209 Minimum Size Subarray Sum

    def minSubArrayLen(self, s, nums):
        if len(nums) == 0 or sum(nums) < s:
            return 0
        result,cum_sub,xsum = math.inf,[],0
        #compute sum of subarray
        for x in range(len(nums)):
            xsum += nums[x]
            cum_sub.append(xsum)
        #let x be a fix point indicating the starting position of subarray
        for x in range(len(cum_sub)):
            left,right,substract,index_min = x,len(cum_sub)-1,0,math.inf
            if x-1 >= 0:
                substract = cum_sub[x-1] #substract is the part we need to remove since we shift the starting pos x, thus
all aforehand pos (1..x-1) need to be substracted !
            while left <= right:
                middle = int((left+right)/2)
                if cum_sub[middle]-substract < s:
                    left = middle + 1
                elif cum_sub[middle]-substract == s:
                    index_min = middle - x + 1
                    break
                else:
                    right = middle - 1
                    if middle-1 >= x and cum_sub[middle-1]-substract < s or middle == x: #check if middle is the turning point where
  value of sum before that is less than target, if so then middle is our desired pos,alternatively middle is the leftmost pos of search
  domain
                        index_min = middle -x + 1
                        break
            result = min(result,index_min)
        return result