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Data Structures and Algorithms → Introduction to DSA 32

The output of: auto f=function<int(int)>([](int n){return n*n;}); cout<<f(7);
49
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The output of: map<string,int> freq; string words[]={"a","b","a","c","b","a"}; for(auto w:words)freq[w]++; cout<<freq["a"]<<freq["b"]<<freq["c"];
321
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The output of: vector<pair<int,int>> v={{3,1},{1,3},{2,2}}; sort(v.begin(),v.end()); cout<<v[0].first<<v[0].second;
13
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The output of: priority_queue<pair<int,int>> pq; pq.push({1,2}); pq.push({3,1}); pq.push({2,3}); cout<<pq.top().first;
3
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The output of: auto it=find(begin({5,3,8,1,9}),end({5,3,8,1,9}),8); cout<<*it;
8
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What is the time complexity of std::sort?
O(n log n) average
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What is the space complexity of quicksort (average)?
O(log n) recursion stack
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Which sort is best for nearly sorted arrays?
Insertion Sort
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Counting sort is not a comparison sort and runs in:
O(n + k) where k is range of values
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Bucket sort is efficient when input is:
Uniformly distributed in a known range
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Tim sort (used in Python and Java) combines:
Insertion sort for small runs + merge sort
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The output of: int arr[]={5,2,8,1,9}; int n=5; for(int i=0;i<n-1;i++) for(int j=0;j<n-i-1;j++) if(arr[j]>arr[j+1]) swap(arr[j],arr[j+1]); cout<<arr[0];
1
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What is the maximum comparisons in binary search for n=1024 elements?
11
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Interpolation search works best when:
Data is uniformly distributed (better than binary search)
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Exponential search is useful when:
Array is sorted and size is unknown (infinite/very large)
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Jump search works by:
Jumping ahead by sqrt(n) steps then linear search back
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The output of: int a[]={1,1,2,2,3}; cout<<distance(a,unique(a,a+5));
3
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What is Big Theta of the best sort algorithm for general data?
O(n log n)
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The output of: int n; cin>>n; cout<<(n%15==0?"FizzBuzz":n%3==0?"Fizz":n%5==0?"Buzz":to_string(n)); with n=15:
FizzBuzz
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FizzBuzz for n=9 outputs:
Fizz
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FizzBuzz for n=10 outputs:
Buzz
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FizzBuzz for n=7 outputs:
7
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The output of: int n=4; int count=0; for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) if(i!=j) count++; cout<<count;
12
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The output of: string s="aabbcc"; map<char,int> m; for(char c:s) m[c]++; for(auto [k,v]:m) if(v==1) cout<<k; if there were unique chars
No output (all appear twice)
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The output of: int arr[]={1,2,3,4,5}; cout<<*prev(end(arr));
5
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The output of: vector<int> v={1,2,3}; v.insert(v.end(),{4,5,6}); cout<<v.size();
6
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The output of: array<int,5> a={1,2,3,4,5}; cout<<a.back();
5
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The output of: array<int,5> a; a.fill(7); cout<<a[2];
7
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The output of: bitset<8> bs(170); cout<<bs;
10101010
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The output of: bitset<8> bs("10110100"); cout<<bs.count();
4
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bitset::flip() does:
Flips all bits (0 to 1 and 1 to 0)
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The output of: bitset<4> a("1010"), b("1100"); cout<<(a&b);
1000
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Data Structures and Algorithms → Sorting Algorithms 5

What is the space complexity of merge sort?
O(n)
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What is the space complexity of heap sort?
O(1) in-place
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Radix sort time complexity for n numbers with d digits:
O(d*n)
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Shell sort is a generalization of:
Insertion sort (with gap sequences)
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The output of: int arr[]={64,34,25,12,22,11,90}; // selection sort: for(int i=0;i<6;i++){int m=i; for(int j=i+1;j<7;j++) if(arr[j]<arr[m]) m=j; swap(arr[i],arr[m]);} cout<<arr[0];
11
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Data Structures and Algorithms → Linked List 1

Which sort is best for linked lists?
Merge Sort
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Data Structures and Algorithms → Arrays 2

Binary search on sorted array {1,3,5,7,9,11,13}: how many comparisons to find 7?
3
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Ternary search divides array into:
Three parts (finds max/min of unimodal function)
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