সি ++: স্কোর = 453,324,048
ঠিক আছে, এটি পুনরায় কাজ করতে কিছু সময় প্রয়োজন, তবে আমি এটি সমাধান করার উপায় এখানে।
সমাধান স্থান অধ্যয়ন করার পরে, আমি স্থির করেছিলাম যে আমার কৌশলটি হবে:
- লক্ষ্য সংখ্যার কাছাকাছি যাওয়ার জন্য দক্ষিণ পদক্ষেপগুলি ব্যবহার করে
- যদি লক্ষ্যটি ইতিবাচক হয় তবে এই পথটি অনুসরণ করুন: nnnesssssessssssss
- যদি লক্ষ্যটি নেতিবাচক হয় তবে এই পথটি অনুসরণ করুন: esssssssseessssss গ। যদি লক্ষ্যটি 0 থেকে 20 এর মধ্যে হয় তবে এটি "পুরানো ফ্যাশন পথ" সমাধান করুন (আমরা যতক্ষণ না পৌঁছাচ্ছি ততবার সম্ভাব্য পথের উপর ট্রেইল এবং ত্রুটি)।
- একবার আমাদের "সেরা স্থান" হয়ে গেলে ("ওভার" না দিয়ে লক্ষ্যের কাছাকাছি পৌঁছান), আমরা 2 বা 3 দ্বারা গুণ করে আরও কাছে যেতে সক্ষম হতে পারি; সুতরাং 0 থেকে 9 পদক্ষেপের পূর্ব দিকে যান এবং তারপরে দক্ষিণে এক ধাপ। সেই পথটি রাখুন যা আমাদের লক্ষ্যটির সবচেয়ে নিকটতম হয়।
- "রান" উত্তর বা পূর্বদিকে ততক্ষণ আমরা লক্ষ্যমাত্রার 45 পয়েন্টের মধ্যে আছি (প্রতি 10 ধাপে উত্তরে, স্কোরের 45 পয়েন্ট যুক্ত করুন, প্রতি 10 ধাপ পূর্বে, স্কোরকে 45 দ্বারা হ্রাস করবে)।
- আমরা লক্ষ্যটির 10 পয়েন্টের মধ্যে রয়েছি না কেন একই দিকে আরও কয়েকটি পদক্ষেপ নিন
- এই জায়গা থেকে "পুরানো ফ্যাশন উপায়" করুন, এটি এখন এত কঠিন হওয়া উচিত নয়।
এখানে আমার ফলাফল: মোট স্কোর 453324048
এবং পথগুলি:
0) to reach 49445094, it takes 1311037 steps, by doing: nnnesssssesssssseeeeese(n * 1311010)enen
1) to reach 71259604, it takes 1320313 steps, by doing: nnnesssssesssssseeeeeese(n * 1320280)nnnnnneee
2) to reach 78284689, it takes 1956998 steps, by doing: nnnesssssesssssseeeeeees(e * 1956970)eeee
3) to reach 163586986, it takes 2483885 steps, by doing: nnnesssssessssssse(n * 2483860)nnnnnnn
4) to reach 171769219, it takes 4302163 steps, by doing: nnnesssssessssssse(n * 4302130)nnnnnnnnnnennnn
5) to reach 211267178, it takes 13079485 steps, by doing: nnnesssssessssssse(n * 13079460)nnnnnen
6) to reach 222235492, it takes 15516886 steps, by doing: nnnesssssessssssse(n * 15516860)nnnnnnnn
7) to reach 249062828, it takes 12390325 steps, by doing: nnnesssssessssssseeees(e * 12390290)eeeeenenneene
8) to reach 252588742, it takes 11606785 steps, by doing: nnnesssssessssssseeees(e * 11606760)een
9) to reach 263068669, it takes 9277915 steps, by doing: nnnesssssessssssseeees(e * 9277880)eeeeenennneee
10) to reach 265657839, it takes 8702543 steps, by doing: nnnesssssessssssseeees(e * 8702510)eeeeenennee
11) to reach 328787447, it takes 5326312 steps, by doing: nnnesssssessssssseeeese(n * 5326280)nnnnennnn
12) to reach 344081398, it takes 8724966 steps, by doing: nnnesssssessssssseeeese(n * 8724940)enn
13) to reach 363100288, it takes 12951386 steps, by doing: nnnesssssessssssseeeese(n * 12951360)enn
14) to reach 363644732, it takes 13072373 steps, by doing: nnnesssssessssssseeeese(n * 13072340)nnnnnnnnen
15) to reach 372642304, it takes 15071833 steps, by doing: nnnesssssessssssseeeese(n * 15071800)nnnnnnnenn
