circular tour

Given gas stations with gas at each gas station and distance between them, return any gas station starting from which a loop exists. All gas stations need to be visited, in order, only once.

Note:
- A loop exists if there is enough gas starting from any gas station. i.e. loop exists if total gas >= total distance (assume 1 mpg).
- If a loop exists clockwise for gas stations, it also does anti-clockwise. So direction does not matter.

We get this array with a surplus or deficit at each gas station.
- If sum >= 0 at the end, a loop exists. The loop gas station is the first one after which sum stays >= 0 till end. This logic does not work for all valid loop gas stations but works for at least one gas station if loop exists (see examples with -).

d: -1  4 -3 -1  1
s: -1  3  0 -1  0
       -        |

d: -1  3 -4  0  1
s: -1  2 -2 -2 -1
                  // no loop

d: -1  6 -3 -1  1
s: -1  5  2  1  2
       |        -

d: -1  5 -7  4  2 -6  5
s: -1  4 -3  1  3 -3  2
             -        |

point:
    gas
    distance

The start is the first point where the surplus is >= 0 and stays so till the end.

point circularTour(points):
    loopstart = 0
    surplus = 0
    for i, point in points:
        surplus += point.gas - (point.distance / mpg)
        if surplus < 0:
            loopstart = i +1
    if !(0 <= loopstart < points.length()):
        return null
    return points[loopstart]

Without i.

point circularTour(points):
    loopstart = null
    surplus = 0
    for point in points:
        loopstart = loopstart ?? point
        surplus += point.gas - (point.distance / mpg)
        if surplus < 0:
            loopstart = null
    return loopstart

[Hat tip to B]