2Q) You are given a permutation P of length N. This permutation represents a graph of N nodes where for each node i from 1 to N there is an ongoing edge from that node to node P[i].
A permutation is an array of length N, consisting of each of the integers from 1 to N in some order.
The longest path in the graph is the path that satisfies the following conditions: تھا
• It starts at some node U and ends at some node V.
It visits each node no more than once.
• Among all the possible paths, it's the longest one.
Find the total number of possible pairs of indices of the permutation (i, j), such that:
• If P[i] and P[j] are swapped, then the resulting graph has the maximum possible longest path among all the possible swaps.
Since the answer is very large, print it modulo 109+7.
Input Format
The first line contains an integer, N, denoting the number of elements in P.
Each line i of the N subsequent lines (where 0 ≤ i < N) contains an integer describing P[i].
Sample Test Cases
Case 1
Input:
3
1
2
3
Output:
3
Explanation:
Given N 3, P= [1, 2, 3].
Here, if we swap "P[1]" and "P[2]" we will get P = [2, 1, 3]", node "1" can go to node "2" and we can consider that the longest path, and also node "2" can go to node "1", we also can generate the following two permutations:
Case 2
Input:
6
2
3
1
S
6
4
Output:
9
Explanation:
Given N 6, P [2, 3, 1, 5, 6, 4].
Here, we have two cycles, the nodes in the first cycle are "[1, 2, 3]" and the nodes in the second cycle are "[4, 5, 6]".
We can show that if we swap any of the first three elements in the permutation with any element from the last three elements, the cycles will be merged, so the answer is "339".
Case 3
Input:
7
2
3
1
5
4
7
6
Output:
12
Explanation:
Given N 7, P [2, 3, 1, 5, 4, 7, 6].
Here, if we swap any element from the first three elements with any element from the last four elements we'll get a longest path of length "6", and from that the number of swaps to obtain that length (the maximum possible reachable length of the graph) is "3 * 4 = 12".
A permutation is an array of length N, consisting of each of the integers from 1 to N in some order.
The longest path in the graph is the path that satisfies the following conditions: تھا
• It starts at some node U and ends at some node V.
It visits each node no more than once.
• Among all the possible paths, it's the longest one.
Find the total number of possible pairs of indices of the permutation (i, j), such that:
• If P[i] and P[j] are swapped, then the resulting graph has the maximum possible longest path among all the possible swaps.
Since the answer is very large, print it modulo 109+7.
Input Format
The first line contains an integer, N, denoting the number of elements in P.
Each line i of the N subsequent lines (where 0 ≤ i < N) contains an integer describing P[i].
Sample Test Cases
Case 1
Input:
3
1
2
3
Output:
3
Explanation:
Given N 3, P= [1, 2, 3].
Here, if we swap "P[1]" and "P[2]" we will get P = [2, 1, 3]", node "1" can go to node "2" and we can consider that the longest path, and also node "2" can go to node "1", we also can generate the following two permutations:
Case 2
Input:
6
2
3
1
S
6
4
Output:
9
Explanation:
Given N 6, P [2, 3, 1, 5, 6, 4].
Here, we have two cycles, the nodes in the first cycle are "[1, 2, 3]" and the nodes in the second cycle are "[4, 5, 6]".
We can show that if we swap any of the first three elements in the permutation with any element from the last three elements, the cycles will be merged, so the answer is "339".
Case 3
Input:
7
2
3
1
5
4
7
6
Output:
12
Explanation:
Given N 7, P [2, 3, 1, 5, 4, 7, 6].
Here, if we swap any element from the first three elements with any element from the last four elements we'll get a longest path of length "6", and from that the number of swaps to obtain that length (the maximum possible reachable length of the graph) is "3 * 4 = 12".
👍3
3Q) General Ali has devised a strategic game to reduce an enemy army of N soldiers to just 1sdier
The game allows the following three types of moves:
1. Reduce the enemy army by 1 soldier.
2. Reduce the enemy army by half of its current soldiers, rounding down to the nearest integer
3. Reduce the enemy army by two-thirds of its current soldiers, rounding down to the nearest integer
Each move must ensure that the resulting number of soldiers is an integer
Find the minimum number of moves required to reduce enemy army to just 1 soldier
Input Format
The first line contains an integer, N, denoting the number of enemy soldiers.
Constraints
1 <= N <= 10^9
Sample Test Cases
Case 1
Input: 5
Output:
3
Explanation:
Given N 5.