16) to reach 374776630, it takes 15546133 steps, by doing: nnnesssssessssssseeeese(n * 15546100)nnnnnenene
17) to reach 377945535, it takes 16250331 steps, by doing: nnnesssssessssssseeeese(n * 16250300)nnnnennn
18) to reach 407245889, it takes 11107325 steps, by doing: nnnesssssessssssseeeees(e * 11107300)ne
19) to reach 467229432, it takes 2222403 steps, by doing: nnnesssssessssssseeeeese(n * 2222370)nnnnnnnee
20) to reach 480714605, it takes 5219109 steps, by doing: nnnesssssessssssseeeeese(n * 5219080)neenn
21) to reach 491955034, it takes 7716983 steps, by doing: nnnesssssessssssseeeeese(n * 7716950)nnnnennnn
22) to reach 522126455, it takes 14421745 steps, by doing: nnnesssssessssssseeeeese(n * 14421710)nnnnnneneee
23) to reach 532351066, it takes 16693875 steps, by doing: nnnesssssessssssseeeeese(n * 16693850)n
24) to reach 542740616, it takes 14866179 steps, by doing: nnnesssssessssssseeeeees(e * 14866150)eeeen
25) to reach 560336635, it takes 10955953 steps, by doing: nnnesssssessssssseeeeees(e * 10955920)eeeeennen
26) to reach 563636122, it takes 10222731 steps, by doing: nnnesssssessssssseeeeees(e * 10222700)eeeeene
27) to reach 606291383, it takes 743785 steps, by doing: nnnesssssessssssseeeeees(e * 743760)e
28) to reach 621761054, it takes 2693968 steps, by doing: nnnesssssessssssseeeeeese(n * 2693940)nnn
29) to reach 648274119, it takes 8585761 steps, by doing: nnnesssssessssssseeeeeese(n * 8585730)nnnnnn
30) to reach 738259135, it takes 5286413 steps, by doing: nnnesssssessssssseeeeeees(e * 5286380)eeneneee
31) to reach 738287367, it takes 5280141 steps, by doing: nnnesssssessssssseeeeeees(e * 5280110)nneenn
32) to reach 748624287, it takes 2983042 steps, by doing: nnnesssssessssssseeeeeees(e * 2983010)eeeenee
33) to reach 753996071, it takes 1789313 steps, by doing: nnnesssssessssssseeeeeees(e * 1789280)eeeennee
34) to reach 788868538, it takes 5960183 steps, by doing: nnnesssssessssssseeeeeeese(n * 5960150)nnenene
35) to reach 801184363, it takes 8697033 steps, by doing: nnnesssssessssssseeeeeeese(n * 8697000)nnenene
36) to reach 807723631, it takes 10150197 steps, by doing: nnnesssssessssssseeeeeeese(n * 10150170)n
37) to reach 824127368, it takes 13795475 steps, by doing: nnnesssssessssssseeeeeeese(n * 13795440)nnnnnnnne
38) to reach 824182796, it takes 13807795 steps, by doing: nnnesssssessssssseeeeeeese(n * 13807760)nnnnnenee
39) to reach 833123975, it takes 15794722 steps, by doing: nnnesssssessssssseeeeeeese(n * 15794690)nennnn
40) to reach 849666906, it takes 14397917 steps, by doing: nnnesssssessssssseeeeeeees(e * 14397880)eeeeeeeenee
41) to reach 854952292, it takes 13223389 steps, by doing: nnnesssssessssssseeeeeeees(e * 13223350)eeeeeeeeneeen
42) to reach 879834610, it takes 7693981 steps, by doing: nnnesssssessssssseeeeeeees(e * 7693950)eeenn
43) to reach 890418072, it takes 5342102 steps, by doing: nnnesssssessssssseeeeeeees(e * 5342070)eeennn
