43 Multiply Strings

43 Multiply Strings


https://www.youtube.com/watch?v=q3vpdwWR0ag&t=1s

https://leetcode.com/problems/multiply-strings/discuss/17605/Easiest-JAVA-Solution-with-Graph-Explanation


class Solution {
    public String multiply(String nums1, String nums2) {
      int n = nums1.length();
      int m = nums2.length();
      int[] result = new int[n + m];
      
      for(int i = n -1; i >= 0; i--){
        for(int j = m - 1; j >= 0; j--){
          int mul = (nums1.charAt(i) - '0') * (nums2.charAt(j) - '0');
              //Integer.valueOf(nums1.charAt(i)) * Integer.valueOf(nums2.charAt(j));
          int p1 = i + j;
          int p2 = i + j + 1;
          
          int sum = mul + result[p2];
          result[p2] = sum % 10;
          result[p1] += sum / 10;
        }
      }
      
      
      StringBuilder sb = new StringBuilder();
      /
      for(int i = 0; i < result.length; i++){
        if(sb.length() == 0 && result[i] == 0){
          continue;
        }else{
          sb.append(result[i]);
        }
      }
      
      if(sb.length() == 0){
        return "0";
      }else{
        return sb.toString();
      }
    }
}



1. 
number in the form of a string 
for example
String nums = "123" 
  is a string 
represents the number 123 
  if we want to get a single number  2 from this string 
  
  we can do
    (nums.charAt(1) - '0') = 2 


2.   
   
  when the int[] result = 00123
    we want only 123 
    so we need to skip 00
    how?
    okay , so when the stringbuilder.length() == 0
    and the current number is 0 
    we continue
        
3. 
   in the example 123 * 45 
  
  when 3 * 5 
  
  3's index is 2 (index 0 is 1)
  5's index is 1 (index 0 is 4)
  
  so their position in the result is 2+1, 2+1+1
  
  
  4. 

its easier with the graph 

2 5
0 8
---
p1 p2 


suppose we get 08 from 4 * 2 
  mul = 8
  
  
  // int sum = mul + pos[p2];
  8 + 5 = 13 = sum  
  
  // pos[p2] = (sum) % 10;

  13 % 10 = 3 is for p2 position 
  
  
  // pos[p1] += sum / 10;
  13 / 10 + 2 = 1 + 2 = 3  is for p1 position 

use int[] array , instead of use stringbuilder 

Because we need to accumulate  digits on the same index 

And the result length is no bigger than n + m 

 

the two for loops is from the last index to index 0

Because its the last index of a , * , the last index of b, the second last index of b, the third last index of b, .. so on until the index 0 of b, 

 

 

 

And its the second last index of a , * ,   the last index of b, the second last index of b, the third last index of b, .. so on until the index 0 of b,

 

And the third last index of a, *, the last index of b, the second last index of b, the third last index of b, .. so on until the index 0 of b

 

.

.

.

The index  0 of a, *, the last index of b, the second last index of b, the third last index of b, .. so on until the index 0 of b,

 

 

if you multiply the index i of a, and the index j of b, then their product is in the new index of 

I +j and I + j + 1. 

 

Int sum = a[I] * b[j];

 

 int p1 = i + j;

 int p2 = i + j + 1;

 

So the order of p1 and p2 is like this: p1 p2

 

 

to add the sum into the result has a process like this: 

sum = Sum + result[p2] 

This is the new sum , 

And the digit for p2 is sum % 10

And the carry is sum / 10

And we need to add the carry into result[p1] 

 

 

 

===

So the output should be a string, and now we have an int[] array 

So we need to convert this int[] array into a string 

One thing to keep in mind is that we might not be able to occupy all the spaces in the 

Int array, so the unoccupied space is 0 by default

 

When converting the int[] array into the string, we skip the leading 0, 

we know its leading 0 when result[I] == 0 and sb.length() == 0, (we haven’t append anything into the stringbuilder ) ,use continue to the next I 

 

if the result is 0, 12 * 0 = 0, our multiplication for 0 works , then when we append the result int[] array into the stringbuilder, we append nothing , and the stringbuilder .length== 0, then return 0, else return stringbuilder 

 

 

 

 

Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.

Example 1:

Input: num1 = "2", num2 = "3"
Output: "6"

Example 2:

Input: num1 = "123", num2 = "456"
Output: "56088"

Note:

1. The length of both num1 and num2 is < 110.
2. Both num1 and num2 contain only digits 0-9.
3. Both num1 and num2 do not contain any leading zero, except the number 0 itself.
4. You must not use any built-in BigInteger library or convert the inputs to integer directly.