最大子序和1. 暴力法工夫复杂度:O(N^2)空间复杂度:O(1)设置两层for循环存储第一个数字的值,顺次加上前面的数字,只存储最大值依此类推
class Solution{public: int maxSubArray(vector<int> &nums) { int max = INT_MIN; int numsSize = int(nums.size()); for (int i = 0; i < numsSize; i++) { int sum = 0; for (int j = i; j < numsSize; j++) { sum += nums[j]; if (sum > max) { max = sum; } } } return max; }};2. 动静布局工夫复杂度:O(N)空间复杂度:O(1)一一加值比拟,存储最大值一旦遇到加值后的后果 < 0,则只保留之前计算的最大值,从新开始下一个加值比拟
class Solution{public: int maxSubArray(vector<int> &nums) { int result = INT_MIN; int numsSize = int(nums.size()); //dp[i]示意nums中以nums[i]结尾的最大子序和 vector<int> dp(numsSize); dp[0] = nums[0]; result = dp[0]; for (int i = 1; i < numsSize; i++) { dp[i] = max(dp[i - 1] + nums[i], nums[i]); result = max(result, dp[i]); } return result; }};3.贪婪算法工夫复杂度:O(N)空间复杂度:O(1)与动静布局基本一致class Solution{public: int maxSubArray(vector<int> &nums) { //相似寻找最大最小值的题目,初始值肯定要定义成实践上的最小最大值 int result = INT_MIN; int numsSize = int(nums.size()); int sum = 0; for (int i = 0; i < numsSize; i++) { sum += nums[i]; result = max(result, sum); //如果sum < 0,从新开始找子序串 if (sum < 0) { sum = 0; } } return result; }};4. 分治法工夫复杂度:O(nlog(n))空间复杂度:O(log(n))class Solution{public: int maxSubArray(vector<int> &nums) { //相似寻找最大最小值的题目,初始值肯定要定义成实践上的最小最大值 int result = INT_MIN; int numsSize = int(nums.size()); result = maxSubArrayHelper(nums, 0, numsSize - 1); return result; } int maxSubArrayHelper(vector<int> &nums, int left, int right) { if (left == right) { return nums[left]; } int mid = (left + right) / 2; int leftSum = maxSubArrayHelper(nums, left, mid); //留神这里应是mid + 1,否则left + 1 = right时,会有限循环 int rightSum = maxSubArrayHelper(nums, mid + 1, right); int midSum = findMaxCrossingSubarray(nums, left, mid, right); int result = max(leftSum, rightSum); result = max(result, midSum); return result; } int findMaxCrossingSubarray(vector<int> &nums, int left, int mid, int right) { int leftSum = INT_MIN; int sum = 0; for (int i = mid; i >= left; i--) { sum += nums[i]; leftSum = max(leftSum, sum); } int rightSum = INT_MIN; sum = 0; //留神这里i = mid + 1,防止反复用到nums[i] for (int i = mid + 1; i <= right; i++) { sum += nums[i]; rightSum = max(rightSum, sum); } return (leftSum + rightSum); }};