44) to reach 917604533, it takes 699395 steps, by doing: nnnesssssessssssseeeeeeeese(n * 699360)nnnneene
45) to reach 932425141, it takes 3992863 steps, by doing: nnnesssssessssssseeeeeeeese(n * 3992830)nennnn
46) to reach 956158605, it takes 9266963 steps, by doing: nnnesssssessssssseeeeeeeese(n * 9266930)nnnnen
47) to reach 957816726, it takes 9635434 steps, by doing: nnnesssssessssssseeeeeeeese(n * 9635400)nnnennn
48) to reach 981534928, it takes 14906145 steps, by doing: nnnesssssessssssseeeeeeeese(n * 14906110)nnnnnnnn
49) to reach 987717553, it takes 16280059 steps, by doing: nnnesssssessssssseeeeeeeese(n * 16280030)nn
আমি নিশ্চিত যে কিছু ক্লিভার "দক্ষিণ / পশ্চিম" চাল (4 দ্বারা বিভাজক এবং 5 দ্বারা গুণমান; উদাহরণস্বরূপ) এর মাধ্যমে উন্নতি করার উপায় আছে; তবে এটিকে কোডিং করা এবং নিশ্চিত হওয়া যে আপনি কোলে নেমেছেন না বা আটকা পড়েছেন না তা জটিল y
আর একটি সমাধানের পথ হতে পারে লক্ষ্য থেকে কোনও "যুক্তিসঙ্গত" সংখ্যায় ফিরে যাওয়ার চেষ্টা করা এবং তারপরে কেবল সেই ছোট সংখ্যার পথ খুঁজে পাওয়া; তবে আপনাকে এটি ঠিক "লক্ষ্য" করতে হবে, যাতে পদক্ষেপের সংখ্যাটি মেলে। কৌশলযুক্ত, তবে এটি সমাধানের সেরা উপায় হতে পারে।
যাইহোক, এখানে আমার কোড কোডটি রয়েছে:
#include <stdio.h>
#include <vector>
#include <queue>;
using namespace std;
long long upperLimit;
long long lowerLimit;
bool bDebugInfo = false;
//bool bDebugInfo = true;
// a point struct (x and y)
struct point
{
int x;
int y;
point():x(0),y(0)
{
}
bool operator ==(const point& other)
{
return (x==other.x) && (y==other.y);
}
void ApplyDirection(char direction)
{
switch (direction)
{
case 'n':
y++;
break;
case 'w':
x--;
break;
case 'e':
x++;
break;
case 's':
y--;
break;
}
}
};
// each state is of this formate
struct botState
{
int nStep;
long long number;
vector<char> path;
botState()
:nStep(0),
number(0)
{
}
botState* clone()
{
botState* tmp = new botState();
tmp->nStep = nStep;
tmp->number = number;
tmp->path = path;
return tmp;
}
void clone(botState* other)
{
nStep = other->nStep;
number = other->number;
path = other->path;
}
};
bool changeNumberWithDirection(long long &number, char direction, int step)
{
switch (direction)
{
case 'n':
number += (step%10);
break;
case 'w':
if (step%10)
number /= (step%10);
else
return false;
break;
case 'e':
number -= (step%10);
break;
case 's':
number *= (step%10);
break;
default:
return false;
}
return true;
}
bool tryToAddStep(queue<botState*>& queueOfStates, const botState* pState, char direction, char cStarDirection)
{
botState* pTmpState;
long long newNumber;
int newStep = pState->nStep+1;
newNumber = pState->number;
if (!changeNumberWithDirection(newNumber, direction, newStep))
return false;
if (newNumber > upperLimit)
return false;
if (newNumber < lowerLimit)
return false;
if ((newNumber == 0) && (newStep%10 == 0))
return false; // no need to return back to 0 after 10 or more steps, we already have better ways to do this.
