39. Combination Sum

Given a set of candidate numbers (C) (without duplicates) 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.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]]

这仍然是一个递归回溯问题，遵循以下几个步骤：

1）按照测试用力画出递归树（注意递归过程的变化）；

2）根据递归的变的部分抽象出递归所用参数；

3）在递归树中考虑清楚递归终止条件和递归过程。

解题代码

class Solution {private:    vector<vector<int>> res;    void generateCombinations(vector<int>& candidates, int start, int target, vector<int> &c){        if (start == candidates.size()) return; // 遍历完了，退出        // 递归终止，找到组合的情况        if (target == 0){            res.push_back(c);            return;        }        // 递归过程        for (int i = start; i < candidates.size(); i++){            // 考察当前元素有没有可能放到答案中，当前考察元素已经超过target直接考察下一个元素            if (target < candidates[i]) continue;            c.push_back(candidates[i]);            // 递归过程：因为可重复取值，因此还是尝试从i开始继续寻找            generateCombinations(candidates, i, target - candidates[i], c);            c.pop_back(); // 递归回溯，为下一次递归推入做准备        }        return;    }public:    vector<vector<int>> combinationSum(vector<int>& candidates, int target) {        res.clear();        // 边界条件        if (candidates.empty()) return res;        vector<int> c;        generateCombinations(candidates, 0, target, c);        return res;    }};

测试代码

class TestHelper{    Solution s;public:    void run(){        int candiate[] = {8,7,4,3},target = 11;        vector<int> vec(candiate, candiate + 4);        Utils::showVecInfo(vec);        vector<vector<int>> res = s.combinationSum(vec, target);        // 显示结果信息        Utils::showVecInfo(res);    }};

所用到的工具

namespace Utils {    // 显示vector信息    void showVecInfo(vector<int> & v) {        cout << endl << "vector : [ ";        for (vector<int>::iterator it = v.begin(); it != v.end(); it++)        {            cout << *it << " ";        }        cout << " ]" << endl;    }    // 显示vector信息    void showVecInfo(vector<vector<int>> & v) {        cout << endl << "vector<vector<int>> : " << endl;        cout << "\t\t\t[" << endl;        for (vector<vector<int>>::iterator iter = v.begin(); iter != v.end(); iter++){            vector<int> combination = *iter;            cout << "\t\t\t  [ ";            for (vector<int>::iterator it = combination.begin(); it != combination.end(); it++)            {                cout << *it << " ";            }            cout << "]" << endl;        }        cout << "\t\t\t]" << endl;    }}

运行结果

vector : [ 8 7 4 3  ]vector<vector<int>> :                        [                          [ 8 3 ]                          [ 7 4 ]                          [ 4 4 3 ]                        ]请按任意键继续. . .