Remember the story of Little Match Girl? By now, you know exactly what matchsticks the little match girl has, please find out a way you can make one square by using up all those matchsticks. You should not break any stick, but you can link them up, and each matchstick must be used exactly one time.
Your input will be several matchsticks the girl has, represented with their stick length. Your output will either be true or false, to represent whether you could make one square using all the matchsticks the little match girl has.
Example 1:
Input: [1,1,2,2,2]
Output: true
Explanation: You can form a square with length 2, one side of the square came two sticks with length 1.
Example 2:
Input: [3,3,3,3,4]
Output: false
Explanation: You cannot find a way to form a square with all the matchsticks.
Note:
The length sum of the given matchsticks is in the range of 0 to 10^9.
The length of the given matchstick array will not exceed 15.
题目的问题抽象出来就是:在n个数中能否找出4组数,使得他们的和相等。
题目显然是一个递归问题,循环条件是4组数的和,返回条件是将n个数都用到后,每组数的和是否相等。
public boolean makesquare(int[] nums) {
if (nums == null || nums.length < 4) {
return false;
}
int tmp = 0;
for (int i : nums) {
tmp += i;
}
if (tmp % 4 != 0) {
return false;
}
Arrays.sort(nums);
return robot(0, nums, new int[4], tmp / 4);
}
private boolean robot(int pos, int[] nums, int[] sum, int each) {
if (pos == nums.length) {
return sum[0] == each && sum[1] == each && sum[2] == each;
}
for (int i = 0; i < 4; i++) {
int index = nums.length - 1 - pos;
if (sum[i] + nums[index] > each) {
continue;
}
sum[i] += nums[index];
if (robot(pos + 1, nums, sum, each)) {
return true;
}
sum[i] -= nums[index];
}
return false;
}