// build the x,y points of the path up to this point
point tmpPoint;
vector<point> pointsInPath;
pointsInPath.push_back(tmpPoint);
for (int i=0; i<pState->path.size(); i++)
{
if (pState->path.at(i) == '*')
{
for (int j=0; j<100; j++)
{
tmpPoint.ApplyDirection(cStarDirection);
pointsInPath.push_back(tmpPoint);
}
}
else
{
tmpPoint.ApplyDirection(pState->path.at(i));
pointsInPath.push_back(tmpPoint);
}
}
tmpPoint.ApplyDirection(direction);
// check for over lap
for (int i=0; i<pointsInPath.size(); i++)
{
if (tmpPoint == (pointsInPath.at(i)))
return false;
}
pTmpState = new botState();
pTmpState->nStep = newStep;
pTmpState->number= newNumber;
pTmpState->path = pState->path;
pTmpState->path.push_back(direction);
queueOfStates.push(pTmpState);
return true;
}
bool isBetterNum(long long newNum, long long oldBest, long long target)
{
long long newDiff = (newNum > target) ? newNum - target : target - newNum ;
long long oldDiff = (oldBest > target) ? oldBest - target : target - oldBest;
return (newDiff < oldDiff);
}
bool tryToJumpDown(long long num, botState* pState, int& nTimes)
{
// if where the bot is, we have a clear path to go as far east as we could ever want, we can just do as many sets of eeeeeeeeee (e*10) as needed, til we are close enough to the target
point tmpPoint;
vector<point> pointsInPath;
pointsInPath.push_back(tmpPoint);
for (int i=0; i<pState->nStep; i++)
{
tmpPoint.ApplyDirection(pState->path.at(i));
pointsInPath.push_back(tmpPoint);
}
for (int i=0; i<pointsInPath.size(); i++)
{
if ((pointsInPath.at(i).x > tmpPoint.x) && (pointsInPath.at(i).y == tmpPoint.y))
return false; // we have a point blocking our path up!
}
long long tmpTimes = (pState->number - num)/45;
if ((tmpTimes>1) && (tmpTimes<upperLimit))
{
tmpTimes--;
tmpTimes*=10;
nTimes = (int)tmpTimes;
pState->nStep+=nTimes;
pState->number-=(tmpTimes/10)*45;
pState->path.push_back('*');
return true;
}
return false;
}
bool tryToJumpUp(long long num, botState* pState, int& nTimes)
{
// if where the bot is, we have a clear path to go as far north as we could ever want, we can just do as many sets of nnnnnnnnnn (n*10) as needed, til we are close enough to the target
point tmpPoint;
vector<point> pointsInPath;
pointsInPath.push_back(tmpPoint);
for (int i=0; i<pState->nStep; i++)
{
tmpPoint.ApplyDirection(pState->path.at(i));
pointsInPath.push_back(tmpPoint);
}
for (int i=0; i<pointsInPath.size(); i++)
{
if ((pointsInPath.at(i).x == tmpPoint.x) && (pointsInPath.at(i).y > tmpPoint.y))
return false; // we have a point blocking our path up!
}
long long tmpTimes = (num - pState->number)/45;
if ((tmpTimes>1) && (tmpTimes<upperLimit))
{
tmpTimes--;
tmpTimes*=10;
nTimes = (int)tmpTimes;
pState->nStep+=nTimes;
pState->number+=(tmpTimes/10)*45;
pState->path.push_back('*');
return true;
}
return false;
}
typedef char* PChar;
bool buildPath(long long num, PChar& str, int& nLen, int& nScore, botState* startState, int nTimes)
{
long long nBest = 0;
int nMaxSteps = 0;
long long nMax = 0;
long long nMin = 0;
int nCleanUpOnStep= 12;
long long nFromLastCleanUp = 0;
bool bInCleanUp = false;
char cDirection = ' ';
if (nTimes>0)
cDirection = 'n';
else if (nTimes<0)
{
cDirection = 'e';
nTimes*=-1;
}
if (startState->nStep >= nCleanUpOnStep)
nCleanUpOnStep= startState->nStep+10;
str = NULL;
nLen = 0;
botState* bestState = new botState();
bestState->clone(startState);
queue<botState*> queueOfStates;
queueOfStates.push(bestState); // put the starting state into the queue
while (!queueOfStates.empty()) // while we still have states in the queue, process them
{
botState* pState = queueOfStates.front();
queueOfStates.pop(); // take a state out of the queue
if (!str) // no solution yet
{
if (pState->number == num) // check if this is a solution
{
// we solved it!
