CS1010 AY20/21 S1 Lecture 9

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# Lecture 9

### 19 October 2020

.smaller[
Admin Matters<br>
Unit 23: Searching<br>
Unit 24: Sorting<br>
]
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### Assignment 6

- Due Tuesday night (23:59)
- Graded on correctness (including syntax, practices, approach, and logic), style, efficiency, and documentation.

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### Tutorial/Lab 8

- Problem Sets 23-24
- Assignment 6

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### Catch-Up Session III

- Saturday, 24 October, 10 am - 12 pm
- Meant to review concepts that you are still unclear 
- Please post questions on Piazza Live Q&A and vote for which 
  questions you want us to answer
- NOT a "help me debug" session (we have office hours for that)

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- Attendence to office hours and past catch-up sessions have been
  significantly lower compared to previous batches
- Yet, more students seem to be struggling
- This is Week 9 out of your 4-year programme.  It is not too late
  to ask for help.

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background-image: url(figures/midterm-distribution.png)

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# Searching

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.tiny[
```C
long search(long n, const long list[n], long q) {
  for (long i = 0; i < n; i += 1) {
    if (list[i] == q) {
      return i;
  }
  return -1;
}
```
]

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- Must we scan through every element?  
- What if the input is sorted?

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![property](figures/search-and-sort-dark/search-and-sort-dark.001.png)

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.tiny[
```C
long search(const long list[], long i, long j, long q) {
  if (i > j) {
    return -1;
  }
  long mid = (i+j)/2;
  if (list[mid] == q) {
    return mid;
  } 
  if (list[mid] > q) {
    return search(list, i, mid-1, q);
  } 
  return search(list, mid+1, j, q);
}
```
]

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![property](figures/search-and-sort-dark/search-and-sort-dark.002.png)

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.moretiny[
```C
long search(const long list[], long i, long j, long q) {
  // q not in list[0..i-1, j+1..n-1]
  if (i > j) {
	// q not in ..
    return -1;
  }
  long mid = (i+j)/2;
  if (list[mid] == q) {
    return mid;
  } 
  if (list[mid] > q) {
	// q not in ..
    return search(list, i, mid-1, q);
  } 
  // q not in ..
  return search(list, mid+1, j, q);
}
```
]

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### Running Time for Binary Search

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### Counting Sort: O(?)
.moretiny[
```C
void counting_sort(const long in[], long out[], long len)
{
  long freq[MAX + 1] = { 0 };
  for (long i = 0; i < len; i += 1) {
    freq[in[i]] += 1;
  }
  long outpos = 0;
  for (long i = 0; i <= MAX; i += 1) {
    for (long j = outpos; j < outpos + freq[i]; j += 1) {
      out[j] = i;
    }
    outpos += freq[i];
  }
}
```
]

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### Selection Sort: O(?)
.moretiny[
```C
long max(long last, const long list[])
{
  long max_so_far = list[0];
  long max_index = 0;
  for (long i = 1; i <= last; i += 1) {
    if (list[i] > max_so_far) {
      max_so_far = list[i];
      max_index = i;
    }
  }
  return max_index;
}
```
]

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### Selection Sort: O(?)
.moretiny[
```C
void selection_sort(long length, long list[])
{
  for (long i = 1; i < length; i += 1) {
    long max_pos = max(length - i, list);
    if (max_pos != length - i) {
      swap(&list[max_pos], &list[length - i]);
    }
  }
}
```
]
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### Counting Sort vs. Selection Sort

- Counting sort is fast because the range of the inputs is limited
- Selection sort is slower and is more general

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### Bubble Sort and Insertion Sort

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.tiny[
Version: 1.0

Last Updated: Sun Oct 18 07:59:19 +08 2020
]