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1 | 1 | package backtracking;
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| 2 | + |
2 | 3 | import java.util.*;
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| 4 | + |
3 | 5 | /**
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4 | 6 | * Created by gouthamvidyapradhan on 25/05/2019 Remember the story of Little Match Girl? By now, you
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5 | 7 | * know exactly what matchsticks the little match girl has, please find out a way you can make one
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19 | 21 | * sum of the given matchsticks is in the range of 0 to 10^9. The length of the given matchstick
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20 | 22 | * array will not exceed 15.
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21 | 23 | *
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22 |
| - * Solution: O(2 ^ N): Generate a power set of all combination of numbers for the given array which sum up to the |
23 |
| - * length of a side of square. |
24 |
| - * Now, to check if a square can be made using all the sides sticks of different length, generate a hash for for each of |
25 |
| - * the combination which was generated in the previous step. The hash function should be such that it uses unique |
26 |
| - * indexes of each match stick. If 4 different hash values are formed using unique and all indices then a square is |
27 |
| - * possible. |
| 24 | + * <p>Solution: O(2 ^ N): Generate a power set of all combination of numbers for the given array |
| 25 | + * which sum up to the length of a side of square. Now, to check if a square can be made using all |
| 26 | + * the sides sticks of different length, generate a hash for for each of the combination which was |
| 27 | + * generated in the previous step. The hash function should be such that it uses unique indexes of |
| 28 | + * each match stick. If 4 different hash values are formed using unique and all indices then a |
| 29 | + * square is possible. |
28 | 30 | */
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29 | 31 | public class MatchsticksToSquare {
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30 |
| - /** |
31 |
| - * Main method |
32 |
| - * @param args |
33 |
| - */ |
| 32 | + /** |
| 33 | + * Main method |
| 34 | + * |
| 35 | + * @param args |
| 36 | + */ |
34 | 37 | public static void main(String[] args) {
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35 |
| - int[] A = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 10, 10}; |
| 38 | + int[] A = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 6, 10, 10}; |
36 | 39 | System.out.println(new MatchsticksToSquare().makesquare(A));
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37 | 40 | }
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38 | 41 |
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39 |
| - class Pair { |
40 |
| - int value, i; |
41 |
| - Pair(int value, int i){ |
42 |
| - this.value = value; |
43 |
| - this.i = i; |
44 |
| - } |
| 42 | + class Pair { |
| 43 | + int value, i; |
| 44 | + |
| 45 | + Pair(int value, int i) { |
| 46 | + this.value = value; |
| 47 | + this.i = i; |
45 | 48 | }
|
| 49 | + } |
46 | 50 |
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47 |
| - public boolean makesquare(int[] nums) { |
48 |
| - if(nums.length == 0) return false; |
49 |
| - int sum = 0; |
50 |
| - for(int n : nums){ |
51 |
| - sum += n; |
52 |
| - } |
53 |
| - int side = sum / 4; |
54 |
| - if((sum % 4) != 0) return false; |
55 |
| - List<List<Pair>> list = powerSet(nums, side); |
56 |
| - Set<Integer> hashIndex = new HashSet<>(); |
57 |
| - int cons = 0; |
58 |
| - for(int i = 0; i < nums.length; i ++){ |
59 |
| - cons |= (1 << i); |
| 51 | + public boolean makesquare(int[] nums) { |
| 52 | + if (nums.length == 0) return false; |
| 53 | + int sum = 0; |
| 54 | + for (int n : nums) { |
| 55 | + sum += n; |
| 56 | + } |
| 57 | + int side = sum / 4; |
| 58 | + if ((sum % 4) != 0) return false; |
