}
}
/*
* return the new palindrome
*/
return newpal;
}
/*
* nextpal - return next palindrome from a value
*
@@ -218,8 +282,8 @@ define nextpal(val)
local newval; /* val+1 */
local newvaldigits; /* digits in newval */
local half; /* upper half of newval */
local newhalf; /* half+1 */
local pal; /* palindrome test value */
local newpal; /* new palindrome */
/* case: negative value */
if (val < 0) {
@@ -263,10 +327,61 @@ define nextpal(val)
}
/*
* the lower half of val is larger than upper half,
* so we need to find an even larger palindrome
* we need to find an even larger palindrome
*/
newhalf = half+1;
newpal = palnextpal(pal);
/*
* return the new palindrome
*/
return newpal;
}
/*
* palprevpal - return previous palindrome from a palindrome
*
* NOTE: We assume base 10 digits and place 1 is the units digit.
*
* given:
* pal a palindrome
*
* returns:
* previous palindrome < pal
*/
define palprevpal(pal)
{
local paldigits; /* digits in pal */
local half; /* upper half of newval */
local newhalf; /* half+1 */
local newpal; /* new palindrome */
/* case: negative value */
if (pal < 0) {
return -(palnextpal(-pal));
}
/* case: single digit palindrome */
if (pal < 10) {
newpal = pal-1;
return newpal;
}
/* case: 10 or 11 */
if (pal < 12) {
newpal = 9;
return newpal;
}
/*
* start with upper half
*/
half = upperhalf(pal);
/*
* prep to find a smaller palindrome
*/
newhalf = half-1;
/*
* form palindrome from new upper half
@@ -275,26 +390,27 @@ define nextpal(val)
* half changes the number of digits as this will impact
* or even/odd number of digits processing.
*/
paldigits = digits(pal);
if (digits(newhalf) == digits(half)) {
/* no change in half digits: process as normal */
if (iseven(newvaldigits)) {
pal = mkpal(newhalf);
if (iseven(paldigits)) {
newpal = mkpal(newhalf);
} else {
pal = mkpalmiddigit(newhalf // 10, newhalf % 10);
newpal = mkpalmiddigit(newhalf // 10, newhalf % 10);
}
} else {
/* change in half digits: process as opposite */
if (iseven(newvaldigits)) {
pal = mkpalmiddigit(newhalf // 10, newhalf % 10);
if (iseven(paldigits)) {
newpal = mkpalmiddigit(newhalf // 10, newhalf % 10);
} else {
pal = mkpal(newhalf);
newpal = mkpal(newhalf);
}
}
/*
* return the new palindrome
*/
return pal;
return newpal;
}
@@ -314,9 +430,8 @@ define prevpal(val)
local newval; /* val-1 */
local newvaldigits; /* digits in newval */
local half; /* upper half of newval */
local newhalf; /* half-1 */
local pal; /* palindrome test value */
local middle; /* middle digit of newval */
local newpal; /* new palindrome */
/* case: negative value */
if (val < 0) {
@@ -360,38 +475,14 @@ define prevpal(val)
}
/*
* the lower half of val is smaller than upper half,
* so we need to find an even smaller palindrome
* we need to find an even smaller palindrome
*/
newhalf = half-1;
/*
* form palindrome from new upper half
*
* We need to watch for the corner case where changing the
* half changes the number of digits as this will impact
* or even/odd number of digits processing.
*/
if (digits(newhalf) == digits(half)) {
/* no change in half digits: process as normal */
if (iseven(newvaldigits)) {
pal = mkpal(newhalf);
} else {
pal = mkpalmiddigit(newhalf // 10, newhalf % 10);
}
} else {
/* change in half digits: process as opposite */
if (iseven(newvaldigits)) {
pal = mkpalmiddigit(newhalf // 10, newhalf % 10);
} else {
pal = mkpal(newhalf);
}
}
newpal = palprevpal(pal);
/*
* return the new palindrome
*/
return pal;
return newpal;
}
@@ -429,7 +520,7 @@ define nextprimepal(val)
/*
* compute the next palindrome
*/
pal = nextpal(pal);
pal = palnextpal(pal);
dpal = digits(pal);
/* case: 11 is the only prime palindrome with even digit count */
@@ -507,7 +598,7 @@ define prevprimepal(val)
/*
* compute the previous palindrome
*/
pal = prevpal(pal);
pal = palprevpal(pal);
dpal = digits(pal);
/* case: 11 is the only prime palindrome with even digit count */