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| /****************************************************************************
**
** The Total Is Right Game
** Game rules: http://en.wikipedia.org/wiki/Des_chiffres_et_des_lettres#Le_compte_est_bon_.28.22the_total_is_right.22.29
**
** Author: Franck Dernoncourt <franck.dernoncourt@gmail.com> (2009)
**
** Home Page : http://www.francky.me
**
** This program is free software; you can redistribute it and/or
** modify it under the terms of the GNU General Public License
** as published by the Free Software Foundation; either
** version 3 of the License, or (at your option) any later version.
**
** This program is distributed in the hope that it will be useful,
** but WITHOUT ANY WARRANTY; without even the implied warranty of
** MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
** GNU General Public License for more details.
**
****************************************************************************/
/** Naming convention for functions and variables: lower CamelCase .**/
#include <iostream> /* cout */
#include <time.h> /* To seed the random function */
using namespace std; /* For sake of laziness & clarity */
/*
* Constant: NUM_NUMBERS
* -----------------------
* This constant determines how many numbers are distributed when the game starts.
*/
const int NUM_NUMBERS = 6;
/*
* Constant: MAX_SOLUTIONS
* -----------------------
* This constant determines how many solutions can be stored by the solution's set.
*/
const long int MAX_SOLUTIONS = 1000000;
/*
* Constant: AVAILABLE_NUMBERS_NUMBER
* -----------------------
* This constant determines among how many numbers the random function will pick up numbers.
*/
const int AVAILABLE_NUMBERS_NUMBER = 14;
/*
* Constant: AVAILABLE_NUMBERS
* -----------------------
* This constant determines what numbers can be given when the game starts.
*/
const int AVAILABLE_NUMBERS[AVAILABLE_NUMBERS_NUMBER] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 25, 50, 75, 100};
/*
* Constant: GOAL_NUMBER_MIN
* -----------------------
* This constant determines the minimum goal number
*/
const int GOAL_NUMBER_MIN = 100;
/*
* Constant: GOAL_NUMBER_MAX
* -----------------------
* This constant determines the maximum goal number
*/
const int GOAL_NUMBER_MAX = 999;
/*
* Struct / type: SolutionT
* -----------------------
* This struct is used to store one solution
*/
struct SolutionT {
int depth;
char operationsUsed[NUM_NUMBERS];
int usedNumbers[NUM_NUMBERS*2];
}
typedef SolutionT;
/*
* Global variable: solutions
* -----------------------
* This variable stores all solutions that
* will be found by the recursive function recSolve
*/
SolutionT solutions[MAX_SOLUTIONS];
/*
* Global variable: numOfSolutions
* -----------------------
* This variable stores the number of solutions that
* will be found by the recursive function recSolve
*/
int numOfSolutions = 0;
/*
* Function: displayArray
* Usage: displayArray(array)
* -----------------------------------------
* This function displays the content of an array
*/
void displayArray(int numbers[NUM_NUMBERS]) {
for (int i=0; i<NUM_NUMBERS; i++) {
cout << "The number " << i + 1 << " is: " << numbers[i] << endl;
}
}
/*
* Function: getArray
* Usage: getArray(array)
* -----------------------------------------
* This function gets the content of an array from the user
*/
void getArray(int numbers[NUM_NUMBERS]) {
for (int i=0; i<NUM_NUMBERS; i++) {
cout << "Enter number " << i + 1 << " : ";
cin >> numbers[i];
}
}
/*
* Function: recSolve
* Usage: recSolve(depth, numberToReach, numbers, operationsUsed, usedNumbers, bestDepth)
* -----------------------------------------
* This recursive function generates a lot of solutions
* for the given problem and store them in the global
* variable SolutionT solutions[MAX_SOLUTIONS].
* Note that in any case it gives the BEST solution, i.e.
* the one that use fewest operations as possible, which corresponds
* to the smallest recursive depth stored in int depth.
