सी ++ 11
आगे का छोटा अपडेट: बहुत कम जोड़-घटाव करें, और सभी संख्याओं का प्रयास करें A * B + C। मेरा मानना है कि समय सीमा के भीतर, यह इष्टतम के काफी करीब है, यह मानते हुए कि आप केवल उपयोग करते हैं +, *और !। मैं अपने से अधिक समय वाले लोगों के लिए अन्य ऑपरेटरों को छोड़ देता हूं!
लघु अद्यतन: 11 और 111 जैसे भाज्य और संख्याओं का उपयोग करने के लिए कठिन प्रयास करें। यह भी तय है कि मैं !अपनी लागत में गिनती नहीं कर रहा था
नया परिणाम:
प्राथमिक स्कोर = 3,810,660
माध्यमिक स्कोर = 12/09/2016 20:00
2532 1एस, 1505 ऑपरेटर।
विभिन्न टोटके एक साथ किए। मेरा कार्यक्रम 111..111 के सभी factorials और संख्याओं के लिए सबसे छोटा प्रोग्राम सेट करके शुरू होता है। (मुझे नहीं लगता कि यह हार्ड-वायरिंग नियम का गलत है, क्योंकि ये इन नंबरों को बनाने के सबसे छोटे तरीके हैं। मैं पुनर्व्यवस्थित कर सकता हूं। मेरा कोड इसलिए मैं अपने गतिशील प्रोग्रामिंग में इन पैटर्नों की जांच करता हूं यदि आप चाहते हैं)। फिर विभिन्न रूपों की कोशिश करते हुए एक आंशिक गतिशील प्रोग्रामिंग दृष्टिकोण करें:
- ए + बी
- ए * बी + सी
- ए! + बी
- 11 .... 11 + बी
दुर्भाग्य से मैं एक नंबर को डिकम्पोज करने के सभी तरीकों की कोशिश नहीं कर सकता हूं, इसलिए मैं फैक्टरियल और 11 ... 11 के लिए चुनता हूं केवल निकटतम संख्या का प्रयास करने के लिए, ए + बी के लिए ए / 2 के पास चीजों की कोशिश करने के लिए, और ए * बी + के लिए। सी केवल काफी छोटे रूप में प्रयास करने के लिए।
थोड़े-थोड़े समय के अंतराल पर (विशेष रूप से A * B - C) ओवरशूट करने की कोशिश करके, कुछ को '' आज़माने के लिए इसे बढ़ाना आसान होगा, लेकिन मुझे केवल बढ़ने की कोशिश करना पसंद है।
इसके अलावा, अनुकूलन स्थिति को अनुकूलित करना बहुत मुश्किल है (मुझे यह पसंद नहीं है!) क्योंकि सिद्धांत रूप में आप अलगाव में प्रत्येक संख्या के लिए 'सर्वोत्तम' मूल्य के साथ नहीं आ सकते हैं, आपको विश्व स्तर पर अपने उत्तरों पर विचार करना होगा। (जो मैं करने का इरादा नहीं है)।
चेतावनी: इस कार्यक्रम के लिए 64-बिट मशीन और लगभग 10GB मेमोरी की आवश्यकता होती है (जैसा कि मैं अक्षम रूप से सभी आंशिक रूप से गणना किए गए परिणामों के लिए एक विशाल सरणी बनाता हूं)।
कार्यक्रम:
#include <algorithm>
#include <vector>
#include <string>
#include <assert.h>
#include <iostream>
#include <cmath>
std::vector<int> numints;
std::vector<int> numops;
std::vector<std::string> strings;
void fill_all_ones(long maxval)
{
int val = 1;
int len = 1;
std::string name = "1";
while(val < maxval) {
val = val * 10 + 1;
len++;
name = name + "1";
numints[val] = len;
strings[val] = name;
}
}
void get_best_for_next_full(long i);
// let's just assume this is the best way to make factorials
void fill_all_factorials(long maxval)
{
// skip 1 and 2
long result = 6;
long val = 3;
while(result < maxval) {
get_best_for_next_full(val);
strings[result] = "(" + strings[val] + ")!";
numints[result] = numints[val];
numops[result] = numops[val] + 1;
val++;
result = result * val;
}
}
long get_nearest_all_ones(long i)
{
int val = 11;
int prevval = 1;
while(val < i) {
prevval = val;
val = val * 10 + 1;
}
return prevval;
}
long get_nearest_factorial(long i)
{
int val = 6;
int prevval = 2;
int step = 3;
while(val < i) {
prevval = val;
step++;
val = val * step;
}
return prevval;
}
int getlen(long i);
void get_best_for_next_full(long i)
{
if(numints[i] > 0)
return;
int best = INT_MAX; // we'll do better than this
std::string beststring = "invalid2";
