LeetCode 528. Random Pick with Weight

原题链接在这里：https://leetcode.com/problems/random-pick-with-weight/

题目：

Given an array w of positive integers, where w[i] describes the weight of index i, write a function pickIndex which randomly picks an index in proportion to its weight.

Note:

1. 1 <= w.length <= 10000
2. 1 <= w[i] <= 10^5
3. pickIndex will be called at most 10000 times.

Example 1:

Input:
["Solution","pickIndex"]
[[[1]],[]]
Output: [null,0]

Example 2:

Input:
["Solution","pickIndex","pickIndex","pickIndex","pickIndex","pickIndex"]
[[[1,3]],[],[],[],[],[]]
Output: [null,0,1,1,1,0]

Explanation of Input Syntax:

The input is two lists: the subroutines called and their arguments. Solution's constructor has one argument, the array w. pickIndex has no arguments. Arguments are always wrapped with a list, even if there aren't any.

题解：

The given input array means for current index i, the weight is w[i].

e.g. w = [20, 20, 60]. The weight of choosing 0 is 20, the weight of choosing 1 is 20, the weight of choosing 2 is 60, totally it is 100.

In order to choose by weight, we need to accumlat the total weight, and pick a random number within [1, total weight].

sum = [20, 40, 100]

And binary search where this weight would land.

If sum[mid] == pick, then simply return mid.

Else if sum[mid] < pick, say pick = 50, sum[mid] = 40, then it can't be index 1, since 1 is from 20 to 40. l = mid + 1.

Else if sum[mid] > pick, say pick = 30, sum[mid] = 40, then it could still be index 1, since 1 is from 20 to 40. r = mid.

When using above transion, while loop condision is l < r, it can't be l <= r. Otherwise, it would get out of loop.

Time Complexity: pickIndex, O(logw.length).

Space: O(1). It doesn't have extra array, it is changing input w array.

AC Java:

 class Solution {
     int [] sum;
     Random rand;

     public Solution(int[] w) {
         for(int i = 1; i<w.length; i++){
             w[i] += w[i-1];
         }

         this.sum = w;
         this.rand = new Random();
     }

     public int pickIndex() {
         int len = sum.length;
         int n = sum[len-1];
         int pick = rand.nextInt(n) + 1;

         int l = 0;
         int r = len-1;
         while(l < r){
             int mid = l + (r - l) / 2;
             if(sum[mid] == pick){
                 return mid;
             }else if(sum[mid] < pick){
                 l = mid + 1;
             }else{
                 r = mid;
             }
         }

         return l;
     }
 }

 /**
  * Your Solution object will be instantiated and called as such:
  * Solution obj = new Solution(w);
  * int param_1 = obj.pickIndex();
  */

类似Random Pick Index, Linked List Random Node.