Move 1: Reduce by 1 soldier (5 -> 4)
Move 2: Reduce by half (4-> 2)
Move 3: Reduce by half (21)
Hence, the answer for this case is equal to 3.
Case 2
Input:
1
Output:
e
Explanation:
Given N 1.
There is only 1 soldier already, so to moves are required to reduce the umeny soldiers to
Therefore, the minimum number of noves needed is 8.
The game allows the following three types of moves:
1. Reduce the enemy army by 1 soldier.
2. Reduce the enemy army by half of its current soldiers, rounding down to the nearest integer
3. Reduce the enemy army by two-thirds of its current soldiers, rounding down to the nearest integer
Each move must ensure that the resulting number of soldiers is an integer
Find the minimum number of moves required to reduce enemy army to just 1 soldier
Input Format
The first line contains an integer, N, denoting the number of enemy soldiers.
Constraints
1 <= N <= 10^9
Sample Test Cases
Case 1
Input: 5
Output:
3
Explanation:
Given N 5.
Move 1: Reduce by 1 soldier (5 -> 4)
Move 2: Reduce by half (4-> 2)
Move 3: Reduce by half (21)
Hence, the answer for this case is equal to 3.
Case 2
Input:
1
Output:
e
Explanation:
Given N 1.
There is only 1 soldier already, so to moves are required to reduce the umeny soldiers to
Therefore, the minimum number of noves needed is 8.
👍3
4Q) Handson 1: Array Covered Ranges
You are given an array A of length N.
It is given that the number of covered ranges in the subarray from L to R is defined as the minimum number of ranges, such that the following is true
• All the elements of each range appear as elements of the subarray.
• Each element of the subarray appears in exactly one range where 0 < L, R < N+1.
You have to process Q queries given in a 2D array Queries, where each query contains two integers L and R. For each query, you have to find the number of covered ranges in the subarray from L to R in A.
Find the sum of answers to all queries. Since the answer can be very large, return it modulo 109+7
Input Format
The first line contains an integer, N, denoting the number of elements in A.
Each line i of the N subsequent lines (where 0 ≤ i< N) contains an integer describing Ali)
The next line contains an integer, Q, denoting the number of rows in queries.
The next line contains an integer, two, denoting the number of columns in queries.
Each line i of the Q subsequent lines (where 0 ≤ i < Q) contains two space separated integers each describing the row queries[i].
Constraints
1 <= N <= 10 ^ 6
1 <= A[i] <= 10 ^ 6
1 <= Q <= 10 ^ 6
2 <= two <= 2
1 <= queries[i][j] <= N
Sample Test Cases
Case 1
Input:
1
1
1
2
11
P
Output:
1
Explanation:
Given N = 1 A = [1] Q = 1 two = 2, Queries - [[1, 1]] .
The number of covered ranges in (1) is 1 (the range is [1, 1]).
Hence, the sum of answer of queries is equal to 1.
Case 2
Input:
2
1
3
2
2
11
12
Output:
3
Explanation:
Given N = 2 A = [1, 3] Q = 2 two 2, Queries [[1, 1], [1, 2]].
The number of covered ranges in (1) is 1 in range [1, 1], while the number of covered ranges in (1, 3} is 2 in range [1, 2].
Hence, the sum of answer of queries is equal to 3.
Case 3
Input:
2
1
2
2
2
11
12
Output:
2
Explanation:
Given N = 2 A = [1, 2] Q = 2 two. 2, Queries [ [1, 1] [1, 2]].
The number of covered ranges in both (1) and (1, 2} is 1 in range [1, 1] and [1, 2] respectively.
Hence, the sum of answer of queries is equal to 2.
You are given an array A of length N.
It is given that the number of covered ranges in the subarray from L to R is defined as the minimum number of ranges, such that the following is true
• All the elements of each range appear as elements of the subarray.
• Each element of the subarray appears in exactly one range where 0 < L, R < N+1.
You have to process Q queries given in a 2D array Queries, where each query contains two integers L and R. For each query, you have to find the number of covered ranges in the subarray from L to R in A.
Find the sum of answers to all queries. Since the answer can be very large, return it modulo 109+7
Input Format
The first line contains an integer, N, denoting the number of elements in A.
Each line i of the N subsequent lines (where 0 ≤ i< N) contains an integer describing Ali)
The next line contains an integer, Q, denoting the number of rows in queries.