int nOffset=0;
nLen = pState->nStep - nTimes + 17;
str = new char[nLen+1];
if (bDebugInfo)
printf("solved!\n");
nScore = pState->nStep;
for (int i=0; i<pState->path.size(); i++)
{
if (pState->path.at(i)=='*')
{
sprintf(str+i, "(%c * %11d)", cDirection, nTimes);
if (bDebugInfo)
printf("(%c * %11d)", cDirection, nTimes);
nOffset=16;
}
else
{
str[i+nOffset] = pState->path.at(i);
if (bDebugInfo)
printf("%c", str[i+nOffset]);// print solution while making the string
}
}
if (bDebugInfo)
printf("\n");
str[nLen]='\0';
}
else
{ // no solution yet, we need to go deeper
if (pState->number < nMin)
nMin = pState->number;
if (pState->number > nMax)
nMax = pState->number;
if ((!bInCleanUp) && (queueOfStates.size()>1000000))
{
nCleanUpOnStep=nMaxSteps+10;
bInCleanUp = true;
}
if (pState->nStep > nMaxSteps)
{ // a little tracing, so we can see progress
nMaxSteps = pState->nStep;
// printf("current states have %d steps, reached a max of %lld, and a min of %lld\n", nMaxSteps, nMax, nMin);
if (nMaxSteps >= nCleanUpOnStep)
{
nCleanUpOnStep+=10;
bInCleanUp = true;
}
}
if (isBetterNum(pState->number, nBest, num))
{ // a little tracing, so we can see progress
nBest = pState->number;
if (bDebugInfo)
printf("Got closer to the target, %lld, with %d steps (target is %lld, diff is %lld)\n", nBest, pState->nStep, num, num-nBest);
if (bestState != pState)
delete bestState;
bestState = pState;
}
if (!bInCleanUp)
{
tryToAddStep(queueOfStates, pState, 'n', cDirection);
tryToAddStep(queueOfStates, pState, 'e', cDirection);
if (!nTimes) // once we did the "long walk in one direction" don't do the west or south moves any more
{
tryToAddStep(queueOfStates, pState, 'w', cDirection);
tryToAddStep(queueOfStates, pState, 's', cDirection);
}
}
}
}
if (pState!=bestState)
delete pState; // this is not java, we need to keep the memory clear.
if ((bInCleanUp) && (queueOfStates.empty()))
{
queueOfStates.push(bestState); // put the starting state into the queue
bInCleanUp = false;
long long diff = nFromLastCleanUp-bestState->number;
if (!nTimes)
{
if ((diff>0) && (diff<100))
if (tryToJumpDown(num, bestState, nTimes))
cDirection = 'e';
if ((diff<0) && (diff>-100))
if (tryToJumpUp(num, bestState, nTimes))
cDirection = 'n';
if (nTimes)
nCleanUpOnStep = bestState->nStep;
}
nFromLastCleanUp = bestState->number;
}
}
delete bestState; // this is not java, we need to keep the memory clear.
