From 1009e7be7f6c4c79c11441a99cd76070a37bfba2 Mon Sep 17 00:00:00 2001
From: Zhenchao Gan <303542123@qq.com>
Date: Wed, 30 Nov 2016 20:53:09 -0800
Subject: [PATCH] fix 22.1.3

---
 C21-Data-Structures-for-Disjoint-Sets/21.1.md | 70 ++++++++++---------
 1 file changed, 36 insertions(+), 34 deletions(-)

diff --git a/C21-Data-Structures-for-Disjoint-Sets/21.1.md b/C21-Data-Structures-for-Disjoint-Sets/21.1.md
index 4129e6e0..50650cd5 100644
--- a/C21-Data-Structures-for-Disjoint-Sets/21.1.md
+++ b/C21-Data-Structures-for-Disjoint-Sets/21.1.md
@@ -1,35 +1,37 @@
-### Exercises 21.1-1
-***
-Suppose that CONNECTED-COMPONENTS is run on the undirected graph G = (V, E), where V = {a, b, c, d, e, f, g, h, i, j, k} and the edges of E are processed in the following order: (d, i), (f, k), (g, i), (b, g), (a, h), (i, j), (d, k), (b, j), (d, f), (g, j), (a, e), (i, d). List the vertices in each connected component after each iteration of lines 3-5.

-### `Answer`
-{a} {b} {c} {d} {e} {f} {g} {h} {i} {j} {k} 
-
-1. (d,i) => {a} {b} {c} {d i} {e} {f} {g} {h} {j} {k} 
-2. (f,k) => {a} {b} {c} {d i} {e} {f k} {g} {h} {j}
-3. (g,i) => {a} {b} {c} {d g i} {e} {f k} {h} {j}
-4. (b,g) => {a} {b d g i} {c} {e} {f k} {h} {j}
-5. (a,h) => {a h} {b d g i} {c} {e} {f k} {j}
-6. (i,j) => {a h} {b d g i j} {c} {e} {f k}
-7. (d,k) => {a h} {b d g i j f k} {c} {e}
-8. (b,j) => {a h} {b d g i j f k} {c} {e}
-9. (d,f) => {a h} {b d g i j f k} {c} {e}
-10. (g,j) => {a h} {b d g i j f k} {c} {e}
-11. (a,e) => {a e h} {b d g i j f k} {c}
-
-### Exercises 21.1-2
-***
Show that after all edges are processed by CONNECTED-COMPONENTS, two vertices are in the same connected component if and only if they are in the same set.
-
-### `Answer`
-If two vertices are not in the same set, meaning that no edge connecting the set of one vertice with the other. So two vertices are in the same connected component if and only if they are in the same set.
-
-### Exercises 21.1-3
-***
+### Exercises 21.1-1
+***
+Suppose that CONNECTED-COMPONENTS is run on the undirected graph G = (V, E), where V = {a, b, c, d, e, f, g, h, i, j, k} and the edges of E are processed in the following order: (d, i), (f, k), (g, i), (b, g), (a, h), (i, j), (d, k), (b, j), (d, f), (g, j), (a, e), (i, d). List the vertices in each connected component after each iteration of lines 3-5.
+
+### `Answer`
+{a} {b} {c} {d} {e} {f} {g} {h} {i} {j} {k} 
+
+1. (d,i) => {a} {b} {c} {d i} {e} {f} {g} {h} {j} {k} 
+2. (f,k) => {a} {b} {c} {d i} {e} {f k} {g} {h} {j}
+3. (g,i) => {a} {b} {c} {d g i} {e} {f k} {h} {j}
+4. (b,g) => {a} {b d g i} {c} {e} {f k} {h} {j}
+5. (a,h) => {a h} {b d g i} {c} {e} {f k} {j}
+6. (i,j) => {a h} {b d g i j} {c} {e} {f k}
+7. (d,k) => {a h} {b d g i j f k} {c} {e}
+8. (b,j) => {a h} {b d g i j f k} {c} {e}
+9. (d,f) => {a h} {b d g i j f k} {c} {e}
+10. (g,j) => {a h} {b d g i j f k} {c} {e}
+11. (a,e) => {a e h} {b d g i j f k} {c}
+
+### Exercises 21.1-2
+***
+Show that after all edges are processed by CONNECTED-COMPONENTS, two vertices are in the same connected component if and only if they are in the same set.
+
+### `Answer`
+If two vertices are not in the same set, meaning that no edge connecting the set of one vertice with the other. So two vertices are in the same connected component if and only if they are in the same set.
+
+### Exercises 21.1-3
+***
 During the execution of CONNECTED-COMPONENTS on an undirected graph G = (V, E) with k connected components, how many times is FIND-SET called? How many times is UNION called? Express your answers in terms of |V|, |E|, and k.
-
-### `Answer`
-* FIND-SET : |E|
-* UNION : |V| - k
-
-***
-Follow [@louis1992](https://github.com/gzc) on github to help finish this task.
-
+
+### `Answer`
+* FIND-SET : 2|E|
+* UNION : |V| - k
+
+***
+Follow [@louis1992](https://github.com/gzc) on github to help finish this task.
+