Bouncing back from the losses caused by last spring's supermarket price war, Giant Food Inc. reported strong gains in fourth quarter sales and profits that indicate Giant may collect long term benefits from the costly effort to capture more business.

After losing $2.24 million in the first half of the year, Giant ended 1981 with profits of $16.77 million ($3.41 a share) down only 8 percent from 1980's record earnings of $18.3 million ($3.74). Sales increased 13.5 percent to $1.68 billion from $1.48 billion.

The comparison with last year understates Giant's performance, however, because the company's 1980 fiscal calendar had 53 weeks while fiscal 1981 was 52 weeks long. The extra week added 20 to 30 cents a share to Giant's earnings last year; without that bonus week's profits, Giant's 1981 profits were down only about 15 cents a share. Throwing out the extra week would mean 1981's sales were up 15.8 percent, far more than the average gain of 11 percent reported by 32 big food chains, the company noted.

Giant's fourth quarter earnings were up almost 18 percent from last year's despite the extra week included in the 1980 figures. Profits totaled $12.23 million ($2.49) up from $10.3 million ($2.10).

Fourth quarter sales totaled $549.8 million, up $514.7 million or 6.8 percent. Taking account of the extra week in 1980, however, the gain came to 13.3 percent.

Giant acknowledged the food price war that started last April hurt its earnings but said the gains for the year came because "the company remained aggressive in its pricing and kept the patronage of many of the new customers who had begun to shop its stores, resulting in substantial sales and earnings gains for its second half."