This document describes the Uniform Cost Search (UCS) pathfinding algorithm. UCS is similar to Dijkstra's algorithm in that it finds the lowest-cost path between a start and target node by exploring all nodes in order of lowest cost first. The key differences are that UCS uses the function g(x) to calculate the cost of a node instead of h(x), and it calculates cost as the sum of path distances traveled so far rather than estimating distance to the target. Pseudocode is provided to illustrate the step-by-step process of UCS to find the lowest-cost path between two nodes on a graph.

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2 {(A,13),(E,11)} {(S,12),(D,11)}
3 {(A,13),(B,DE)(F,13)} {(S,12),(D,11),(E,11)}
#(!
4 5 4
A E
5 2
A D
3 4
12+
0
12S
(1)
11+
3=
14
7+
4=
11
(2)
4+
9=
13
5+
6=
11
(3)
+
(4)
4+
B B F
+
11=
+
4+
13=
17
3+
10=
13
( % ) #* + * +# +
0 {(S,12)} {}
1 {(A,14),(D,11)} {(S,12)}
2 {(A,13),(E,11)} {(S,12),(D,11)}
3 {(A,13),(B,DE)(F,13)} {(S,12),(D,11),(E,11)}
4 {(B,17),(F,13)} {(S,12),(D,11),(E,11),(A,13)}
#!
4 5 4
A E
5 2
A D
3 4
12+
0
12S
(1)
11+
3=
14
7+
4=
11
(2)
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13
5+
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11
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G
3
B B F
+
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+
4+
13=
17
3+
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13
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(5)
( % ) #* + * +# +
0 {(S,12)} {}
1 {(A,14),(D,11)} {(S,12)}
2 {(A,13),(E,11)} {(S,12),(D,11)}
3 {(A,13),(B,DE)(F,13)} {(S,12),(D,11),(E,11)}
4 {(B,17),(F,13)} {(S,12),(D,11),(E,11),(A,13)}
5 {(B,17),(G,13)} {(S,12),(D,11),(E,11),(A,13),(F,13)}
#!
4 5 4
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A D
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12+
0
12S
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11+
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11
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G
3
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+
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+
4+
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17
3+
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13
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13=
13
(5)
(6)
( % ) #* + * +# +
0 {(S,12)} {}
1 {(A,14),(D,11)} {(S,12)}
2 {(A,13),(E,11)} {(S,12),(D,11)}
3 {(A,13),(B,DE)(F,13)} {(S,12),(D,11),(E,11)}
4 {(B,17),(F,13)} {(S,12),(D,11),(E,11),(A,13)}
5 {(B,17),(G,13)} {(S,12),(D,11),(E,11),(A,13),(F,13)}
6 {(B,17)} {(S,12),(D,11),(E,11),(A,13),(F,13),(G,13)}
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