XTU 1249 Rolling Variance
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Rolling Variance
Accepted : 77 Submit : 212Time Limit : 3000 MS Memory Limit : 65536 KB Special JudgeRolling Variance
Bobo learnt that the variance of a sequence
Bobo has a sequence
Input
The input contains at most
The first line contains
The second line contains
Output
For each set,
Your answer will be considered correct if its absolute or relative error does not exceed
Sample Input
3 21 3 25 31 3 2 4 5
Sample Output
1.414213560.707106781.000000001.000000001.52752523
解题思路:先求出m个连续的数的平均值a,然后求(ai-a)^2
求和:(a0+a)^2+(a1+a)^2+(a2+a)^2+(a3+a)^2+···
=a0^2+2*a*a0+a^2+a1^2+2*a*a1+a^2+a2^2+2*a*a2+a^2+·····
=(a0^2+a1^2+····)+a2^2+2*a*(a0+a1+a2+····)+(a^2+a^2+a^2+·····)
代码如下:
#include <stdio.h>#include <math.h>#include <string.h>#define maxn 100001int a[maxn],b[maxn];int main(){ int n,m,c; while(scanf("%d %d",&n,&m)!=EOF) { int i; for(i=1; i<=n; i++) { scanf("%d",&c); a[i]=a[i-1]+c;///前i个数的和 b[i]=b[i-1]+c*c;///前i个数的平方和 } for(i=m; i<=n;i++) { double s=0; s=1.0*(a[i]-a[i-m])/(1.0*m);///求出平均数 s=b[i]-b[i-m]+s*s*m-2.0*s*(a[i]-a[i-m]); printf("%0.8lf\n",(double)sqrt(s/(m-1))); } } return 0;}
aa¯
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