SOLN: Minimum window substring (#192)

Author: retiman

src/sliding-window/minimum-window-substring.ts

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+// DIFFICULTY: HARD
+//
+// Given two strings s and t of lengths m and n respectively, return the minimum window substring of s such that every
+// character in t (including duplicates) is included in the window. If there is no such substring, return the empty
+// string "".
+//
+// The testcases will be generated such that the answer is unique.
+//
+// @see {@link https://leetcode.com/problems/minimum-window-substring/}
+export { minWindow };
+
+// SOLUTION:
+//
+// This can be solved using the sliding window technique with a bunch of extra bookkeeping.  The right pointer will be
+// expanded until we have a valid window, then the left pointer will be shrunk to the minimum size window that still
+// satisfies the requirements.
+//
+// COMPLEXITY:
+//
+// Time complexity is O(m + n) because we iterate through both the source and the target strings.
+//
+// The want map is O(n) space complexity because we store character frequency of the target string.  The got map is
+// O(m) space complexity because we store character frequency of the source string.  Together it's O(m + n).
+function minWindow(s: string, t: string): string {
+  // It is not possible to return a minimum window here; the target substring MUST be shorter than the source string.
+  if (t.length > s.length) {
+    return '';
+  }
+
+  // First we need to create a frequency map, so we can easily check if a substring has all the characters in t.  This
+  // is required because the characters in t can be duplicated, and we require the same number of duplicates in the
+  // source substring.
+  const want = new Map<string, number>();
+  for (const c of t) {
+    const freq = want.get(c) || 0;
+    want.set(c, freq + 1);
+  }
+
+  // Define both pointers to start at the source string, and start by expanding the right pointer.  Once a valid window
+  // is discovered, we contract the left pointer.
+  let left = 0;
+  let right = 0;
+
+  // Define a map to keep track of the characters we have seen so far in the window.  This will let us know when we have
+  // a valid window.
+  //
+  // We also keep track of which characters we've 'gotten' so far.  That is, if we have a requirement to contain X
+  // number of 'a' characters, and we have seen X characters, then we have 'gotten' that character.  When we have
+  // 'gotten' all characters in the string, we have a valid window.
+  const got = new Map<string, number>();
+  let gotten = 0;
+
+  // Keep track of our minimum window substring.  The left pointer should point to the start, and the size will tell us
+  // the length of the window, allowing us to call s.substring() later.
+  //
+  // If we run through the algorithm and don't get a valid window, because minSize never got updated, then we return ''.
+  let minLeft = 0;
+  let minSize = Infinity;
+
+  // Begin by expanding the right pointer until we have a valid window.
+  while (right < s.length) {
+    // Update the frequency of the character that we have got.
+    const c = s[right];
+    const freq = got.get(c) || 0;
+    got.set(c, freq + 1);
+
+    // If it turns out that we got exactly the frequency of character c that we wanted, then the requirement to contain
+    // X number of character c has been satisfied.
+    if (want.has(c) && want.get(c) === got.get(c)) {
+      gotten++;
+    }
+
+    // If we've gotten all the characters at exactly the right frequency, then we have a valid window.  In that case,
+    // we can begin shrinking the window to see if it stays valid.
+    while (gotten === want.size) {
+      const k = s[left];
+
+      // Calculate the size of the window.  Note that left and right are INCLUSIVE indexes, so if we want the window
+      // size of say [0, 1, 2, 3] with left = 0 and right = 3 (a window size of 4), we should do 3 - 0 + 1 = 4.
+      //
+      // So make sure to add 1 here to get the correct size.
+      const size = right - left + 1;
+      if (size < minSize) {
+        minSize = size;
+        minLeft = left;
+      }
+
+      // Now try to contract the window by moving the left pointer.  When we do this, we have to update the frequency
+      // of characters we've gotten so far, and update the gotten count.
+      //
+      // Update the frequency of the character that we are about to lose.  Then if we have got fewer characters than
+      // wanted, we decrement the 'gotten' count because we no longer have a valid window.
+      got.set(k, got.get(k)! - 1);
+      if (want.has(k) && got.get(k)! < want.get(k)!) {
+        gotten--;
+      }
+
+      // After performing the bookkeeping, we can now shrink the window by moving the left pointer.
+      left++;
+    }
+
+    // Keep expanding the right window until we have a valid window.
+    right++;
+  }
+
+  // This means we didn't find any valid window.
+  if (minSize === Infinity) {
+    return '';
+  }
+
+  return s.substring(minLeft, minLeft + minSize);
+}

test/sliding-window/minimum-window-substring.test.ts

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+import { minWindow } from '../../src/sliding-window/minimum-window-substring';
+
+describe('minimum window substring', () => {
+  test('minWindow - test case 1', async () => {
+    expect(minWindow('ADOBECODEBANC', 'ABC')).toStrictEqual('BANC');
+  });
+});