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Update 9.3.md. #516

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23 changes: 14 additions & 9 deletions docs/Chap09/9.3.md
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Original file line number Diff line number Diff line change
Expand Up @@ -72,8 +72,8 @@ Pre-calculate the positions of the quantiles in $O(k)$, we use the $O(n)$ select
```cpp
PARTITION(A, p, r)
x = A[r]
i = p
for k = p to r
i = p - 1
for k = p to r - 1
if A[k] < x
i = i + 1
swap A[i] with A[k]
Expand All @@ -99,7 +99,7 @@ RANDOMIZED-SELECT(A, p, r, i)
if i == k
return q, A[q]
if i < k
r = q
r = q - 1
else
p = q + 1
i = i - k
Expand All @@ -111,6 +111,8 @@ k-QUANTITLES-SUB(A, p, r, pos, f, e, quantiles)
return
mid = (f + e) / 2
q, val = RANDOMIZED-SELECT(A, p, r, pos[mid])
if mid - 1 >= f
k-QUANTILES-SUB(A, p, q, pos, f, mid - 1, quantiles)
quantiles[mid] = val
k = q - p + 1
for i = mid + 1 to e
Expand All @@ -120,15 +122,18 @@ k-QUANTITLES-SUB(A, p, r, pos, f, e, quantiles)

```cpp
k-QUANTITLES(A, k)
if k == 1
return []

num = A.size() / k
mod = A.size() % k
pos = num[1..k]
for i = 1 to mod
pos[i] = pos[i] + 1
for i = 1 to k
pos = [1..(k-1)]
for i = 1 to k - 1
pos[i] = i <= mod ? num + 1 : num
for i = 2 to k - 1
pos[i] = pos[i] + pos[i - 1]
quantiles = [1..k]
k-QUANTITLES-SUB(A, 0, A.length, pos, 0, pos.size(), quantiles)
quantiles = [1..(k-1)]
k-QUANTITLES-SUB(A, 1, A.length, pos, 1, pos.size(), quantiles)
return quantiles
```

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