Pro.ID22131 TitleTrinucleotide Title链接http://10.20.2.8/oj/exercise/problem?problem_id=22131 AC0 Submit80 Ratio0.00% 时间&空间限制描述Bioinformatics, as a new subject, get its great development in science. Researches in DNA (Deoxyribonucleic acid) are very popular today. We know that DNA is made up with nucleotides, which are 'A', 'T', 'C', 'G'. Studying from some thesis, we know "Genomic Signature"(基因特征组), another hotspot in bioinformatics, is preserved in short DNA fragments. So in this problem, we focus on "Trinucleotide"(三核苷酸) — DNA fragments with length 3. There are 64 species of trinucleotide, which are "AAA", "AAG", ... ,"GGG". In a DNA sequence with length L, there are (L-2) trinucleotides. We use statistical method to do some analyses. See below: For these (L-2) trinucleotides, we give each of them a label, from 1 to L-2. We select every pairs of trinucleotides, there are (L-2)*(L-3)/2 pairs totally. If a pair of two trinucleotides is same, we note down the distance of these two trinucleotides. The distance is defined as the differences between the labels. According these "Sample Data"(样本数据) we noted down, we need to calculate the "Variance"(方差) of the sample data. Do you still remember how to calculate the variance? S2=[(x1-X)2+{x2-X)2 .. .+ (xn-X)2]/n, X=(x1+x2+.. .+xn)/n. If the sample data size n=0, we assume that S2=X=0. For example, for the DNA sequence ATATATA: We label the trinucleotides. L1 : ATA, L2 : TAT, L3 : ATA, L4 : TAT, L5 : AtA (L1, L3)=2, (L1, L5)=4, (L3, L5)=2, (L2, L4)=2. So the sample data is 2, 4, 2, 2. The average X=(2+4+2+2)/4=2.5 . The variance S2= [(2-2.5)2+(4-2.5)2+(2-2.5)2+(2-2.5)2]/4 = 0.75 Now I give you a DNA sequence, please calculate the variance mentioned aboves. 输入The first line of input there is one integer T ( T ≤ 100), giving the number of test cases in the input. For each test case, there is a string consists with 'A', 'T', 'C', 'G', which is the DNA sequence. The length of the string will be no less than 3 and no more than 100000. 输出Description Bioinformatics, as a new subject, get its great development in science. Researches in DNA (Deoxyribonucleic acid) are very popular today. We know that DNA is made up with nucleotides, which are 'A', 'T', 'C', 'G'. Studying from some thesis, we know "Genomic Signature"(基因特征组), another hotspot in bioinformatics, is preserved in short DNA fragments. So in this problem, we focus on "Trinucleotide"(三核苷酸) — DNA fragments with length 3. There are 64 species of trinucleotide, which are "AAA", "AAG", ... ,"GGG". In a DNA sequence with length L, there are (L-2) trinucleotides. We use statistical method to do some analyses. See below: For these (L-2) trinucleotides, we give each of them a label, from 1 to L-2. We select every pairs of trinucleotides, there are (L-2)*(L-3)/2 pairs totally. If a pair of two trinucleotides is same, we note down the distance of these two trinucleotides. The distance is defined as the differences between the labels. According these "Sample Data"(样本数据) we noted down, we need to calculate the "Variance"(方差) of the sample data. Do you still remember how to calculate the variance? S2=[(x1-X)2+{x2-X)2 .. .+ (xn-X)2]/n, X=(x1+x2+.. .+xn)/n. If the sample data size n=0, we assume that S2=X=0. For example, for the DNA sequence ATATATA: We label the trinucleotides. L1 : ATA, L2 : TAT, L3 : ATA, L4 : TAT, L5 : AtA (L1, L3)=2, (L1, L5)=4, (L3, L5)=2, (L2, L4)=2. So the sample data is 2, 4, 2, 2. The average X=(2+4+2+2)/4=2.5 . The variance S2= [(2-2.5)2+(4-2.5)2+(2-2.5)2+(2-2.5)2]/4 = 0.75 Now I give you a DNA sequence, please calculate the variance mentioned aboves. Input The first line of input there is one integer T ( T ≤ 100), giving the number of test cases in the input. For each test case, there is a string consists with 'A', 'T', 'C', 'G', which is the DNA sequence. The length of the string will be no less than 3 and no more than 100000. Output For each test case, output one line with the answer S2, rounded to 1e-6. If the "Relative error" between your answer and standard output is less than 1e-8, we consider you are right. Sample Input 1 Sample Output 0.750000 Source 样例输入1 样例输出0.750000 作者 |
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