int ones = -1;
int ops = -1;
for(long loop = 1; loop <= i/2; loop++)
{
int new_val = getlen(loop) + getlen(i - loop);
if(new_val < best) {
best = new_val;
ones = numints[loop] + numints[i - loop];
beststring = "(" + strings[loop] + "+" + strings[i - loop] + ")";
ops = numops[loop] + numops[i - loop] + 1;
}
}
for(long loop = 2; loop * loop <= i; loop++)
{
long divisor = i / loop;
long rem = i - loop*divisor;
assert(rem >= 0);
int new_val;
if(rem == 0)
{
new_val = getlen(divisor) + getlen(loop);
}
else
{
new_val = getlen(divisor) + getlen(rem) + getlen(loop);
}
if(new_val < best) {
best = new_val;
if(rem == 0) {
ones = numints[divisor] + numints[loop];
beststring = "(" + strings[divisor] + "*" + strings[loop] + ")";
ops = numops[divisor] + numops[loop] + 1;
} else {
ones = numints[divisor] + numints[loop] + numints[rem];
beststring = "(" + strings[divisor] + "*" + strings[loop] + "+" + strings[rem] + ")";
ops = numops[divisor] + numops[loop] + numops[rem] + 2;
}
}
}
numints[i] = ones;
strings[i] = beststring;
numops[i] = ops;
}
void check_divising(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops);
void check_adding(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops);
void get_best_for_next_partial(long i)
{
if(numints[i] > 0)
return;
long best = INT_MAX; // we'll do better than this
long ones = 1;
std::string beststring = "invalid";
long ops = 1;
// Special: Try a nearby all ones
{
long loop = get_nearest_all_ones(i);
check_adding(i, loop, best, ones, beststring, ops);
}
// Special: Try nearest factorial
{
long loop = get_nearest_factorial(i);
check_adding(i, loop, best, ones, beststring, ops);
}
for(long loop = 2; loop * loop <= i; loop++)
{
check_divising(i, loop, best, ones, beststring, ops);
}
numints[i] = ones;
strings[i] = beststring;
numops[i] = ops;
}
void check_adding(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops)
{
int new_val = getlen(loop) + getlen(i - loop);
if(new_val < best) {
best = new_val;
ones = numints[loop] + numints[i - loop];
beststring = "(" + strings[loop] + "+" + strings[i - loop] + ")";
ops = numops[loop] + numops[i - loop] + 1;
}
}
void check_divising(const long i, const long loop, long& best, long& ones, std::string& beststring, long& ops)
{
long divisor = i / loop;
long rem = i - loop*divisor;
assert(rem >= 0);
int new_val;
if(rem == 0)
{
new_val = getlen(divisor) + getlen(loop);
}
else
{
new_val = getlen(divisor) + getlen(rem) + getlen(loop);
}
if(new_val < best) {
best = new_val;
if(rem == 0) {
ones = numints[divisor] + numints[loop];
beststring = "(" + strings[divisor] + "*" + strings[loop] + ")";
ops = numops[divisor] + numops[loop] + 1;
}
else {
ones = numints[divisor] + numints[loop] + numints[rem];
beststring = "(" + strings[divisor] + "*" + strings[loop] + "+" + strings[rem] + ")";
ops = numops[divisor] + numops[loop] + numops[rem] + 2;
}
}
}
long count = 0;
long countops = 0;
const int little_cutoff = 200000;
int getlen(long i)
{
if(numints[i] == 0) {
if(i < little_cutoff)
get_best_for_next_full(i);
else
get_best_for_next_partial(i);
}
if(numints[i] == 0) {
std::cout << i << " failure!" << numops[i] << ":" << strings[i] << std::endl;
exit(1);
}
return numints[i] + numops[i];
