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+# Review 1
+<style>
+html {
+    -webkit-print-color-adjust: exact;
+}
+</style>
+
+* Hajin Ju, 2024062806
+
+## Problem 1
+
+1
+Fill in the blank entries when the numbers are sorted by insertion sort in non-decreasing order.
+
+```python { cmd, output='html' hide }
+from bs4 import BeautifulSoup as bs
+
+data = [
+[(7, False), (4, False), (3, False), (6, False), (8, False), (1, False), (2, False)],
+[(7, True), (4, False), (3, False), (6, False), (8, False), (1, False), (2, False)],
+[(4, True), (7, True), None, None, None, None, None],
+]
+
+soup = bs("<div></div>", 'lxml')
+td_style = "border: 1px solid black; padding: 10px; text-align: center; font-size: 1.2rem; min-width: 3rem;"
+td_style_high = "border: 1px solid black; padding: 10px; text-align: center; font-size: 1.2rem; min-width: 3rem; background-color: lightgray;"
+
+for i in range(3):
+    table = soup.new_tag("table")
+    table["style"] = "display: flex; justify-content: center;"
+    tr = soup.new_tag("tr")
+    for d in data[i]:
+        td = soup.new_tag("td")
+        if d:
+            td['style'] = td_style_high if d[1] else td_style
+            td.string = str(d[0]) if d else " "
+        else:
+            td["style"] = td_style
+            td.string = " "
+        tr.append(td)
+    table.append(tr)
+    soup.div.append(table)
+
+print(soup.prettify())
+```
+
+### Solution 1
+
+```python { cmd, output='html', hide }
+from bs4 import BeautifulSoup as bs
+
+data = [
+[(7, False), (4, False), (3, False), (6, False), (8, False), (1, False), (2, False)],
+]
+
+# insertion sorting process
+
+for i in range(len(data[0])):
+    cur =  data[-1].copy()
+    cur[i] = (cur[i][0], True)
+    key = cur[i][0]
+    while i > 0:
+        i -= 1
+        if key >= cur[i][0]:
+            break
+        else:
+            temp = cur[i + 1]
+            cur[i + 1] = cur[i]
+            cur[i] = temp
+        
+    data.append(cur)
+        
+
+
+soup = bs("<div></div>", 'lxml')
+td_style = "border: 1px solid black; padding: 10px; text-align: center; font-size: 1.2rem; min-width: 3rem;"
+td_style_high = "border: 1px solid black; padding: 10px; text-align: center; font-size: 1.2rem; min-width: 3rem; background-color: lightgray;"
+
+for i in range(len(data)):
+    table = soup.new_tag("table")
+    table["style"] = "display: flex; justify-content: center;"
+    tr = soup.new_tag("tr")
+    for d in data[i]:
+        td = soup.new_tag("td")
+        if d:
+            td['style'] = td_style_high if d[1] else td_style
+            td.string = str(d[0]) if d else " "
+        else:
+            td["style"] = td_style
+            td.string = " "
+        tr.append(td)
+    table.append(tr)
+    soup.div.append(table)
+
+print(soup.prettify())
+```
+
+
+## Problem 2
+
+Fill in the blanks with proper number of iterations.
+
+### Solution 2
+
+```
+// INSERTION-SORT(A)             // cost // number of iterations
+for j = 2 to n                   // c1   // n - 1
+    key = A[j]                   // c2   // n - 1
+    i = j - 1                    // c3   // n - 1
+    while i > 0 and A[i] > key   // c4   // tj
+        A[i + 1] = A[i]          // c5   // tj - 1
+        i = i - 1                // c6   // tj - 1
+    A[i + 1] = key               // c7   // n - 1
+```
+
+## Problem 3
+
+What is the running time of insertion sort when the input size is $n$?
+
+### Solution 3
+
+* best case: $\theta(n)$ $t_j = 1$
+
+* worst case: $\theta(n^2)$ $t_j = j$