C ++: स्कोर = 453,324,048
ठीक है, इसे फिर से तैयार करने के लिए कुछ समय चाहिए, लेकिन यहां जिस तरह से मैंने इसे हल किया है।
समाधान स्थान का अध्ययन करने के बाद, मैंने तय किया कि मेरी रणनीति होगी:
- लक्ष्य संख्या के करीब पहुंचने के लिए दक्षिण चरणों का उपयोग करता है
- यदि लक्ष्य सकारात्मक है, तो इस मार्ग का अनुसरण करें: nnnesssssessssssss
- यदि लक्ष्य नकारात्मक है, तो इस मार्ग का अनुसरण करें: Esssssssseessssss c। यदि लक्ष्य 0 और 20 के बीच है, तो इसे "पुराने फैशन के तरीके" को हल करें (निशान और हर संभव पथ पर त्रुटि जो हम उस तक पहुंचते हैं)।
- एक बार जब हम अपना "सर्वोत्तम स्थान" प्राप्त कर लेते हैं (लक्ष्य के करीब पहुँच जाते हैं, "बिना" "), तो हम 2 या 3 से गुणा करके पास होने में सक्षम हो सकते हैं; इसलिए पूर्व से 0 से 9 कदम के बीच ले जाएं, और फिर एक कदम दक्षिण में। उस मार्ग को बनाए रखें जो हमें लक्ष्य के सबसे करीब पहुंचाता है।
- "रन" उत्तर, या पूर्वी टिल हम लक्ष्य के 45 बिंदुओं के भीतर हैं (प्रत्येक 10 कदम उत्तर में, स्कोर में 45 अंक जोड़ते हैं, जैसे बुद्धिमान, हर 10 कदम पूर्व में, स्कोर को 45 से कम कर देता है)।
- उसी दिशा में कुछ और कदम उठाएं, टिल हम लक्ष्य के 10 बिंदुओं के भीतर हैं
- इस बिंदु से "पुराने फैशन का रास्ता" करें, यह अब उतना कठिन नहीं होना चाहिए।
यहां मेरा परिणाम है: कुल स्कोर 453324048 है
और रास्ते:
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
मुझे यकीन है कि कुछ क्लीवर "दक्षिण / पश्चिम" चाल (4 से विभाजित और 5 से गुणा करके; उदाहरण के लिए) इस पर सुधार करने का एक तरीका है; लेकिन इसे कोड करना, और यह सुनिश्चित करना कि आप गोद में नहीं हैं या फंस गए हैं, मुश्किल है।
एक और समाधान पथ, लक्ष्य से नीचे जाने की कोशिश करने के लिए हो सकता है, एक "उचित" नंबर पर, और फिर, बस उस छोटी संख्या के लिए एक रास्ता खोजें; लेकिन आपको इसे सही तरीके से "लक्ष्य" करना होगा, ताकि चरण संख्या मेल खा जाए। मुश्किल, लेकिन इसे हल करने का सबसे अच्छा तरीका हो सकता है।
वैसे भी, यहाँ मेरा कोड कोड है:
#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;
}