}
const std::vector<long> vals = {945536, 16878234, 32608778, 42017515, 48950830, 51483452, 52970263, 54278649, 63636656, 78817406, 89918907, 90757642, 95364861, 102706605, 113965374, 122448605, 126594161, 148064959, 150735075, 154382918, 172057472, 192280850, 194713795, 207721209, 220946392, 225230299, 227043979, 241011012, 248906099, 249796314, 250546528, 258452706, 276862988, 277140688, 280158490, 286074562, 308946627, 310972897, 322612091, 324445400, 336060042, 346729632, 349428326, 352769482, 363039453, 363851029, 392168304, 401975104, 407890409, 407971913, 425780757, 459441559, 465592122, 475898732, 482826596, 484263150, 506235403, 548951531, 554295842, 580536366, 587051904, 588265985, 588298051, 590968352, 601194306, 607771869, 618578932, 626776380, 667919873, 681786366, 689854904, 692055400, 697665495, 711608194, 734027104, 750869335, 757710567, 759967747, 777616154, 830071127, 833809927, 835873060, 836438554, 836945593, 863728236, 864158514, 871273503, 881615667, 891619600, 897181691, 918159061, 920521050, 924502226, 929983535, 943162304, 950210939, 950214176, 962610357, 974842859, 988572832};
const long biggest = 988572832;
int main(void)
{
numints.push_back(2);
strings.push_back("(1-1)");
numops.push_back(1);
numints.push_back(1);
strings.push_back("1");
numops.push_back(0);
numints.push_back(2);
strings.push_back("(1+1)");
numops.push_back(1);
numints.resize(biggest + 1);
strings.resize(biggest + 1);
numops.resize(biggest + 1);
fill_all_ones(biggest);
fill_all_factorials(biggest);
for(long i = 0; i < little_cutoff; ++i)
get_best_for_next_full(i);
for(long v : vals) {
get_best_for_next_partial(v);
std::cout << v << ":" << strings[v] << "\n";
count += numints[v];
countops += numops[v];
}
std::cout << count << ":" << countops << ":" << count * countops << "\n";
}
परिणाम:
945536:((1111*(1+(11+11))+(1+1))*((1+11)*(1+(1+1))+1)+1)
16878234:(((1+(1+1111))*(1+(1+(1+111)))+(11+11))*((1+11)*11+1)+(1+1))
32608778:((((((1+(1+1)))!+(111+11111))*(11*11)+111)*(1+11)+1)*(1+1))
42017515:((11)!+((((1+111)*11)*11+1)*((1+11)*(1+11)+11)))
48950830:((((11+11)*(1+11))+(11111*(1+(1+1))))*((1+111)*(1+(1+11))+1)+1)
51483452:(((1+(1+1111))*(1+111)+1)*(11+(((1+11)*11+(1+1))*(1+(1+1))))+111)
52970263:((11+((1111*11+(1+(1+1)))*(1+(1+1))))*(111*(1+(1+11))+1)+11)
54278649:((11)!+(((1+(11+(11+(11+1111))))*111+1)*(1+(1+111))+1))
63636656:((((11+111)*(1+(1+1)))*(1+111)+11)*(1+(111+((((1+(1+1)))!)!*(1+1)))))
78817406:(((((111*(11+11)+1)*(1+1))*(1+111)+111)*(1+11)+1)*(1+11)+(1+1))
89918907:(((111+((1+(1+((1+(1+1)))!)))!)*(1+1))*(1+1111)+((11*11)*(1+(1+1))))
90757642:((1111+((11+11111)*(1+1)))*(111*(11+((1+(1+(1+1))))!)+1)+(1+111))
95364861:((11)!+(((((((11+11)*11)+11111)*111)*11+(1+1))*(1+1))*(1+1)+1))
102706605:(((11)!+(((111+((11*11)*11))*(1+(((1+(1+1)))!)!))*11))*(1+1)+1)
113965374:((((111*(1+(1+(1+11))))*1111+((1+(11+11))*11+1))*11+1)*((1+(1+1)))!)
122448605:(((((1+(1+1)))!)!+((111*11)*11))*((1+(((1+(1+1)))!)!)*(1+11)+1)+(1+1))
126594161:(((((11*11)+(((1+(1+1)))!)!)*(1+111))*(1+11)+1)*(1+111)+1)
148064959:((11)!+(((111*111+(1+11))*111+1)*((1+(1+11))*((1+(1+1)))!+1)+(1+(1+1))))
150735075:(((111*111+(1+1))*(1+1111)+(1+11))*11+(1+((1+(1+1)))!))
