hdu 2086 A1 = ?
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有如下方程:Ai = (Ai-1 + Ai+1)/2 - Ci (i = 1, 2, 3, .... n).
若给出A0, An+1, 和 C1, C2, .....Cn.
若给出A0, An+1, 和 C1, C2, .....Cn.
请编程计算A1 = ?
由原式可推:
A1 + A2 + A3 + ... + An = (A0 + A1 + 2*A2 + 2*A3 + .. .+ 2*An-1 + An + An+1) / 2 - c1 - c2 - c3 - .... - cn
==> A1 + An = A0 + An+1 - 2(c1 + c2 + c3 + ... +cn)
A1 + A1 = A0 + A2 - 2*c1
A1 + A2 = A0 + A3 - 2(c1 + c2)
...................
(n + 1)*A1 = n*A0 + An+1 - 2(n*c1 + (n-1)*c2 + (n-2)*c3 + .. .+ cn)
#include<stdio.h>#define N 3001int main(){ int n; float a, b; float c[N]; float sum; while(~scanf("%d", &n)) { sum = 0; scanf("%f%f", &a, &b); for (int i = 1; i <= n; i++) { scanf("%f", &c[i]); c[i] *= (n-i+1); sum += c[i]; } sum *= 2; float ans = (n*a + b - sum) / (n+1); printf("%.2f\n", ans); }}
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