51、剑指offer--构建乘积数组

题目描述

给定一个数组A[0,1,...,n-1],请构建一个数组B[0,1,...,n-1],其中B中的元素B[i]=A[0]*A[1]*...*A[i-1]*A[i+1]*...*A[n-1]。不能使用除法。

 

解题思路：B[I] = (A[0]*A[1]*...*A[I-1]) * (A[I+1]*A[I+2]*...*A[n-1])

C[i] = A[0]*A[1]*...*A[I-1] = C[i-1]*A[i-1];

D[i] = A[I+1]*A[I+2]*...*A[n-1] = A[i+1]*D[i+2];

B[i] = C[i]*D[i];

class Solution {
public:
    //B[i]=A[0]*A[1]*...*A[i-1]*A[i+1]*...*A[n-1]
    //从左到右算 B[i]=A[0]*A[1]*...*A[i-1]
    //从右到左算B[i]*=A[i+1]*...*A[n-1]
    //C[i] = C[i-1] * A[i-1]
    //D[i] = D[i+1] * A[i+1];
    vector<int> multiply(const vector<int>& A) {
        int length = A.size();
        vector<int> B(length);
        B[0] = 1;
        for(int i=1;i<length;i++)
        {
            B[i] = B[i-1] * A[i-1];
        }
        double temp = 1;
        for(int i=length-2;i>=0;--i)
        {
            temp = temp * A[i+1];
            B[i] *= temp;
        }
        return B;
    }
};