21. Find the length of the longest increasing subsequence for the given sequence:
{-10, 24, -9, 35, -21, 55, -41, 76, 84}
{-10, 24, -9, 35, -21, 55, -41, 76, 84}
22. In which of the following cases will the edit distance between two strings be zero?
23. What is the output of the following program?
#include<stdio.h>
#include<limits.h>
int min_jumps(int *arr, int strt, int end)
{
int idx;
if(strt == end)
return 0;
if(arr[strt] == 0) // jump cannot be made
return INT_MAX;
int min = INT_MAX;
for(idx = 1; idx <= arr[strt] && strt + idx <= end; idx++)
{
int jumps = min_jumps(arr, strt + idx, end) + 1;
if(jumps < min)
min = jumps;
}
return min;
}
int main()
{
int arr[] ={1, 2, 3, 4, 5, 4, 3, 2, 1},len = 9;
int ans = min_jumps(arr, 0, len-1);
printf("%d\n",ans);
return 0;
}
#include<stdio.h>
#include<limits.h>
int min_jumps(int *arr, int strt, int end)
{
int idx;
if(strt == end)
return 0;
if(arr[strt] == 0) // jump cannot be made
return INT_MAX;
int min = INT_MAX;
for(idx = 1; idx <= arr[strt] && strt + idx <= end; idx++)
{
int jumps = min_jumps(arr, strt + idx, end) + 1;
if(jumps < min)
min = jumps;
}
return min;
}
int main()
{
int arr[] ={1, 2, 3, 4, 5, 4, 3, 2, 1},len = 9;
int ans = min_jumps(arr, 0, len-1);
printf("%d\n",ans);
return 0;
}24. In the worst case, the minimum number of insertions to be made to convert the string into a palindrome is equal to the length of the string.
25. What is the time complexity of Kadane's algorithm?
26. You are given infinite coins of denominations 1, 3, 4. What is the total number of ways in which a sum of 7 can be achieved using these coins if the order of the coins is not important?
27. Longest common subsequence is an example of . . . . . . . .
28. What is the output of the following implementation of Kadane's algorithm?
#include<stdio.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int kadane_algo(int *arr, int len)
{
int ans, sum, idx;
ans =0;
sum =0;
for(idx =0; idx < len; idx++)
{
sum = max_num(0,sum + arr[idx]);
ans = max_num(sum,ans);
}
return ans;
}
int main()
{
int arr[] = {2, 3, -3, -1, 2, 1, 5, -3}, len = 8;
int ans = kadane_algo(arr,len);
printf("%d",ans);
return 0;
}
#include<stdio.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int kadane_algo(int *arr, int len)
{
int ans, sum, idx;
ans =0;
sum =0;
for(idx =0; idx < len; idx++)
{
sum = max_num(0,sum + arr[idx]);
ans = max_num(sum,ans);
}
return ans;
}
int main()
{
int arr[] = {2, 3, -3, -1, 2, 1, 5, -3}, len = 8;
int ans = kadane_algo(arr,len);
printf("%d",ans);
return 0;
}29. What is the time complexity of the brute force implementation of the maximum sum rectangle problem?
30. You are given n dice each having f faces. You have to find the number of ways in which a sum of S can be achieved. This is the dice throw problem. Which of the following methods can be used to solve the dice throw problem?
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