473 Matchsticks to Square

You are given an integer array matchsticks where matchsticks[i] is the length of the ith matchstick. You want to use all the matchsticks to make one square. You should not break any stick, but you can link them up, and each matchstick must be used exactly one time.

Return true if you can make this square and false otherwise.

Example 1:

Input: matchsticks = [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: matchsticks = [3,3,3,3,4]
Output: false
Explanation: You cannot find a way to form a square with all the matchsticks.

Solution:

class Solution {
    public boolean makesquare(int[] matchsticks) {
        // base case 
        if (matchsticks == null || matchsticks.length <= 3){
            return false;
        }

        int total = 0;

        for (int i = 0; i < matchsticks.length; i++){
            total = total + matchsticks[i];
        }

        if (total % 4 != 0){
            return false;
        }

        int target = total / 4;

        int index = matchsticks.length -1;
        int top = 0;
        int bottom = 0;
        int left = 0;
        int right = 0;

        Arrays.sort(matchsticks);
        return dfs(matchsticks, index, top, bottom, left, right, target);

    }

    public static boolean dfs(int[] matchsticks, int index, int top, int bottom, int left, int right, int target){
        if (top == target && bottom == target && left == target && right == target){
            return true;
        }

        if (top > target || bottom > target || left > target || right > target){
            return false;
        }

        int cur = matchsticks[index];

        if (dfs(matchsticks, index -1, top+ cur, bottom, left, right, target) == true){
            return true;
        }

        if (dfs(matchsticks, index -1, top, bottom + cur, left, right, target) == true){
            return true;
        }

        if (dfs(matchsticks, index -1, top, bottom, left +cur, right, target) == true){
            return true;
        }

        if (dfs(matchsticks, index -1, top, bottom, left, right+cur, target) == true){
            return true;
        }

        return false;
    }
}


/*
 3 + 3 +3 +3 + 4 = 12 + 4 = 16 /4     -> 4 

 1 + 1 + 2 + 3 =  2 + 5 = 7 / 4 

            1    1     2     2     4                 matchsticks[index] 
                    top, bottom, left, right
                    [0, 0, 0, 0]
                    /          \       \           \         
  index 0     [1, 0, 0,0]    [0,1,0,0] [0,0,1,0]   [0,0,0,1] 
               /|\ \
   1          [2,0,0,0]

   2    [4,0,0,0]



   top == target && bottom == target left == target right == target 
   return true;

   return false 
   top > target 
 */

 // TC: O(branch^level) O(4^n)
 // SC: O(n)

class Solution {
    public boolean makesquare(int[] matchsticks) {
        // base case 
        if (matchsticks == null || matchsticks.length <= 3){
            return false;
        }

        int total = 0; 

        for (int i = 0; i < matchsticks.length; i++){
            total = matchsticks[i] + total;
        }

        if (total % 4 != 0){
            return false;
        }

        int index = 0;
        int top = 0;
        int bottom = 0;
        int left = 0;
        int right = 0;
        int target = total/4;
        return dfs(matchsticks, index, top, bottom, left, right, target);
    }

    private static boolean dfs(int[] matchsticks, int index, int top, int bottom , int left, int right, int target){

        if (top == target && bottom == target && left == target && right == target){
            return true;
        }

        if (top > target || bottom > target || left > target || right > target){
            return false;
        }

        int cur = matchsticks[index];

        if (dfs(matchsticks, index +1, top + cur, bottom, left, right, target) == true){
            return true;
        }

        if (dfs(matchsticks, index +1, top, bottom+cur, left, right, target) == true){
            return true;
        }

        if (dfs(matchsticks, index +1, top, bottom, left + cur, right, target) == true){
            return true;
        }

        if (dfs(matchsticks, index +1, top, bottom, left, right + cur, target) == true){
            return true;
        }
        return false;
    }
}
//TC: O(4^n)
//SC: O(n)


// TLE