A320 Captain reported experiencing considerable instability on short final at SFO due to the B777 on the takeoff roll in front of them.

Narrative

Vectored off the arrival (DYMND 5) for the FMS Bridge Visual 28R we were stepped down from 7000 ft. Each step and subsequent vector was to line us up for the approach and spot traffic. We were told to spot a E175 at 9 o'clock joining the approach for Runway 28R. We called traffic in sight and were cleared to 4000 ft. After we leveled at 4000 ft. we were told this traffic we had in sight was breaking off the approach and there was now new traffic to spot; 10:30-11:00. We were to follow them into SFO. We DID NOT see the traffic. We continued on the lateral course but not allowed lower due to traffic not in sight. So on we went; with Approach continuing to call out the position of the traffic to no avail. We could not see this aircraft. When we finally spotted them; they were low so as to be VERY hard to discern from the terrain below. By then it was too late. We got the approach clearance and began to chase the vertical path. By 1000 ft. we were not stabilized and we went around. By the time we came back and landed on 28L; 2 other aircraft had gone around for reasons unknown. Again; it was a VFR day. Finally; coming into land on 28L; Tower decides to line up a 777 on 28L prior to our arrival. Spacing is such that I tell the First Officer 'this will get ugly'. It did. The 777 was cleared for immediate when we were a mile out. By the time he was lifting off we were crossing the threshold of 28L and had the ride of our lives until I managed to touchdown. Honestly; I thought about going around when we hit it; but looking at their flight path on the climb and what ours would be; I felt it safest to wrestle my aircraft to the ground.