154382918:((1111*(1+11)+1)*(((1+(11+(111+111)))*(1+1))+11111)+111)
172057472:((((((1+11)*11)*11+1)*(1+(1+1)))+11111)*(11+11111)+((1+11)*11))
192280850:(((11111*(1+11)+11)*(1+(((1+(1+1)))!)!)+(11+111))*(1+1))
194713795:((11)!+((((111+11111)*(1+(1+(1+111)))+((1+(1+1)))!)*11)*11+1))
207721209:(((111*111)*(1+(11+11))+(1+1))*(1+(1+(11+(((1+(1+1)))!)!)))+(1+(1+(1+1))))
220946392:((11)!+((((1+(1+(1+1111)))*(11+111))*111+11)*(1+11)+(1+(1+(1+1)))))
225230299:((111111111+((111*111+(1+((1+(1+1)))!))*(11+111)+(11+11)))*(1+1)+1)
227043979:((((((11+11)*11)+11111)*(1+(1+1))+1)*1111+(1+(1+1)))*((1+(1+1)))!+1)
241011012:(((11)!+((11)!+((11)!+((11+1111)*((1+111)*((1+(1+1)))!+1)))))*(1+1))
248906099:(((11111+(((((1+(1+1)))!)!*111)*(1+1)))*(1+111)+111)*(1+(1+11)))
249796314:(((11)!+(((((1+(1+1)))!)!+((1+1111)*(1+11)))*(11+111)+111))*((1+(1+1)))!)
250546528:((11)!+(((111*111)*(1+(1+(1+11)))+11)*(111*11)+(1+(11+1111))))
258452706:(((11)!+(((((1+(1+1)))!)!*((1+(1+1)))!+1)*(11+(((1+(1+1)))!)!)))*((1+(1+1)))!)
276862988:(((11+(1111*(1+1)))*(((1+(1+1)))!+1111))*111+(((1+(1+1)))!+11))
277140688:(((111*111+(1+(1+(1+(1+11)))))*(1+1))*(11+(111+11111))+(1+111))
280158490:((11)!+(((1+(111+111111))*(((1+(1+1)))!)!+(1+(1+1)))*(1+(1+1))+1))
286074562:(((11)!+((((11+1111)*(11+11))*(1+1)+1)*(1+(11+1111))))*(1+(1+1))+1)
308946627:((11)!+((((1+1111)*(((1+(1+1)))!)!+((11+11)*(1+1)))*(1+111)+1)*(1+(1+1))))
310972897:((11111*(1+(1+1))+1)*(((1111+(111*11))*(1+1))*(1+1)+1)+11)
322612091:((((((1+11)*(1+11))*(1+11)+(1+1))*111+1)*(1+111))*(1+(1+(1+(1+11))))+11)
324445400:(((1111111+(1+(1+1)))*(1+1))*((1+11)*(1+11)+(1+1))+(1+111))
336060042:(((1+1111)*(1+(11+111))+(1+111))*(11+((111*11+1)*(1+1)))+(1+1))
346729632:(((1+(1+(11111+(111*111))))*((1+111)*11+1)+(1+(1+(1+11))))*(1+11))
349428326:(((((11+11)*11)*11+1)*(1+1111)+1)*(1+(((1+(1+1)))!+111)))
352769482:(((1+11111)*(111*(11+11))+((11+111)*((1+1)*(1+1)+1)))*(1+(1+11)))
363039453:(((((1+111)*(1+111)+1)*(1+1))*(1+(1+11))+11)*(1+(1+1111)))
363851029:((((111*11+1)*1111+11)*((1+11)*11+(1+1))+(1+11))*(1+1)+1)
392168304:(((((1+(1+1111))*(1+111))*11+1)*(1+(1+11))+11)*(11+11))
401975104:(((((1+11)*(1+11)+1)*111)*111+11)*((1+111)*(1+1)+1)+(1+(1+(1+1))))
407890409:(((1+11111)*11)*((1+1111)*(1+(1+1))+1)+((1+1111)*(1+1)+1))
407971913:((11)!+((11)!+(((1+(1+11111))*(1+1)+1)*(((11+111)*11)*11+1)+(1+1111))))
425780757:(((1111+((((1+11)*11)+11111)*(1+(1+1))))*11+1)*1111+((1+(1+1)))!)