The next line contains an integer, two, denoting the number of columns in queries.
Each line i of the Q subsequent lines (where 0 ≤ i < Q) contains two space separated integers each describing the row queries[i].
Constraints
1 <= N <= 10 ^ 6
1 <= A[i] <= 10 ^ 6
1 <= Q <= 10 ^ 6
2 <= two <= 2
1 <= queries[i][j] <= N
Sample Test Cases
Case 1
Input:
1
1
1
2
11
P
Output:
1
Explanation:
Given N = 1 A = [1] Q = 1 two = 2, Queries - [[1, 1]] .
The number of covered ranges in (1) is 1 (the range is [1, 1]).
Hence, the sum of answer of queries is equal to 1.
Case 2
Input:
2
1
3
2
2
11
12
Output:
3
Explanation:
Given N = 2 A = [1, 3] Q = 2 two 2, Queries [[1, 1], [1, 2]].
The number of covered ranges in (1) is 1 in range [1, 1], while the number of covered ranges in (1, 3} is 2 in range [1, 2].
Hence, the sum of answer of queries is equal to 3.
Case 3
Input:
2
1
2
2
2
11
12
Output:
2
Explanation:
Given N = 2 A = [1, 2] Q = 2 two. 2, Queries [ [1, 1] [1, 2]].
The number of covered ranges in both (1) and (1, 2} is 1 in range [1, 1] and [1, 2] respectively.
Hence, the sum of answer of queries is equal to 2.
👍5
5Q) string trimmetris
Int get ans
// write your code here
18 11 J
13
14
16
30
int meint) (
Insyrm with stateles cin.tiele); cout 10 (8)
string inutise
Test case
HandsOnSquares Beauty
Summary
Questions
You me quen a square grid A of
You want to choose two non intersecting apuate sob-grids with no common row or column such that the sum of both sub grids is maximized.
Return the maximum possible sum
Input Format
The next line contains an integer. 4. denoting the number of columns in A
Each line i of the N subsequent lines (where N) contains N space separated integers each describing the row Ali
Constraints
1N500
-100 <= A[i][j] <= 100
Int get ans
// write your code here
18 11 J
13
14
16
30
int meint) (
Insyrm with stateles cin.tiele); cout 10 (8)
string inutise
Test case
HandsOnSquares Beauty
Summary
Questions
You me quen a square grid A of
You want to choose two non intersecting apuate sob-grids with no common row or column such that the sum of both sub grids is maximized.
Return the maximum possible sum
Input Format
The next line contains an integer. 4. denoting the number of columns in A
Each line i of the N subsequent lines (where N) contains N space separated integers each describing the row Ali
Constraints
1N500
-100 <= A[i][j] <= 100
6Q) You are given an integer N and a number
Let's define the cost of a string consisting of lowercase Latin letters as the cyelle distance between any two consecutive characters in that string,
Vadlaa
= Questions
For example, the cost of the string "abzy"
can be calculated as follows:
Minimum Cyclic Distance(a, b) + Minimum Cyclic Distance(b, z) +
Minimum CyclicDistance(z, v) = 1 + 2 + 4 = 7.
It is given that two strings of length N are different if their characters differ in at least one position from 1 to N.
Find the number of the distinct strings $ which satisfies the following two conditions
• The length of S is exactly equal to N.
• The cost of S is divisible by • The length of S is exactly equal to N.
The cost of S is divisible by K. vadlaa
Since the answer can be very large, print it modulo 109+7.
Input Format
The first line contains an N. denoting integ N the length of the required string.
The next line contains an integer, K. denoting the given number K.
Error
Constraints
2 <= N <= 10^5
.1 <= K <= 100
Sample Test Cases
Case 1
Input:
2
2
Output:
338
Explanation:
Given N= 2, K=2
In this case, one of the possible strings is "ac", also "ce". We can show that there are exactly "338" strings that satisfy the conditions.
So, answer is 338.
Let's define the cost of a string consisting of lowercase Latin letters as the cyelle distance between any two consecutive characters in that string,
Vadlaa
= Questions
For example, the cost of the string "abzy"
can be calculated as follows:
Minimum Cyclic Distance(a, b) + Minimum Cyclic Distance(b, z) +
Minimum CyclicDistance(z, v) = 1 + 2 + 4 = 7.
It is given that two strings of length N are different if their characters differ in at least one position from 1 to N.