*/
void recSolve(int depth, int goal, int myNumbers[NUM_NUMBERS], char operationsUsed[NUM_NUMBERS], int usedNumbers[NUM_NUMBERS*2], int bestDepth) {
/* BASE CASES - CASE 1 out of 3 */
/* Goal is reached, which means one of the myNumbers is equal
* to the goal, and we must stop the recursivity here
*/
for (int i=0; i < NUM_NUMBERS; i++) {
if (goal == myNumbers[i] ) {
/* We update bestDepth */
if (bestDepth > depth) bestDepth = depth;
/* We store the solutions in global variables numOfSolutions and solutions */
numOfSolutions++;
solutions[numOfSolutions-1].depth = depth;
for(int j=0; j < depth; j++) solutions[numOfSolutions-1].operationsUsed[j] = operationsUsed[j];
for(int j=0; j < depth*2; j++) solutions[numOfSolutions-1].usedNumbers[j] = usedNumbers[j];
return;
}
}
/* BASE CASES - CASE 2 out of 3 */
/* Depth is > NUM_NUMBERS, therefore there is no solution */
if (depth >= 6) return;
/* BASE CASES - CASE 3 out of 3 */
/* We only go into this branch if it's not deeper than the
* best solution found so far
*/
if (depth >= bestDepth) return;
/* The Total Is Right Game allows 4 operation :
* Addition, substraction, multiplication and division.
* We'll generate them all and recursively call recSolve()
* each time it seems to be necessary.
*/
/* Operation 1 out of 4:
* ADDITION
* n*(n-1)/2 possibilities, where n = myNumbers.size() because the addition is commutative
*Operand1 + Operand2, and we store it in Operand1's former location in the array myNumbers
*/
operationsUsed[depth]='+';
for (int indexOperand1=0; indexOperand1 < NUM_NUMBERS; indexOperand1++) {
if (myNumbers[indexOperand1] == 0) continue;
for (int indexOperand2=indexOperand1+1; indexOperand2 < NUM_NUMBERS; indexOperand2++) {
if (myNumbers[indexOperand2] == 0) continue;
usedNumbers[depth*2] = myNumbers[indexOperand1];
usedNumbers[depth*2+1] = myNumbers[indexOperand2];
myNumbers[indexOperand1] += myNumbers[indexOperand2];
int tempOperand1 = myNumbers[indexOperand1];
int tempOperand2 = myNumbers[indexOperand2];
myNumbers[indexOperand2] = 0; /* we delete the used number */
recSolve(depth + 1, goal,myNumbers, operationsUsed, usedNumbers, bestDepth);
/* We reverse the operations */
myNumbers[indexOperand2] = tempOperand2;
myNumbers[indexOperand1] -= myNumbers[indexOperand2];
/* if we reached the goal, stop recursion */
if ( tempOperand1 == goal) return;
}
}
/* Operation 2 out of 4:
* SUBSTRACTION
* n² possibilities, where n = myNumbers.size() because the substraction is not commutative
* Operand1 - Operand2, and we store it in Operand1's former location in the array myNumbers
*/
operationsUsed[depth]='-';
for (int indexOperand1=0; indexOperand1 < NUM_NUMBERS; indexOperand1++) {
if (myNumbers[indexOperand1] == 0) continue;
for (int indexOperand2=0; indexOperand2 < NUM_NUMBERS; indexOperand2++) {
if (myNumbers[indexOperand2] == 0) continue;
if ( myNumbers[indexOperand1] == myNumbers[indexOperand2] ) continue;
usedNumbers[depth*2] = myNumbers[indexOperand1];
usedNumbers[depth*2+1] = myNumbers[indexOperand2];
myNumbers[indexOperand1] -= myNumbers[indexOperand2];
int tempOperand1 = myNumbers[indexOperand1];
int tempOperand2 = myNumbers[indexOperand2];
myNumbers[indexOperand2] = 0; /* we delete the used number */
recSolve(depth + 1, goal,myNumbers, operationsUsed, usedNumbers, bestDepth);
/* We reverse the operations */
myNumbers[indexOperand2] = tempOperand2;
myNumbers[indexOperand1] += myNumbers[indexOperand2];
/* If we reached the goal, stop recursion */
if ( tempOperand1 == goal) return;
}
}
/* Operation 3 out of 4:
* MULTIPLICATION
* n*(n-1)/2 possibilities, where n = myNumbers.size() because the multiplication is commutative
* Operand1 * Operand2, and we store it in Operand1's former location in the array myNumbers
*/
operationsUsed[depth]='*';
for (int indexOperand1=0; indexOperand1 < NUM_NUMBERS; indexOperand1++) {
if (myNumbers[indexOperand1] == 0) continue;
for (int indexOperand2=indexOperand1+1; indexOperand2 < NUM_NUMBERS; indexOperand2++) {
if (myNumbers[indexOperand2] == 0) continue;
