// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
n := len(dist)
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k := 0; k < n; k++ {
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
n := len(dist)
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k := 0; k < n; k++ {
// With k now allowed as a waypoint, retry every source/target pair.
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
n := len(dist)
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k := 0; k < n; k++ {
// With k now allowed as a waypoint, retry every source/target pair.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
n := len(dist)
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k := 0; k < n; k++ {
// With k now allowed as a waypoint, retry every source/target pair.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like math.MaxInt64/2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
func floydWarshall(dist [][]int) {
n := len(dist)
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k := 0; k < n; k++ {
// With k now allowed as a waypoint, retry every source/target pair.
for i := 0; i < n; i++ {
for j := 0; j < n; j++ {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if dist[i][k]+dist[k][j] < dist[i][j] {
dist[i][j] = dist[i][k] + dist[k][j]
}
}
}
}
}# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
pass# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
# Core idea: grow the set of allowed intermediate vertices one at a time.
# After iteration k, dist[i][j] is the best path using only 0..k as stops.
pass# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
n = len(dist)
# Core idea: grow the set of allowed intermediate vertices one at a time.
# After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k in range(n):
pass# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
n = len(dist)
# Core idea: grow the set of allowed intermediate vertices one at a time.
# After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k in range(n):
# With k now allowed as a waypoint, retry every source/target pair.
pass# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
n = len(dist)
# Core idea: grow the set of allowed intermediate vertices one at a time.
# After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k in range(n):
# With k now allowed as a waypoint, retry every source/target pair.
for i in range(n):
for j in range(n):
pass# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
n = len(dist)
# Core idea: grow the set of allowed intermediate vertices one at a time.
# After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k in range(n):
# With k now allowed as a waypoint, retry every source/target pair.
for i in range(n):
for j in range(n):
# Is detouring i -> k -> j shorter than the best i -> j so far?
pass# dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
# edge" (use something like 10**18 so k-path sums stay comparable).
# floyd_warshall relaxes it in place into all-pairs shortest distances.
def floyd_warshall(dist):
n = len(dist)
# Core idea: grow the set of allowed intermediate vertices one at a time.
# After iteration k, dist[i][j] is the best path using only 0..k as stops.
for k in range(n):
# With k now allowed as a waypoint, retry every source/target pair.
for i in range(n):
for j in range(n):
# Is detouring i -> k -> j shorter than the best i -> j so far?
if dist[i][k] + dist[k][j] < dist[i][j]:
dist[i][j] = dist[i][k] + dist[k][j]// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist) {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if (dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j];
}
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Number.MAX_SAFE_INTEGER / 2 so k-path sums stay exact).
// floydWarshall relaxes it in place into all-pairs shortest distances.
function floydWarshall(dist: number[][]): void {
const n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (let k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (let i = 0; i < n; i++) {
for (let j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if (dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j];
}
}
}
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
int n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
}
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
int n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
}
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
int n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
}
}
}
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
int n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}
}class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like Long.MAX_VALUE / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
public void floydWarshall(long[][] dist) {
int n = dist.length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if (dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j];
}
}
}
}
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
int n = dist.Length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
}
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
int n = dist.Length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
}
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
int n = dist.Length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
}
}
}
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
int n = dist.Length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}
}public class Solution {
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like long.MaxValue / 2 so k-path sums don't overflow).
// FloydWarshall relaxes it in place into all-pairs shortest distances.
public void FloydWarshall(long[][] dist) {
int n = dist.Length;
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if (dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j];
}
}
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes the n x n matrix in place into all-pairs shortest
// distances.
void floydWarshall(long long** dist, int n) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if (dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j];
}
}
}
}
}#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
}
};#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
}
};#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
int n = (int)dist.size();
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
}
}
};#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
int n = (int)dist.size();
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
}
}
};#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
int n = (int)dist.size();
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
}
}
}
}
};#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
int n = (int)dist.size();
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
}
}
}
}
};#include <vector>
using namespace std;
class Solution {
public:
// dist[i][j] holds the edge weight from i to j, or a large sentinel for "no
// edge" (use something like LLONG_MAX / 2 so k-path sums don't overflow).
// floydWarshall relaxes it in place into all-pairs shortest distances.
void floydWarshall(vector<vector<long long>>& dist) {
int n = (int)dist.size();
// Core idea: grow the set of allowed intermediate vertices one at a time.
// After iteration k, dist[i][j] is the best path using only 0..k as stops.
for (int k = 0; k < n; k++) {
// With k now allowed as a waypoint, retry every source/target pair.
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
// Is detouring i -> k -> j shorter than the best i -> j so far?
if (dist[i][k] + dist[k][j] < dist[i][j]) {
dist[i][j] = dist[i][k] + dist[k][j];
}
}
}
}
}
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