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Author: jimit105

0912-random-pick-with-weight/README.md

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+<p>You are given a <strong>0-indexed</strong> array of positive integers <code>w</code> where <code>w[i]</code> describes the <strong>weight</strong> of the <code>i<sup>th</sup></code> index.</p>
+
+<p>You need to implement the function <code>pickIndex()</code>, which <strong>randomly</strong> picks an index in the range <code>[0, w.length - 1]</code> (<strong>inclusive</strong>) and returns it. The <strong>probability</strong> of picking an index <code>i</code> is <code>w[i] / sum(w)</code>.</p>
+
+<ul>
+	<li>For example, if <code>w = [1, 3]</code>, the probability of picking index <code>0</code> is <code>1 / (1 + 3) = 0.25</code> (i.e., <code>25%</code>), and the probability of picking index <code>1</code> is <code>3 / (1 + 3) = 0.75</code> (i.e., <code>75%</code>).</li>
+</ul>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<pre>
+<strong>Input</strong>
+[&quot;Solution&quot;,&quot;pickIndex&quot;]
+[[[1]],[]]
+<strong>Output</strong>
+[null,0]
+
+<strong>Explanation</strong>
+Solution solution = new Solution([1]);
+solution.pickIndex(); // return 0. The only option is to return 0 since there is only one element in w.
+</pre>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<pre>
+<strong>Input</strong>
+[&quot;Solution&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;,&quot;pickIndex&quot;]
+[[[1,3]],[],[],[],[],[]]
+<strong>Output</strong>
+[null,1,1,1,1,0]
+
+<strong>Explanation</strong>
+Solution solution = new Solution([1, 3]);
+solution.pickIndex(); // return 1. It is returning the second element (index = 1) that has a probability of 3/4.
+solution.pickIndex(); // return 1
+solution.pickIndex(); // return 1
+solution.pickIndex(); // return 1
+solution.pickIndex(); // return 0. It is returning the first element (index = 0) that has a probability of 1/4.
+
+Since this is a randomization problem, multiple answers are allowed.
+All of the following outputs can be considered correct:
+[null,1,1,1,1,0]
+[null,1,1,1,1,1]
+[null,1,1,1,0,0]
+[null,1,1,1,0,1]
+[null,1,0,1,0,0]
+......
+and so on.
+</pre>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= w.length &lt;= 10<sup>4</sup></code></li>
+	<li><code>1 &lt;= w[i] &lt;= 10<sup>5</sup></code></li>
+	<li><code>pickIndex</code> will be called at most <code>10<sup>4</sup></code> times.</li>
+</ul>

0912-random-pick-with-weight/solution.py

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+# Approach 1: Prefix Sums with Binary Search
+
+# Time: O(n) for constructor, O(log n) for `pickIndex`
+# Space: O(n) for constructor, O(1) for `pickIndex`
+
+import random
+
+class Solution:
+
+    def __init__(self, w: List[int]):
+        self.prefix_sums = []
+        prefix_sum = 0
+
+        for weight in w:
+            prefix_sum += weight
+            self.prefix_sums.append(prefix_sum)
+        self.total_sum = prefix_sum
+
+    def pickIndex(self) -> int:
+        target = self.total_sum * random.random()
+
+        low, high = 0, len(self.prefix_sums)
+        while low < high:
+            mid = low + (high - low) // 2
+            if target > self.prefix_sums[mid]:
+                low = mid + 1
+            else:
+                high = mid
+
+        return low
+
+
+# Your Solution object will be instantiated and called as such:
+# obj = Solution(w)
+# param_1 = obj.pickIndex()