🔢 Problem 1: Maximum Subarray Sum
Problem Statement:
Given a one-dimensional array of integers, find the contiguous subarray with the maximum sum.
📥 Input:
Line 1: Integer N (1 ≤ N ≤ 105) – size of the array Line 2: N space-separated integers A[i] (–104 ≤ A[i] ≤ 104)
📤 Output:
Print the maximum sum of any contiguous subarray.
🔍 Sample Input:
8 -2 1 -3 4 -1 2 1 -5
✅ Sample Output:
6
💡 Output Explanation:
The subarray [4, -1, 2, 1] has the maximum sum = 6.
📉 Problem 2: Count Inversions
Problem Statement:
Given an array of integers, count how many pairs (i, j) exist such that i < j and A[i] > A[j].
📥 Input:
Line 1: Integer N (1 ≤ N ≤ 105) Line 2: N integers A[i] (1 ≤ A[i] ≤ 109)
📤 Output:
Number of inversions in the array.
🔍 Sample Input:
5 2 4 1 3 5
✅ Sample Output:
3
💡 Output Explanation:
Inversions are: (2,1), (4,1), (4,3)
📦 Problem 3: Prefix Sum Query
Problem Statement:
Given an array of integers and Q queries, each query asks for the sum of a subarray from index L to R.
📥 Input:
Line 1: Integers N and Q (1 ≤ N, Q ≤ 105) Line 2: N integers A[i] Next Q lines: Two integers L and R (1-based indexing)
📤 Output:
Q lines: each line contains the sum A[L] + ... + A[R]
🔍 Sample Input:
5 3 1 2 3 4 5 1 3 2 4 3 5
✅ Sample Output:
6 9 12
💡 Output Explanation:
Query 1: 1+2+3 = 6 Query 2: 2+3+4 = 9 Query 3: 3+4+5 = 12
🎯 Problem 4: Maximum in Submatrix (2D Array)
Problem Statement:
Given an N×N matrix of integers and a number K, find the maximum value in every K×K submatrix.
📥 Input:
Line 1: Integers N and K (1 ≤ K ≤ N ≤ 500) Next N lines: N space-separated integers each
📤 Output:
Print all maximums of K×K blocks, one per line
🔍 Sample Input:
3 2 1 2 3 4 5 6 7 8 9
✅ Sample Output:
5 6 8 9
💡 Output Explanation:
Four 2×2 submatrices: [1 2] → max = 5 [2 3] [4 5] → max = 6 [5 6] [4 5] → max = 8 [7 8] [5 6] → max = 9 [8 9]
🔁 Problem 5: Matrix Rotation (2D Array)
Problem Statement:
Rotate a square matrix (N×N) 90 degrees clockwise.
📥 Input:
Line 1: Integer N (1 ≤ N ≤ 1000) Next N lines: N integers per row
📤 Output:
The rotated matrix in N lines.
🔍 Sample Input:
3 1 2 3 4 5 6 7 8 9
✅ Sample Output:
7 4 1 8 5 2 9 6 3
💡 Output Explanation:
Rotating the matrix 90° clockwise.
🧠 Problem 1: Count Palindromic Substrings
Problem Statement:
Given a string S, find how many distinct substrings of S are palindromes.
📥 Input:
A single line containing string S (1 ≤ |S| ≤ 1000).
📤 Output:
Print a single integer — the number of palindromic substrings.
🔍 Sample Input:
ababa
✅ Sample Output:
5
💡 Output Explanation:
The palindromic substrings are: a, b, aba, bab, ababa Total = 5
🔡 Problem 2: Group Words by Anagram
Problem Statement: Group N strings into sets of anagrams.
📥 Input:
First line: Integer N (1 ≤ N ≤ 1000) Next N lines: One string per line
📤 Output:
Number of anagram groups.
🔍 Sample Input:
5 listen silent enlist google gogole
✅ Sample Output:
2
💡 Output Explanation:
Group 1: listen, silent, enlist Group 2: google, gogole Total = 2 groups
🔍 Problem 3: Longest Unique Substring
Problem Statement: Find the length of the longest substring without repeating characters.
📥 Input:
A string S (1 ≤ |S| ≤ 105)
📤 Output:
Length of longest unique substring.
🔍 Sample Input:
abcabcbb
✅ Sample Output:
3
💡 Output Explanation:
Longest substrings without repeats: abc, bca, cab Length = 3
🧪 Problem 4: Count Pattern Occurrences
Problem Statement: Count how many times pattern P occurs in string S (including overlaps).
📥 Input:
Line 1: S (1 ≤ |S| ≤ 106) Line 2: P (1 ≤ |P| ≤ 104)
📤 Output:
Number of occurrences.
🔍 Sample Input:
aaaaa aaa
✅ Sample Output:
3
💡 Output Explanation:
"aaa" found at: Index 0 → aaa Index 1 → aaa Index 2 → aaa Total = 3
🧬 Problem 5: Lexicographically Smallest Rotation
Problem Statement: Print the smallest lexicographical rotation of a string.
📥 Input:
One line: a string S (1 ≤ |S| ≤ 1000)
📤 Output:
Smallest rotation of the string.
🔍 Sample Input:
baca
✅ Sample Output:
acab
💡 Output Explanation:
All rotations: baca, acab, caba, abac Sorted: abac, acab, baca, caba Smallest = acab
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