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合并区间

• 合并区间

class Solution {
public:
    vector<vector<int>> merge(vector<vector<int>>& intervals) {
        sort(intervals.begin(), intervals.end());
        vector<vector<int>> ret;
        int left = intervals[0][0], right = intervals[0][1];
        for (int i = 1; i < intervals.size(); i++)
        {
            int a = intervals[i][0], b = intervals[i][1];
            if (a <= right) right = max(right, b);
            else
            {
                ret.push_back({left, right});
                left = a, right = b;
            }
        }
        ret.push_back({left, right});
        return ret;
    }
};

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无重叠区间

• 无重叠区间

class Solution {
public:
    int eraseOverlapIntervals(vector<vector<int>>& intervals) {
        sort(intervals.begin(), intervals.end());
        int ret = 0, right = intervals[0][1];
        for (int i = 1; i < intervals.size(); i++)
        {
            int a = intervals[i][0], b = intervals[i][1];
            if (a < right)
            {
                ret++;// 删除右端点较大的区间
                right = min(right, b);
            }
            else right = b;
        }
        return ret;
    }
};

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用最少数量的箭引爆气球

• 用最少数量的箭引爆气球

贪心策略：我们在射箭的时候，要发挥每一支箭最大的作用，应该把互相重叠的区间统一引爆。

class Solution {
public:
    int findMinArrowShots(vector<vector<int>>& points) {
        sort(points.begin(), points.end());
        int ret = 0, right = points[0][1];
        for (int i = 1; i < points.size(); i++)
        {
            int a = points[i][0], b = points[i][1];
            if (a <= right) right = min(right, b);
            else 
            {
                right = b;
                ret++;
            }
        }
        return ret + 1;
    }
};

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俄罗斯套娃信封问题

• 俄罗斯套娃信封问题

动态规划解法，会超时：

class Solution {
public:
    int maxEnvelopes(vector<vector<int>>& e) {
        sort(e.begin(), e.end());
        int n = e.size(), ret = 0;
        vector<int> dp(n, 1);
        for (int i = 1; i < n; i++)
        {
            for (int j = 0; j < i; j++)
                if (e[i][0] > e[j][0] && e[i][1] > e[j][1])
                    dp[i] = max(dp[i], dp[j] + 1);
            ret = max(ret, dp[i]);
        }
        return ret;
    }
};

重写排序+贪心+二分：

class Solution {
public:
    int maxEnvelopes(vector<vector<int>>& e) {
        sort(e.begin(), e.end(), [](const vector<int>& v1, const vector<int>& v2){
            return v1[0] == v2[0] ? v1[1] > v2[1] : v1[0] < v2[0];
        });
        vector<int> ret;
        ret.push_back(e[0][1]);
        for (int i = 1; i < e.size(); i++)
        {
            int a = e[i][1];
            if (a > ret.back()) ret.push_back(a);
            else 
            {
                int left = 0, right = ret.size() - 1;
                while (left < right)
                {
                    int mid = (left + right) >> 1;
                    if (ret[mid] < a) left = mid + 1;
                    else right = mid;
                }
                ret[left] = a;
            }
        }
        return ret.size();
    }
};

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