c_cpp 53.最大子阵列

Posted 2021-05-14

//思路：累积和（prefix_sum）
//时间：8 ms
class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        if (nums.size() < 0) return 0;
        int prefix_sum = 0;
        int min_sum = 0;
        int result = INT_MIN;
        for (auto n : nums) {
            prefix_sum += n;
            result = max(result, prefix_sum - min_sum);
            min_sum = min(prefix_sum, min_sum);
        }
        return result;
    }
};

//思路：动态规划（dynamic programming）
//时间：8 ms
class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        if (nums.size() < 0) return 0;
        int n = nums.size();
        vector<int> dp(n, 0);
        dp[0] = nums[0];
        for (int i = 1; i != n; ++i) {
            dp[i] = max(0, dp[i-1]) + nums[i]; 
        }
        int max_value = INT_MIN;
        for (auto v : dp) {
            max_value = max(v, max_value);
        }
        return max_value;
    }
};

//思路：贪心算法（greedy solution）
//时间：8 ms
class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        if (nums.size() == 0) return 0;
        int n = nums.size();
        int sum = 0;
        int slice = INT_MIN;
        for (auto n : nums) {
            sum += n;
            slice = max(sum, slice);
            sum = max(0, sum);
        }
        return slice;
    }
};

//思路：剑指offer
//时间：12 ms
class Solution {
public:
    int maxSubArray(vector<int>& nums) {
        int maxSum = INT_MIN;
        int sum = 0;
        for(int i = 0;i < nums.size();++i){
            if(sum <= 0)
                sum = nums[i];
            else
                sum += nums[i];
            if(sum > maxSum)
                maxSum = sum;
        }
        return maxSum;
    }
};