| 59 | + List<List<Pair>> list = powerSet(nums, side); |
| 60 | + Set<Integer> hashIndex = new HashSet<>(); |
| 61 | + int cons = 0; |
| 62 | + for (int i = 0; i < nums.length; i++) { |
| 63 | + cons |= (1 << i); |
| 64 | + } |
| 65 | + for (int i = 0; i < list.size(); i++) { |
| 66 | + for (int j = i + 1; j < list.size(); j++) { |
| 67 | + Set<Integer> indexList = new HashSet<>(); |
| 68 | + List<Pair> list1 = list.get(i); |
| 69 | + List<Pair> list2 = list.get(j); |
| 70 | + int hash = 0; |
| 71 | + for (Pair l1 : list1) { |
| 72 | + indexList.add(l1.i); |
| 73 | + hash |= (1 << l1.i); |
60 | 74 | }
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61 |
| - for(int i = 0; i < list.size(); i ++){ |
62 |
| - for(int j = i + 1; j < list.size(); j ++){ |
63 |
| - Set<Integer> indexList = new HashSet<>(); |
64 |
| - List<Pair> list1 = list.get(i); |
65 |
| - List<Pair> list2 = list.get(j); |
66 |
| - int hash = 0; |
67 |
| - for(Pair l1 : list1){ |
68 |
| - indexList.add(l1.i); |
69 |
| - hash |= (1 << l1.i); |
70 |
| - } |
71 |
| - boolean allUnique = true; |
72 |
| - for(Pair l2 : list2){ |
73 |
| - if(indexList.contains(l2.i)) { |
74 |
| - allUnique = false; |
75 |
| - break; |
76 |
| - } |
77 |
| - indexList.add(l2.i); |
78 |
| - hash |= (1 << l2.i); |
79 |
| - } |
80 |
| - if(allUnique){ |
81 |
| - hashIndex.add(hash); |
82 |
| - int complement = ((~ hash) & cons); |
83 |
| - if(hashIndex.contains(complement)) return true; |
84 |
| - } |
| 75 | + boolean allUnique = true; |
| 76 | + for (Pair l2 : list2) { |
| 77 | + if (indexList.contains(l2.i)) { |
| 78 | + allUnique = false; |
| 79 | + break; |
85 | 80 | }
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| 81 | + indexList.add(l2.i); |
| 82 | + hash |= (1 << l2.i); |
| 83 | + } |
| 84 | + if (allUnique) { |
| 85 | + hashIndex.add(hash); |
| 86 | + int complement = ((~hash) & cons); |
| 87 | + if (hashIndex.contains(complement)) return true; |
| 88 | + } |
86 | 89 | }
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87 |
| - return false; |
88 | 90 | }
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| 91 | + return false; |
| 92 | + } |
89 | 93 |
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90 |
| - private List<List<Pair>> powerSet(int[] nums, int expectedSum){ |
91 |
| - List<List<Pair>> result = new ArrayList<>(); |
92 |
| - generate(0, nums, new ArrayList<>(), result, 0, expectedSum); |
93 |
| - return result; |
94 |
| - } |
| 94 | + private List<List<Pair>> powerSet(int[] nums, int expectedSum) { |
| 95 | + List<List<Pair>> result = new ArrayList<>(); |
| 96 | + generate(0, nums, new ArrayList<>(), result, 0, expectedSum); |
| 97 | + return result; |
| 98 | + } |
95 | 99 |
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96 |
| - private void generate(int i, int[] nums, List<Pair> subList, List<List<Pair>> result, int sum, |
97 |
| - int expected){ |
98 |
| - if(i >= nums.length){ |
99 |
| - if(sum == expected){ |
100 |
| - List<Pair> pairs = new ArrayList<>(subList); |
101 |
| - result.add(pairs); |
102 |
| - } |
103 |
| - } else{ |
104 |
| - if(sum + nums[i] <= expected){ |
105 |
| - subList.add(new Pair(nums[i], i)); |
106 |
| - generate(i + 1, nums, subList, result, sum + nums[i], expected); |
107 |
| - subList.remove(subList.size() - 1); |
108 |
| - } |
109 |
| - generate(i + 1, nums, subList, result, sum, expected); |
| 100 | + private void generate( |
| 101 | + int i, int[] nums, List<Pair> subList, List<List<Pair>> result, int sum, int expected) { |
| 102 | + if (i >= nums.length) { |
| 103 | + if (sum == expected) { |
| 104 | + List<Pair> pairs = new ArrayList<>(subList); |
| 105 | + result.add(pairs); |
110 | 106 | }
|
| 107 | + } else { |
| 108 | + if (sum + nums[i] <= expected) { |
| 109 | + subList.add(new Pair(nums[i], i)); |
| 110 | + generate(i + 1, nums, subList, result, sum + nums[i], expected); |
| 111 | + subList.remove(subList.size() - 1); |
| 112 | + } |
| 113 | + generate(i + 1, nums, subList, result, sum, expected); |
111 | 114 | }
|
| 115 | + } |
112 | 116 | }
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