You are given two strings a๐ and b๐ of length n๐. Then, you are (forced against your will) to answer q๐ queries.For each query, you are given a range bounded by l๐ and r๐. In one operation, you can choose an integer i๐ (lโคiโคr๐โค๐โค๐) and set ai=x๐๐=๐ฅ where x๐ฅ is any character you desire. Output the minimum number of operations you must perform such that sorted(a[l..r])=sorted(b[l..r])sorted(a[l..r])=sorted(b[l..r]). The operations you perform on one query does not affect other queries.For an arbitrary string c๐, sorted(c[l..r])sorted(c[l..r]) denotes the substring consisting of characters cl,cl+1,...,cr๐๐,๐๐+1,...,๐๐ sorted in lexicographical order.InputThe first line contains t๐ก (1โคtโค10001โค๐กโค1000) โ the number of test cases.The first line of each test case contains two integers n๐ and q๐ (1โคn,qโค2โ 1051โค๐,๐โค2โ 105) โ the length of both strings and the number of queries.The following line contains a๐ of length n๐. It is guaranteed a๐ only contains lowercase latin letters.The following line contains b๐ of length n๐. It is guaranteed b๐ only contains lowercase latin letters.The following q๐ lines contain two integers l๐ and r๐ (1โคlโคrโคn1โค๐โค๐โค๐) โ the range of the query.It is guaranteed the sum of n๐ and q๐ over all test cases does not exceed 2โ 1052โ 105.OutputFor each query, output an integer, the minimum number of operations you need to perform in a new line.ExampleinputCopy35 3abcdeedcba1 51 43 34 2zzdeazbe1 31 46 3uwuwuwwuwuwu2 41 31 6outputCopy01022110NoteFor the first query, sorted(a[1..5])=sorted(a[1..5])= abcde and sorted(b[1..5])=sorted(b[1..5])= abcde, so no operations are necessary.For the second query, you need to set a1=๐1= e. Then, sorted(a[1..4])=sorted(b[1..4])=sorted(a[1..4])=sorted(b[1..4])= bcde.
Question
You are given two strings a๐ and b๐ of length n๐. Then, you are (forced against your will) to answer q๐ queries.For each query, you are given a range bounded by l๐ and r๐. In one operation, you can choose an integer i๐ (lโคiโคr๐โค๐โค๐) and set ai=x๐๐=๐ฅ where x๐ฅ is any character you desire. Output the minimum number of operations you must perform such that sorted(a[l..r])=sorted(b[l..r])sorted(a[l..r])=sorted(b[l..r]). The operations you perform on one query does not affect other queries.For an arbitrary string c๐, sorted(c[l..r])sorted(c[l..r]) denotes the substring consisting of characters cl,cl+1,...,cr๐๐,๐๐+1,...,๐๐ sorted in lexicographical order.InputThe first line contains t๐ก (1โคtโค10001โค๐กโค1000) โ the number of test cases.The first line of each test case contains two integers n๐ and q๐ (1โคn,qโค2โ 1051โค๐,๐โค2โ 105) โ the length of both strings and the number of queries.The following line contains a๐ of length n๐. It is guaranteed a๐ only contains lowercase latin letters.The following line contains b๐ of length n๐. It is guaranteed b๐ only contains lowercase latin letters.The following q๐ lines contain two integers l๐ and r๐ (1โคlโคrโคn1โค๐โค๐โค๐) โ the range of the query.It is guaranteed the sum of n๐ and q๐ over all test cases does not exceed 2โ 1052โ 105.OutputFor each query, output an integer, the minimum number of operations you need to perform in a new line.ExampleinputCopy35 3abcdeedcba1 51 43 34 2zzdeazbe1 31 46 3uwuwuwwuwuwu2 41 31 6outputCopy01022110NoteFor the first query, sorted(a[1..5])=sorted(a[1..5])= abcde and sorted(b[1..5])=sorted(b[1..5])= abcde, so no operations are necessary.For the second query, you need to set a1=๐1= e. Then, sorted(a[1..4])=sorted(b[1..4])=sorted(a[1..4])=sorted(b[1..4])= bcde.
Solution
This problem can be solved by using a prefix sum array and a greedy approach. Here are the steps to solve this problem:
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First, create a prefix sum array for both strings a and b. The prefix sum array will store the count of each character from 'a' to 'z' up to the current index. This can be done by iterating over the strings and for each character, incrementing the count in the prefix sum array.
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For each query, get the range l and r. Then, compare the prefix sum arrays of a and b in the range l to r. If the prefix sum arrays are not equal, it means that there are some characters in a that are not in b or vice versa. The minimum number of operations required will be the difference in the counts of these characters.
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If the prefix sum arrays are equal, it means that the sorted substrings of a and b in the range l to r are already equal. So, no operations are required.
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Repeat the above steps for all queries.
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Finally, print the minimum number of operations for each query.
This approach works because the prefix sum array allows us to quickly compare the counts of each character in the range l to r. And the greedy approach ensures that we perform the minimum number of operations.
Similar Questions
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