usedNumbers[depth*2] = myNumbers[indexOperand1];
usedNumbers[depth*2+1] = myNumbers[indexOperand2];
myNumbers[indexOperand1] *= myNumbers[indexOperand2];
int tempOperand1 = myNumbers[indexOperand1];
int tempOperand2 = myNumbers[indexOperand2];
myNumbers[indexOperand2] = 0; /* we delete the used number */
recSolve(depth + 1, goal,myNumbers, operationsUsed, usedNumbers, bestDepth);
/* We reverse the operations */
myNumbers[indexOperand2] = tempOperand2;
myNumbers[indexOperand1] /= myNumbers[indexOperand2];
/* if we reached the goal, stop recursion */
if ( tempOperand1 == goal) return;
}
}
/* Operation 4 out of 4:
* DIVISION
* n² possibilities, where n = myNumbers.size() because the division is not commutative
* Operand1 / Operand2, and we store it in Operand1's former location in the array myNumbers
*/
operationsUsed[depth]='/';
for (int indexOperand1=0; indexOperand1 < NUM_NUMBERS; indexOperand1++) {
if (myNumbers[indexOperand1] == 0) continue;
for (int indexOperand2=0; indexOperand2 < NUM_NUMBERS; indexOperand2++) {
if (myNumbers[indexOperand2] == 0) continue;
/* Check if division if possible */
if ( indexOperand1 == indexOperand2
|| myNumbers[indexOperand2] == 0
|| myNumbers[indexOperand1] % myNumbers[indexOperand2] != 0 )
continue;
usedNumbers[depth*2] = myNumbers[indexOperand1];
usedNumbers[depth*2+1] = myNumbers[indexOperand2];
myNumbers[indexOperand1] /= myNumbers[indexOperand2];
int tempOperand1 = myNumbers[indexOperand1];
int tempOperand2 = myNumbers[indexOperand2];
myNumbers[indexOperand2] = 0; /* we delete the used number */
recSolve(depth + 1, goal,myNumbers, operationsUsed, usedNumbers, bestDepth);
/* We reverse the operations */
myNumbers[indexOperand2] = tempOperand2;
myNumbers[indexOperand1] *= myNumbers[indexOperand2];
/* If we reached the goal, stop recursion */
if ( tempOperand1 == goal) return;
}
}
}
/*
* Function: displayBestSolution
* Usage: displayBestSolution()
* -----------------------------------------
* This function displays the best solutions contains in
* the array solutions. The best solution is defined as the
* one whose number of operation is the smallest possible.
* The number of operation is equal to the depth, which refers
* to the depth of the recursive function that found the solutions.
*/
void displayBestSolution() {
int minDepth = NUM_NUMBERS + 1; // i.e. no solution
long unsigned int bestSolIndex = MAX_SOLUTIONS ;
for (long unsigned int i=0; i < numOfSolutions ; i++) {
if (solutions[i].depth < minDepth) {
minDepth = solutions[i].depth;
bestSolIndex = i;
}
}
/* We display the current solution */
/* If no solution */
if (minDepth == NUM_NUMBERS + 1) {
cout << "There is no solution. Did you find one? If yes, you beat me!!!" << endl;
return;
}
/* If solution, which is the case most of the time */
else {
/* First compute all operations total */
int totalOperations[NUM_NUMBERS];
for(int j=0; j < solutions[bestSolIndex].depth; j++) {
switch (solutions[bestSolIndex].operationsUsed[j]) {
case '+':
totalOperations[j]=solutions[bestSolIndex].usedNumbers[j*2]+solutions[bestSolIndex].usedNumbers[j*2+1];
break;
case '-':
totalOperations[j]=solutions[bestSolIndex].usedNumbers[j*2]-solutions[bestSolIndex].usedNumbers[j*2+1];
break;
case '*':
totalOperations[j]=solutions[bestSolIndex].usedNumbers[j*2]*solutions[bestSolIndex].usedNumbers[j*2+1];
break;
case '/':
totalOperations[j]=solutions[bestSolIndex].usedNumbers[j*2]/solutions[bestSolIndex].usedNumbers[j*2+1];
break;
}
}
/* Display all operations */
for(int j=0; j < solutions[bestSolIndex].depth; j++) {
cout << solutions[bestSolIndex].usedNumbers[j*2] << " " << solutions[bestSolIndex].operationsUsed[j] << " "
<< solutions[bestSolIndex].usedNumbers[j*2+1] << " = " << totalOperations[j] << endl;
}
cout << endl << "There are at least " << numOfSolutions - 1 << " other solutions. " << endl;
}
}
/*
* Function: solve
* Usage: solve(numbers, numberToReach)
* -----------------------------------------
* This function
* 1) initializes some variables,
* 2) calls the recursive function recSolve
* 3) displays the best solution.
