Description 采用Gauss消去法,去解方程组; 如果有n个变量,输入n及n个方程的系数,输出解,保留小数点后3位。 X+Y=3 2X+3Y=8 按顺序输出X,Y; 输入用例: 2 1 1 3 2 3 8 输出用例: 1.000 2.000 Input 输入n及n个方程的系数, Output 输出n个变量的值
时间: 2024-03-06 12:51:29 浏览: 97
以下是使用 Python 编写的解决方案:
```python
n = int(input()) # 输入变量个数
a = [] # 系数矩阵
b = [] # 常数矩阵
# 读取输入数据
for i in range(n):
row = list(map(float, input().split()))
a.append(row[:-1])
b.append([row[-1]])
# 构造增广矩阵
for i in range(n):
a[i].append(b[i][0])
# 高斯消元
for i in range(n):
# 找到最大的系数
max_row = i
for j in range(i+1, n):
if abs(a[j][i]) > abs(a[max_row][i]):
max_row = j
# 交换行
a[i], a[max_row] = a[max_row], a[i]
# 消元
for j in range(i+1, n):
factor = a[j][i] / a[i][i]
for k in range(i, n+1):
a[j][k] -= factor * a[i][k]
# 回代求解
x = [0] * n
for i in range(n-1, -1, -1):
x[i] = a[i][n] / a[i][i]
for j in range(i-1, -1, -1):
a[j][n] -= a[j][i] * x[i]
# 输出结果
for i in range(n):
print('{:.3f}'.format(x[i]))
```
输入样例:
```
2
1 1 3
2 3 8
```
输出样例:
```
1.000
2.000
```
阅读全文
相关推荐















