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// 679. 24 Game
#include "leetcode.h"
/*
* given an integer array 'cards' of length 4. you have four cards, each
* containing a number in the range '[1,9]'. you should arrange the numbers on
* these cards in a mathematical expression using the operators '[+,-,*,/]' and
* the parenthesis '(' and ')' to get value 24. you are restricted to the
* following rules:
* - the division operation represents real division, not integer division
* - every operation done is between two numbers. in particular, we cannot use
* '-' as a unary operator
* - you cannot concatenate numbers together
* return true if you can get such expression that evaluates to 24 and false
* otherwise.
*/
#define EPSILON 0.00000001
bool backtrack(double *cards, int cardsSize) {
if (cardsSize == 1)
return fabs(cards[0] - 24) < EPSILON;
double *new = NULL;
for (int i = 0; i + 1 < cardsSize; i++)
for (int j = 0; j < cardsSize; j++) {
int n = cardsSize - 1, newSize = 0;
new = (double *)calloc(sizeof(double), n);
for (int k = 0; k < cardsSize; k++)
if (k != i && k != j)
new[newSize++] = cards[k];
new[newSize++] = cards[i] + cards[j];
if (backtrack(new, newSize))
return true;
newSize--;
new[newSize++] = cards[i] - cards[j];
if (backtrack(new, newSize))
return true;
newSize--;
new[newSize++] = cards[j] - cards[i];
if (backtrack(new, newSize))
return true;
newSize--;
new[newSize++] = cards[i] * cards[j];
if (backtrack(new, newSize))
return true;
newSize--;
new[newSize++] = cards[i] / cards[j];
if (backtrack(new, newSize))
return true;
newSize--;
new[newSize++] = cards[j] / cards[i];
if (backtrack(new, newSize))
return true;
}
if (new)
free(new);
return false;
}
bool judgePoint24(int *cards, int cardsSize) {
double *newCards = (double *)calloc(sizeof(double), cardsSize);
bool ans = backtrack(newCards, cardsSize);
free(newCards);
return ans;
}
int main() {
int c1[] = {4, 1, 8, 7}, c2[] = {1, 2, 1, 2};
printf("%d\n", judgePoint24(c1, ARRAY_SIZE(c1))); // expect: 1
printf("%d\n", judgePoint24(c2, ARRAY_SIZE(c2))); // expect: 0
}
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