*/
void solve(int numbers[NUM_NUMBERS], int numberToReach) {
cout << "Solving..." << endl;
int depth = 0;
int bestDepth = NUM_NUMBERS;
char operationsUsed[NUM_NUMBERS]; /* Store the operations used to find the goal number from the array myNumbers. */
int usedNumbers[NUM_NUMBERS*2];
numOfSolutions = 0;
recSolve(depth, numberToReach, numbers, operationsUsed, usedNumbers, bestDepth);
displayBestSolution();
}
/*
* Function: playRandomGame
* Usage: playRandomGame()
* -----------------------------------------
* Play a normal game with random numbers
*/
void playRandomGame() {
cout << endl << endl << "Normal Game." << endl << endl;
int numbers[NUM_NUMBERS];
int numberToReach;
/* generate available numbers: */
for (int i=0; i<NUM_NUMBERS; i++) {
numbers[i] = AVAILABLE_NUMBERS[rand() % AVAILABLE_NUMBERS_NUMBER];
}
/* generate number to reach: */
numberToReach = rand() % (GOAL_NUMBER_MAX - GOAL_NUMBER_MIN) + GOAL_NUMBER_MIN;
/* Display available numbers */
displayArray(numbers);
cout << endl << "You must reach: " << numberToReach << endl;
cout << endl << "Wanna see the best solution? " << endl;
system("pause");
solve(numbers,numberToReach);
system("pause");
}
/*
* Function: userOwnNumberGame
* Usage: userOwnNumberGame()
* -----------------------------------------
* Solve a problem given by the user
*/
void userOwnNumberGame() {
int numbers[NUM_NUMBERS];
int numberToReach;
cout << endl << endl;
getArray(numbers);
cout << "Enter the goal number: ";
cin >> numberToReach;
solve(numbers,numberToReach);
system("pause");
}
/*
* Function: displayRules
* Usage: displayRules()
* -----------------------------------------
* This function displays the game's rules.
*/
void displayRules() {
cout << endl << endl;
cout << "GAME RULES: (from Wikipedia)" << endl << endl << endl;
cout << "The goal of this game is to arrive at a chosen number (from 101 to 999) "
"using the four basic arithmetic operations (+, -, * and /) applied to six numbers "
"chosen randomly from the following alternatives: 1 to 10; 25; 50; 75; 100 "
"(each number is drawn from the entire set, so the same number may appear more than once). " << endl << endl <<
"Once these six numbers are selected, a three-digit target number is generated. "
"The players combine the numbers arithmetically with the goal of producing the target number. "
"The player may use each of the six numbers originally selected once, "
"and the result of each operation performed with them once - for example, "
"if a player multiplies 4 by 25 to obtain 100, he or she may no longer use the 4 or 25, "
"but may use the 100 in further calculations. It's not mandatory to use all the numbers. All numbers used must be integers.";
cout << endl << endl;
cout << "Example: "<< endl;
cout << "Numbers given : 8 ; 4 ; 4 ; 6 ; 8 ; 9" << endl;
cout << "Target number : 594" << endl;
cout << " 8 + 8 = 16" << endl;
cout << "16 * 4 = 64" << endl;
cout << " 6 - 4 = 2" << endl;
cout << "64 + 2 = 66" << endl;
cout << "66 * 9 = 594" << endl;
system("pause");
}
/*
* Function: main
* Usage: main()
* -----------------------------------------
* This is the program's main function: User menu.
*/
int main()
{
/* initialize random seed: */
srand ( time(NULL) );
cout << "Welcome to The Total is Right game!" << endl;
/* User menu */
int answer = 1;
while( answer!=4 ) {
cout << endl << endl;
cout << "1) Play normal game." << endl;
cout << "2) Enter your own numbers." << endl;
cout << "3) Display rules." << endl;
cout << "4) Quit." << endl;
cout << "Enter your choice: " ;
cin >> answer;
if (answer==1) playRandomGame();
if (answer==2) userOwnNumberGame();
if (answer==3) displayRules();
}
return EXIT_SUCCESS;
} |
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