return str!=NULL;
}
char* positiveSpine = "nnnesssssessssssss";
char* negativeSpine = "esssssssseessssss";
bool canReachNumber(long long num, PChar& str, int& nLen, int& nScore)
{
int nTimes = 0;
botState tmpState;
if ((num>=0) && (num<=20))
return buildPath(num, str, nLen, nScore, &tmpState, nTimes);
botState bestState;
bestState.clone(&tmpState);
char* spine = NULL;
if (num>0)
{
spine = positiveSpine;
}
else
{
spine = negativeSpine;
}
for (int i=0; spine[i]; i++)
{
tmpState.nStep++;
tmpState.path.push_back(spine[i]);
if (!changeNumberWithDirection(tmpState.number, spine[i], tmpState.nStep))
return false;
if ((num>0) && (tmpState.number<num))
{
bestState.clone(&tmpState);
}
else if ((num<0) && (tmpState.number>num))
{
bestState.clone(&tmpState);
}
}
if (bestState.number == num)
return buildPath(num, str, nLen, nScore, &bestState, nTimes);
botState tryPath;
tmpState.clone(&bestState);
for (int i=0; i<9; i++)
{
tryPath.clone(&tmpState);
bool pathOK = true;
for (int j=0; j<i; j++)
{
tryPath.nStep++;
tryPath.path.push_back('e');
if (!changeNumberWithDirection(tryPath.number, 'e', tryPath.nStep))
{
pathOK = false;
break;
}
}
tryPath.nStep++;
tryPath.path.push_back('s');
if (!changeNumberWithDirection(tryPath.number, 's', tryPath.nStep))
{
pathOK = false;
break;
}
if ((pathOK) && (isBetterNum(tryPath.number, bestState.number, num)))
{
bestState.clone(&tryPath);
}
}
// in case we'll need to add, but last step was south, move one to the east.
if ((bestState.path.at(bestState.path.size()-1) == 's') && (bestState.number<num))
{
bestState.nStep++;
bestState.path.push_back('e');
if (!changeNumberWithDirection(bestState.number, 'e', bestState.nStep))
return false;
}
if (bestState.number<num)
{
long long diff = num - bestState.number;
diff/=45;
nTimes = (int)diff*10;
bestState.nStep += nTimes;
bestState.path.push_back('*');
bestState.number += 45*diff;
while (num - bestState.number > 10)
{
bestState.nStep++;
bestState.path.push_back('n');
if (!changeNumberWithDirection(bestState.number, 'n', bestState.nStep))
return false;
}
return buildPath(num, str, nLen, nScore, &bestState, nTimes);
}
else
{
long long diff = bestState.number - num;
diff/=45;
nTimes = (int)diff*10;
bestState.nStep += nTimes;
bestState.path.push_back('*');
bestState.number -= 45*diff;
while (bestState.number - num > 10)
{
bestState.nStep++;
bestState.path.push_back('e');
if (!changeNumberWithDirection(bestState.number, 'e', bestState.nStep))
return false;
}
return buildPath(num, str, nLen, nScore, &bestState, -nTimes);
}
return false;
}
long long aVals[] = {49445094, 71259604, 78284689, 163586986, 171769219, 211267178, 222235492, 249062828, 252588742, 263068669, 265657839, 328787447, 344081398, 363100288, 363644732, 372642304, 374776630, 377945535, 407245889, 467229432, 480714605, 491955034, 522126455, 532351066, 542740616, 560336635, 563636122, 606291383, 621761054, 648274119, 738259135, 738287367, 748624287, 753996071, 788868538, 801184363, 807723631, 824127368, 824182796, 833123975, 849666906, 854952292, 879834610, 890418072, 917604533, 932425141, 956158605, 957816726, 981534928, 987717553};
void main(void)
{
upperLimit = 2147483647; // 2^31 - 1
lowerLimit =-1; // -2^31
lowerLimit *=2147483648; // -2^31
long long num=0;
char* str=NULL;
int nLen = 0;
int nItems = sizeof(aVals)/sizeof(aVals[0]);
int nScore = 0;
long long nTotalScore = 0;
// nItems=1;
for(int i=0; i<nItems; i++)
{
if (canReachNumber(aVals[i], str, nLen, nScore)) //try to reach it
{
printf("%3d) to reach %10lld, it takes %9d steps, by doing: %s\n", i, aVals[i], nScore, str);
nTotalScore+=nScore;
delete str;
}
else
{
if (aVals[i]>0)
printf("Failed to reach %lld, use nenenenenenen..... ('n', followed by %lld pairs of 'en')\n", aVals[i], aVals[i]-1);
else
printf("Failed to reach %lld, use enenenenenene..... ('e', followed by %lld pairs of 'ne')\n", aVals[i], aVals[i]-1);
nTotalScore+=2*aVals[i]-1;
}
}
printf("done, total score is %lld\n", nTotalScore);
return;
}