LeetCode: Combination Sum I && II && III

Title: 

https://leetcode.com/problems/combination-sum/

Given a set of candidate numbers (C) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.

The same repeated number may be chosen from C unlimited number of times.

Note:

• All numbers (including target) will be positive integers.
• Elements in a combination (a1, a2, … , ak) must be in non-descending order. (ie, a1 ≤ a2 ≤ … ≤ ak).
• The solution set must not contain duplicate combinations.

For example, given candidate set 2,3,6,7 and target 7, 
A solution set is: 
[7] 
[2, 2, 3] 

思路：基本是DFS的思想。将数组排序之后，每次对当前的这个元素与target比较，看最多能塞进去几个当前的这个元素。

如果数组有相同元素，可以采用注释掉的语句进行去重，或者在递归函数中去重。不去重也不会影响结果。(去掉蓝色的也没有影响，不过蓝色的是为了去重)

注意结束条件： 一般都是index == size(),但这边应该是0 == target

for (int i = (target / candidates[idx]); i >= 0; i--) {
            record.push_back(candidates[idx]);
}
用来计算最多压入几个当前元素。

for (int i = (target / candidates[idx]); i >= 0; i--) {
            record.pop_back();
            searchAns(ans, record, candidates, target - i * candidates[idx], idx + 1,candidates[idx]);
            //record.pop_back();
       }
弹出栈，再进入递归函数。注意，有可能这个元素就不要压入，所以是i >=0

class Solution {
public:
    vector<vector<int> > combinationSum(vector<int> &candidates, int target) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        sort(candidates.begin(), candidates.end());
        /*vector<int>::iterator pos = unique(candidates.begin(), candidates.end());
        candidates.erase(pos, candidates.end());*/
        vector<vector<int> > ans;
        vector<int> record;
        searchAns(ans, record, candidates, target, 0,-1);
        return ans;
    }

private:
    void searchAns(vector<vector<int> > &ans, vector<int> &record, vector<int> &candidates, int target, int idx, int preValue) {
        if (target == 0) {
            ans.push_back(record);
            return;
        }
        if (  idx == candidates.size() || candidates[idx] > target || preValue == candidates[idx]) {
            return;
        }
        for (int i = (target / candidates[idx]); i >= 0; i--) {
            record.push_back(candidates[idx]);
        }
        for (int i = (target / candidates[idx]); i >= 0; i--) {
            record.pop_back();
            searchAns(ans, record, candidates, target - i * candidates[idx], idx + 1,candidates[idx]);
            //record.pop_back();
        }
    }
};

Title:

https://leetcode.com/problems/combination-sum-ii/

Given a collection of candidate numbers (C) and a target number (T), find all unique combinations in C where the candidate numbers sums to T.

Each number in C may only be used once in the combination.

Note:

• All numbers (including target) will be positive integers.
• Elements in a combination (a1, a2, … , ak) must be in non-descending order. (ie, a1 ≤ a2 ≤ … ≤ ak).
• The solution set must not contain duplicate combinations.

For example, given candidate set 10,1,2,7,6,1,5 and target 8, 
A solution set is: 
[1, 7] 
[1, 2, 5] 
[2, 6] 
[1, 1, 6] 

思路：DFS搜索。与Combination Sum中的不同，每次搜索的备选项是从当前index开始到数组结束的元素。不包括重复元素。

class Solution {
public:
    vector<vector<int> > results;
    vector<vector<int> > combinationSum2(vector<int> &num, int target) {

        if (num.empty() || num.size() == 0)
            return results;
        sort(num.begin(),num.end());
        vector<int> result;
        combine(num,0,target,result);
        return results;
    }

    void combine(vector<int> &num,int startIndex, int target,vector<int> &result){
        if (0 == target){
            //cout<<"add"<<endl;
            results.push_back(result);
            return ;
        }
        if (0 > target)
            return ;
        for (int i = startIndex; i < num.size(); i++){
            if (i > startIndex && num[i] == num[i-1])
                continue;
            result.push_back(num[i]);
            combine(num,i+1,target-num[i],result);
            result.pop_back();
        }
    }
};

 Title: 

https://leetcode.com/problems/combination-sum-iii/

Find all possible combinations of k numbers that add up to a number n, given that only numbers from 1 to 9 can be used and each combination should be a unique set of numbers.

Ensure that numbers within the set are sorted in ascending order.

Example 1:

Input: k = 3, n = 7

Output:

[[1,2,4]]

Example 2:

Input: k = 3, n = 9

Output:

[[1,2,6], [1,3,5], [2,3,4]]

class Solution {
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int> > results;
        if ( k < 1 || n < 1)
            return results;
        vector<int> result;
        DFS(results,result,0,k,n,0);
        return results;
    }
    void DFS(vector<vector<int> >& results, vector<int>& result, int index, int k, int target, int preVal){
        if (index == k && target == 0){
            results.push_back(result);
            return ;
        }
        if (index == k || target <= preVal)
            return ;
        for (int i = preVal+1; i < 10; i++){
            result.push_back(i);
            DFS(results,result,index+1,k,target-i,i);
            result.pop_back();
        }
    }
};