53 Maximum Subarray

求一个数组的最大连续子数组和

时间复杂度O(n)
空间复杂度O(1)

动态规划方法求解：递推公式为DP[i] = DP[i-1] + arr[i], faster than 84%

/**
 * @param {number[]} nums
 * @return {number}
 */
var maxSubArray = function(nums) {
    var max = nums[0]
    var cur = 0
    for(var i = 0; i < nums.length; i++){
        cur += nums[i]
        if(cur < 0 || nums[i] > cur) cur = nums[i]
        max = Math.max(cur, max)
    }
    return max
};

更方便理解的递推

递推公式

• Runtime: 88 ms, faster than 50.81%
• Memory Usage: 37.4 MB, less than 49.28%

var maxSubArray = function(nums) {
    let len = nums.length
    let cur = 0
    let max = nums[0]
    for(let i = 0; i < len; i++) {
        cur = Math.max(cur + nums[i], nums[i])
        max = Math.max(cur, max)
    }
    return max
};