回溯算法入门级详解 + 练习

回溯算法入门级详解 + 练习

题型一：排列、组合、子集相关问题

46.全排列

题目链接

	public List<List<Integer>> permute(int[] nums) {
    
    
        List<List<Integer>> ans = new ArrayList<>();
        int len = nums.length;
        if (len <= 0) return ans;
        boolean[] used = new boolean[len];
        Deque<Integer> combina = new ArrayDeque<>();
        dfsPermute(nums,used,len,ans,combina);
        return ans;
    }

    private void dfsPermute(int[] nums, boolean[] used, int len, List<List<Integer>> ans, Deque<Integer> combina) {
    
    
        if (combina.size() == len){
    
    
            ans.add(new ArrayList<>(combina));
            return;
        }
        for (int i = 0; i < len; i++) {
    
    
            if (!used[i]){
    
    
                combina.addLast(nums[i]);
                used[i] = true;
                dfsPermute(nums,used,len,ans,combina);
                used[i] = false;
                combina.removeLast();
            }
        }
    }

47.全排列Ⅱ

题目链接

	public List<List<Integer>> permuteUnique(int[] nums) {
    
    
        List<List<Integer>> ans = new ArrayList<>();
        int len = nums.length;
        if (len <= 0) return ans;
        Deque<Integer> combina = new ArrayDeque<>();
        boolean[] used = new boolean[len];
        Arrays.sort(nums);
        dfsPermuteUnique(nums,len,ans,combina,used);
        return ans;
    }

    private void dfsPermuteUnique(int[] nums, int len, List<List<Integer>> ans, Deque<Integer> combina, boolean[] used) {
    
    
        if (combina.size() == len){
    
    
            ans.add(new ArrayList<>(combina));
            return;
        }
        for (int i = 0; i < len; i++) {
    
    
            if (used[i]) continue;
            if (i>0 && nums[i] == nums[i-1] && !used[i-1]) continue;
            combina.addLast(nums[i]);
            used[i] = true;
            dfsPermuteUnique(nums,len,ans,combina,used);
            used[i] = false;
            combina.removeLast();
        }
    }

39.组合总和

题目链接

	public List<List<Integer>> combinationSum(int[] candidates, int target) {
    
    
        List<List<Integer>> ans = new ArrayList<>();
        int len = candidates.length;
        if (len <= 0) return ans;
        Arrays.sort(candidates);
        Deque<Integer> combina = new ArrayDeque<>();
        dfsCombinationSum(candidates, target, len, ans, combina, 0);
        return ans;
    }

    private void dfsCombinationSum(int[] candidates, int target, int len, List<List<Integer>> ans, Deque<Integer> combina, int begin) {
    
    
        if (target == 0) {
    
    
            ans.add(new ArrayList<>(combina));
            return;
        }
        for (int i = begin; i < len; i++) {
    
    
            if (target - candidates[i] < 0) {
    
    
                break;
            }
            combina.addLast(candidates[i]);
            dfsCombinationSum(candidates, target - candidates[i], len, ans, combina, i);
            combina.removeLast();
        }
    }

40.组合总和Ⅱ

题目链接

	public List<List<Integer>> combinationSum2(int[] candidates, int target) {
    
    
        List<List<Integer>> ans = new ArrayList<>();
        int len = candidates.length;
        if (len <= 0) return ans;
        Deque<Integer> combina = new ArrayDeque<>();
        Arrays.sort(candidates);
        dfsCombinationSum2(candidates, target, 0, ans, combina, len);
        return ans;
    }

    private void dfsCombinationSum2(int[] candidates, int target, int begin, List<List<Integer>> ans, Deque<Integer> combina, int len) {
    
    
        if (target == 0) {
    
    
            ans.add(new ArrayList<>(combina));
            return;
        }
        for (int i = begin; i < len; i++) {
    
    
            //大剪枝
            if (target - candidates[i] < 0) break;
            //小剪枝，去掉重复结果
            if (i>begin && candidates[i] == candidates[i-1]) continue;
            //选择
            combina.addLast(candidates[i]);
            dfsCombinationSum2(candidates, target - candidates[i], i + 1, ans, combina, len);
            //移除
            combina.removeLast();
        }
    }

77.组合

题目链接

	public List<List<Integer>> combine(int n, int k) {
    
    
        List<List<Integer>> ans = new ArrayList<>();
        Deque<Integer> combine = new ArrayDeque<>();
        dfsCombine(1,n,k,ans,combine);
        return ans;
    }

    private void dfsCombine(int begin ,int n, int k, List<List<Integer>> ans, Deque<Integer> combine) {
    
    
        if (combine.size() == k){
    
    
            ans.add(new ArrayList<>(combine));
            return;
        }
        for (int i = begin; i <= n-(k-combine.size())+1; i++) {
    
    
            combine.addLast(i);
            dfsCombine(i+1,n,k,ans,combine);
            combine.removeLast();
        }
    }

78.子集

题目链接

	public List<List<Integer>> subsets(int[] nums) {
    
    
        List<List<Integer>> ans = new ArrayList<>();
        int len = nums.length;
        if (len <= 0) return ans;
        Deque<Integer> sub = new ArrayDeque<>();
        dfsSubsets(nums,0,len,ans,sub);
        return ans;
    }

    private void dfsSubsets(int[] nums, int index, int len, List<List<Integer>> ans, Deque<Integer> sub) {
    
    
        ans.add(new ArrayList<>(sub));
        for (int i = index; i < len; i++) {
    
    
            sub.addLast(nums[i]);
            dfsSubsets(nums,i+1,len,ans,sub);
            sub.removeLast();
        }
    }

90子集Ⅱ

60.第k个排列

93.复原IP地址