剑指 Offer 57

思路

方法一：枚举 + 暴力

 

class Solution {
public:
    vector<vector<int>> findContinuousSequence(int target) {
        vector<vector<int>> res;
        for(int i = 1; i <= target/2; ++i) {
            vector<int> tmp;
            int sum = 0;
            for(int j = i; j < target && sum < target; ++j) {
                sum += j;
                tmp.push_back(j);
            }

            if(sum == target) {
                res.push_back(tmp);
            }
        }

        return res;
    }
};

 

class Solution {
public:
    vector<vector<int>> findContinuousSequence(int target) {
        vector<vector<int>> vec;
        vector<int> res;
        int sum = 0, limit = (target - 1) / 2; // (target - 1) / 2 等效于 target / 2 下取整
        for (int x = 1; x <= limit; ++x) {
            long long delta = 1 - 4 * (x - 1ll * x * x - 2 * target);
            if (delta < 0) {
                continue;
            }
            int delta_sqrt = (int)sqrt(delta + 0.5);
            if (1ll * delta_sqrt * delta_sqrt == delta && (delta_sqrt - 1) % 2 == 0) {
                int y = (-1 + delta_sqrt) / 2; // 另一个解(-1-delta_sqrt)/2必然小于0，不用考虑
                if (x < y) {
                    res.clear();
                    for (int i = x; i <= y; ++i) {
                        res.push_back(i);
                    }
                    vec.push_back(res);
                }
            }
        }
        return vec;
    }
};

 

class Solution {
public:
    vector<vector<int>> findContinuousSequence(int target) {
        vector<vector<int>> res;
        int l = 1, r = 2;
        while(l < r) {
            int sum = (r-l+1)*(l+r)/2;
            if(sum == target) {
                vector<int> tmp;
                for(int i = l; i <= r; ++i)
                    tmp.push_back(i);
                res.push_back(tmp);
                ++l;
            } else if(sum < target) {
                ++r;
            } else {
                ++l;
            }
        }

        return res;
    }
};

也可以不使用求和公式求sum，而是每次对指针进行移动的时候，同时对sum的值进行改变。代码如下：

class Solution {
public:
    vector<vector<int>> findContinuousSequence(int target) {
        vector<vector<int>> res;
        int i = 1, j = 2;
        int sum = 3;
        while(i < j) {
            if(sum < target) {
                ++j;
                sum += j;
            } else if (sum > target) {
                sum -= i;
                ++i;
            } else {
                vector<int> v;
                for(int k = i; k <= j; ++k) {
                    v.push_back(k);
                }
                res.push_back(v);
                sum -= i;
                ++i;
            }
        }

        return res;
    }
};

参考

力扣官方题解 - 和为s的连续正数序列