459441559:(((11111+(((1+(1+111))*(1+1)+1)*111))*111+1)*(1+(1+(1+111)))+(1+(1+11)))
465592122:(((11)!+((((1111*(11*(1+(1+1))+1)+1)*(1+(11+11)))*(1+1)+1)*111))*(1+1))
475898732:(((11)!+(((((1+111)*11+(1+1))*(1+11))*(1+1)+1)*(1+(1+111))))*11+1)
482826596:(((1+(((111*11)*11)+(11111*(1+1))))*111+1)*(11+111)+((1+(1+1)))!)
484263150:(((111*111+(1+(1+1)))*111+11)*(1+(111+((11+11)*11))))
506235403:(((1+11))!+((((1+(1+1111))*(1+1111)+((11+111)*(1+1)))*11+1)*(1+1)+1))
548951531:((((111+111)*(1+1)+1)*111+11)*11111+((11+111)*(1+11)+1))
554295842:(((1+11))!+((((1+1111)*111+1)*((1+1)*(1+1)+1))*(11+111)+(1+111)))
580536366:(((1+(111+((111*111+11)*(1+11))))*(1+111)+1)*(11+((1+(1+(1+1))))!)+11)
587051904:(((((1+1111)*(1+11))*(1+(1+1))+1)*(111*11+1)+(111*((1+(1+1)))!))*(1+11))
588265985:(((1+11))!+((1+(111+(1111*(1+(1+11)))))*((1+111)*(11*((1+(1+1)))!+1)+(1+(1+1)))))
588298051:((((((11+111)*11)*11)+(11111*(1+(1+1))))*(1+1111)+1)*11)
590968352:(((((((1+(1+1)))!)!+11111)*111+(11+11))*((1+111)*(1+1)+1)+1)*(1+1))
601194306:((((1111*(1+(1+(1+(11+111))))+1)*111+(1+1))*(1+(1+1))+1)*(1+(1+11))+11)
607771869:(((1+11))!+(((11)!+(((1111*11+1)*(1+1))*(1+(11+111))+11))*(1+(1+1))))
618578932:(((((1111*111)*11+1)*(1+1)+1)*(1+1))*(1+(1+(1+111)))+(1+111))
626776380:((((1+(1+(1+1))))!+((((1+(1+1)))!)!+(1111*111)))*(1+(11+((1+((1+(1+1)))!))!)))
667919873:((((((1+(11+111))*11+1)*111+(1+(1+1)))*1111+1)*(1+1))*(1+1)+1)
681786366:(((1+11))!+((11)!+(((11)!+((11)!+((1+(1+11111))*((1+11)*(1+11))+111)))*(1+1))))
689854904:(((11+((11111+((1+1111)*11))*(1+1)))*((11+111)*11+1)+11)*11+(1+1))
692055400:(((1+11))!+(((((1+(1+111))*(1+(1+(1+11))))*11)*11+1)*(1+(1+1111))+1))
697665495:(((1+11))!+(((((((1+(1+1)))!)!*(1+(1+(1+111)))+1)*(1+11))*(1+1)+1)*111))
711608194:(((11)!+(((1+(1+(1+(1+1111))))*(11+((11+111)*(1+1)))+(1+1))*1111))*(1+1))
734027104:(((111*(11+((1+(1+(1+1))))!)+1)*(((1+(1+1)))!+11)+1)*11111+1111)
750869335:((11111111+((1+(((1+(1+1)))!)!)*((1+11)*11+1)+1))*(11*((1+(1+1)))!+1))
757710567:((((((11+111)*11)+111111)*(1+(1+1))+1)*(1+(11+1111))+(1+(1+1)))*(1+1)+1)
759967747:(((11)!+(((1+(1+(111+11111)))*(1+(1+111)))*(1+(11+11))+1))*11)
777616154:((11111*(111+(((111*11+1)*(1+1))*(1+1)))+(11+111))*(1+(1+(1+11))))
830071127:((((1+111)*111)*((1+(1+1)))!+1)*(((1+(1+1)))!+(11+11111))+(111*(1+1)+1))
833809927:((((11+1111)*(1+1)+1)*111+1)*(1+(1+(11+(1111*(1+(1+1))))))+111)
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