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algorithm/PuzzleCoding/src/MinPathSum.java at master · wodgithub/algorithm · GitHub
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PuzzleCoding
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MinPathSum.java
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PuzzleCoding
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src
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MinPathSum.java
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import
java
.
util
.
ArrayList
;
import
java
.
util
.
Arrays
;
/**
* Given a m x n grid filled with non-negative numbers,
* find a path from top left to bottom right which minimizes the sum of all numbers along its path.
* <p/>
* Note: You can only move either down or right at any point in time.
* <p/>
* If we could move to any direction in the path, then we kind of use
* Dijkstra's algorithm to solve this problem. The difference with the
* shotest path problem in graph is that in the graph, different node
* to one node may have path with different weight. But int the grid,
* each neighbor to this cell would sum with the same value. So if we
* would also get minimun sum in fisrt calculate for this cell.
* <p/>
* Since the question ask to move either right or down only, then the
* question merely become Robort move question. With dynamic programming
* we could solve it in O(mn) time complexity.
*/
public
class
MinPathSum
{
public
static
void
main
(
String
[]
args
) {
int
[][]
grid
=
new
int
[][]{
{
1
,
3
,
1
},
{
1
,
5
,
1
},
{
4
,
2
,
1
}
};
// result 7
DijkstraPathSum
(
grid
);
minPahtSum
(
grid
);
int
[][]
a2
=
new
int
[][]{{
3
}};
//3
DijkstraPathSum
(
a2
);
minPahtSum
(
a2
);
int
[][]
a3
=
new
int
[][]{
{
1
,
0
,
4
,
9
,
6
,
0
,
9
,
1
,
8
,
9
,
5
},
{
1
,
2
,
8
,
9
,
2
,
4
,
8
,
1
,
7
,
3
,
2
},
{
5
,
0
,
7
,
9
,
3
,
5
,
1
,
3
,
8
,
2
,
3
},
{
3
,
2
,
2
,
5
,
3
,
3
,
3
,
2
,
0
,
5
,
6
},
{
9
,
6
,
8
,
3
,
6
,
2
,
0
,
1
,
4
,
6
,
1
},
{
1
,
7
,
4
,
8
,
8
,
9
,
7
,
1
,
3
,
2
,
5
},
{
7
,
7
,
8
,
0
,
3
,
0
,
0
,
0
,
8
,
1
,
8
},
{
8
,
7
,
4
,
0
,
9
,
5
,
4
,
7
,
9
,
8
,
5
},
{
5
,
6
,
3
,
5
,
5
,
6
,
0
,
7
,
1
,
7
,
7
},
{
9
,
9
,
2
,
1
,
1
,
2
,
1
,
5
,
0
,
0
,
4
}
};
//40
DijkstraPathSum
(
a3
);
minPahtSum
(
a3
);
}
// only left or down, Dynamic programming to solve this.
public
static
void
minPahtSum
(
int
[][]
grid
) {
if
(
grid
.
length
==
0
) {
System
.
out
.
println
(
"sum path for zero grid "
+
0
);
return
;
}
int
row
=
grid
.
length
;
int
col
=
grid
[
0
].
length
;
// calculate left edge
for
(
int
i
=
row
-
1
;
i
>
0
; --
i
)
grid
[
i
-
1
][
col
-
1
] +=
grid
[
i
][
col
-
1
];
// calculate bottom edge
for
(
int
j
=
col
-
1
;
j
>
0
; --
j
)
grid
[
row
-
1
][
j
-
1
] +=
grid
[
row
-
1
][
j
];
for
(
int
i
=
row
-
2
;
i
>=
0
; --
i
) {
for
(
int
j
=
col
-
2
;
j
>=
0
; --
j
) {
//sum with the less one
grid
[
i
][
j
] +=
(
grid
[
i
+
1
][
j
] <
grid
[
i
][
j
+
1
]) ?
grid
[
i
+
1
][
j
] :
grid
[
i
][
j
+
1
];
}
}
System
.
out
.
println
(
grid
[
0
][
0
]);
}
// Dijkstra's algorithm
public
static
void
DijkstraPathSum
(
int
[][]
grid
) {
if
(
grid
.
length
==
0
) {
System
.
out
.
println
(
"sum path for zero grid "
+
0
);
return
;
}
int
row
=
grid
.
length
;
int
col
=
grid
[
0
].
length
;
boolean
[][]
visit
=
new
boolean
[
row
][
col
];
int
[][]
cost
=
new
int
[
row
][
col
];
for
(
int
i
=
0
;
i
<
row
;
i
++) {
for
(
int
j
=
0
;
j
<
col
;
j
++) {
cost
[
i
][
j
] =
Integer
.
MAX_VALUE
;
}
}
String
[][]
path
=
new
String
[
row
][
col
];
cost
[
0
][
0
] =
grid
[
0
][
0
];
path
[
0
][
0
] =
"0-0"
;
visit
[
0
][
0
] =
true
;
for
(
int
i
=
0
;
i
<
row
;
i
++) {
for
(
int
j
=
0
;
j
<
col
&&
visit
[
i
][
j
];
j
++) {
//left
int
r
=
i
+
1
,
c
=
j
;
if
(
r
<
row
) {
if
(
cost
[
r
][
c
] >
cost
[
i
][
j
] +
grid
[
r
][
c
]) {
cost
[
r
][
c
] =
cost
[
i
][
j
] +
grid
[
r
][
c
];
visit
[
r
][
c
] =
true
;
path
[
r
][
c
] =
String
.
valueOf
(
i
) +
"-"
+
String
.
valueOf
(
j
);
}
}
// down
r
=
i
;
c
=
j
+
1
;
if
(
c
<
col
) {
if
(
cost
[
r
][
c
] >
cost
[
i
][
j
] +
grid
[
r
][
c
]) {
cost
[
r
][
c
] =
cost
[
i
][
j
] +
grid
[
r
][
c
];
visit
[
r
][
c
] =
true
;
path
[
r
][
c
] =
String
.
valueOf
(
i
) +
"-"
+
String
.
valueOf
(
j
);
}
}
}
}
System
.
out
.
println
(
cost
[
row
-
1
][
col
-
1
]);
// System.out.println(Arrays.deepToString(cost));
}
}
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