Algorithm learning departure

A. given an ordered file containing up to 4 billion random 32-bit integers, find a 32-bit integer that is not in the file (at least one such number is missing in the folder-Why ?). How can we solve this problem if it is sufficiently internal? If there are several external "temporary" files available, but only a few hundred bytes of memory, how can this problem be solved?

 

B. Rotate an N-element vector to the left I position. For example, when n = 8 and I = 3, the vector abcdefgh is rotated to defghabc. Simple code uses AN INTERMEDIATE VECTOR OF N element to complete the work in n steps. Can you use only dozens of extra bytes of storage space to complete vector rotation in a proportional time of n.

 

C. Give an English dictionary to find a set of all the modified words. For example, "pots", "stop", and "tops" are different words, because each word can be obtained by changing the order of letters in other words.