Find the number of the distinct strings $ which satisfies the following two conditions
• The length of S is exactly equal to N.
• The cost of S is divisible by • The length of S is exactly equal to N.
The cost of S is divisible by K. vadlaa
Since the answer can be very large, print it modulo 109+7.
Input Format
The first line contains an N. denoting integ N the length of the required string.
The next line contains an integer, K. denoting the given number K.
Error
Constraints
2 <= N <= 10^5
.1 <= K <= 100
Sample Test Cases
Case 1
Input:
2
2
Output:
338
Explanation:
Given N= 2, K=2
In this case, one of the possible strings is "ac", also "ce". We can show that there are exactly "338" strings that satisfy the conditions.
So, answer is 338.
👍3
7Q) you are given a string S with N characters a string T with M characters and an integer K
you can perform the following operation on s atmost K times
change a character at some index in the string to any other character
find the count of maximum number of subsegments in the S that have T as subsequence after applying the operation
Sample input
3
1
1
abc
d
sample output
1
explanation
Given N=3 M=1 K=1 S=abc T=d
we can change s[1] to d and the ans will be 1
give a code such that output for the given input is 1
sample input 2
3
1
1
abc
b
sample output 2
2
you can perform the following operation on s atmost K times
change a character at some index in the string to any other character
find the count of maximum number of subsegments in the S that have T as subsequence after applying the operation
Sample input
3
1
1
abc
d
sample output
1
explanation
Given N=3 M=1 K=1 S=abc T=d
we can change s[1] to d and the ans will be 1
give a code such that output for the given input is 1
sample input 2
3
1
1
abc
b
sample output 2
2
👍3
8Q) You are given an integer N and a number K.
Let's defind the cost of a string consisting of lowercase latin letters as the cyclic distance between any two consecutive characters in string
For example the cost of the string "abzv" can be calculated as follow:
MinimumCyclicDistance(a,b)+
MinimumCyclicDistance(b,z)+
MinimumCyclicDistance(z,v)= 1+2+4=7
It is given that two strings of length N are different if their character differ at least one position from 1 to N
Find the number of the distinct string S which satisfies the following two conditions:
The length of S is exactly equal to N
The code of S is divisible by K
Since the answer can be very large print it modulo 10 to the power 9 + 7
Input format
The first line contains an integer N denoting the length of the requires string.
The next line contains an integer K denoting the given number K
Constraints
2<=N <= 10^5
1<=K<=100
Sample test case
Case 1
Input
2
2
Output
338
Explanation:
In this case, one of the possible strings is "ac", also "ce".
We can show that there Re exactly*338" strings that satisfy the conditions
So the answer is 338.
Case 2;
Input:
3
1
Output
17576
Explanation:
Given N =3, K= 1
In this sample, since every number is divisible by "1", then any string of length "3" is "26 * 26 * 26= 17576".
Case 3:
Input :
2
13
Output
52
Explanation:
In this case, one of the possible strings is"an", also "cp"
We can show that there are exactly "52" strings that satisfy the conditions
Let's defind the cost of a string consisting of lowercase latin letters as the cyclic distance between any two consecutive characters in string
For example the cost of the string "abzv" can be calculated as follow:
MinimumCyclicDistance(a,b)+
MinimumCyclicDistance(b,z)+
MinimumCyclicDistance(z,v)= 1+2+4=7
It is given that two strings of length N are different if their character differ at least one position from 1 to N
Find the number of the distinct string S which satisfies the following two conditions:
The length of S is exactly equal to N
The code of S is divisible by K
Since the answer can be very large print it modulo 10 to the power 9 + 7
Input format
The first line contains an integer N denoting the length of the requires string.
The next line contains an integer K denoting the given number K
Constraints
2<=N <= 10^5
1<=K<=100
Sample test case
Case 1
Input
2
2
Output
338
Explanation:
In this case, one of the possible strings is "ac", also "ce".
We can show that there Re exactly*338" strings that satisfy the conditions
So the answer is 338.
Case 2;
Input:
3
1
Output
17576
Explanation:
Given N =3, K= 1
In this sample, since every number is divisible by "1", then any string of length "3" is "26 * 26 * 26= 17576".
Case 3:
Input :
2
13
Output
52
Explanation:
In this case, one of the possible strings is"an", also "cp"
We can show that there are exactly "52" strings that satisfy the conditions
👍1